# 2008 Talks Abstracts

## 1. Spin-induced non-geodesic motion, Wigner rotation and EPR correlations of massive spin-1/2 particles in a gravitational field

Paul M. Alsing, University of New Mexico

(Session 15: Sunday from 13:00-13:30)

**Abstract**. We investigate in a covariant manner, the spin-induced non-geodesic motion of massive spin-1/2 particles in an arbitrary gravitational field for trajectories that are initially geodesic when spin is ignored. Using the WKB approximation for the wave function in an arbitrary curved spacetime, we compute the O(hbar) correction to the Wigner rotation of the spin-1/2 particle, whose O(1) contribution is zero on timelike geodesics. We consider specific examples in the Schwarzschild metric for motions in the equatorial plane for (i) particles falling in from spatial infinity with non-zero angular momentum and (ii) circular geodesic orbits. For the latter case we consider the Bell inequalities for a perfectly anti-correlated EPR entangled pair of spins as the separate qubits traverse the circular geodesic in opposite directions.

## 2. Scalable Traps and Novel Gates for Quantum Information Processing with Ions

Jason Amini, National Institute of Standards and Technology

(Session 7: Saturday from 11:30-12:00)

Collaborators: J. M. Amini, R. B. Blakestad, J. J. Bollinger, J. Britton, K. R. Brown, J. Chou, R. J. Epstein [a], J. P. Home, D. B. Hume, W. M. Itano, J. D. Jost, E. Knill, C. R. Langer [b], D. Leibfried, C. Ospelkaus, T. Rosenband, S. Seidelin [c], A. VanDevender, J. H. Wesenberg [d], and D. J. Wineland.

**Abstract**. Two of the key goals for the ion trap community are scaling ion traps to hold and manipulate the numbers of qubits needed for useful algorithms and improving the quality of all operations. At NIST, we are testing an 18-zone two-layer trap with an "X" intersection and employing microfabrication techniques to simplify the design and construction of future traps [1]. Combined with novel optical and magnetic gates [2], sympathetic cooling [3], and quantum enabled read-out [4] utilizing different ion species, algorithms with large numbers of ions may become tractable. We have also demonstrated cooling of a microcantilever using an RF resonant circuit [5] and are pursuing the coupling of ions to cantilevers for cooling and entanglement.

[1] See the poster by J. Britton, et al.

[2] See the poster by C. Ospelkaus, et al. See also, D. Leibfried, et al., Phys. Rev. A 76, 032324 (2007).

[3] See the poster by J. Jost, et al.

[4] See the poster by D. Hume, et al.

[5] K.R. Brown, et al., Phys. Rev. Lett. 99, 137205 (2007).

Acknowledgements: Work supported by IARPA and NIST.

[a] Current address: Areté Associates, Longmont, CO 80501, USA

[b] Current address: Lockheed Martin, Huntsville, AL, USA

[c] Current address: University of Grenoble, France.

[d] Current address: Oxford University, U.K.

## 3. Basing quantum theory on information-processing principles

Howard Barnum, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

**Abstract**. The rise of quantum information science has been paralleled by the development of a vigorous research program aimed at obtaining an informational characterization or reconstruction of the quantum formalism, in a broad framework for stochastic theories that encompasses quantum and classical theory, but also a wide variety of other theories that can serve as foils to them. Such a reconstruction, at its most ambitious, is envisioned as playing a role in quantum physics similar to Einstein's reconstruction of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of such an ambitious goal, it could still lead to a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, an understanding which could help guide the search for new quantum algorithms and protocols.

As part of this project, I give a precis of the convex operational framework for possible physical theories, and review work by me and my collaborators, on the information-processing properties of theories in this framework. The main results reviewed are the the fact that the only information that can be obtained in the framework without disturbance is inherently classical, no-cloning and no-broadcasting theorems in the generalized framework, the existence of exponentially secure bit commitment in non-classical theories without entanglement, and the consequences for theories of the existence of a conclusive teleportation scheme. I'll also discuss sufficient conditions for "remote steering" of ensembles using entanglement, rendering insecure bit commitment protocols of the form shown to be secure in the unentangled case.

Acknowledgements: Joint work with various groups of collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.

## 4. Convexity and Positivity in Quantum Information: Part I

Howard Barnum, Los Alamos National Laboratory

(Session 101: Thursday from 16:00-18:00)

**Abstract**. Convex sets and convex cones occur frequently in quantum information theory. For example, normalized density matrices, completely positive maps, separable states, and POVMs all form convex sets. Finding an optimal quantum information processing protocol can often be cast as minimizing a linear function over a compact convex set, a problem for which much is known. This tutorial will cover some of the basic theory of convex sets and optimization over them, and applications to quantum information processing.

The first half of the tutorial will be given by Howard Barnum and will focus on the basic theory in finite dimensions, with topics selected for their applicability to quantum information. It will cover the following:

Outline of Tutorial:

- I. Basic definitions and facts
- Definition of convex and affine sets.
- Compact convex sets, preservation of convexity by affine maps.
- Krein-Milman theorem.
- Brief note on infinite vs. finite dimension.
- Caratheodory's theorem.
- Suspending
*d*-dimensional convex sets as cone bases in*d*+1 real dimensions. - Regular (convex, pointed, full, closed) cones.
- Ordered linear spaces, equivalence of OLS's to spaces with distinguished regular cones.
- Examples: positive orthant, Lorentz cones, and positive semidefinite matrices.
- Quantum information examples: unentangled states, positive maps, and completely positive maps.
- Separating hyperplanes, separation theorems.
- Definition of dual cone.
- Exposed points.
- Order units and operational theories.
- Direct sums of cones.
- Simplices: equivalent definitions, simplices as state-spaces of classical theories. Homogeneity, self-duality, examples.
- Koecher-Vinberg characterization of self-dual homogeneous cones.
- Basic results about optimizing convex and concave functions over compact convex sets.
- General conic convex programming with linear objective function.
- Linear, quadratic, and semidefinite programming.
- Different presentations of programs.
- Sufficient conditions for efficient algorithms; ellipsoid and other methods; LP/SDP/quadratic examples. NP-hard examples.
- Hard convex-set membership problems and Gurvits' proof of NP-hardness of entanglement testing.
- Quantum applications of SDP.
- Reducing dimension with symmetry.
- Duality in convex conic optimization, lower bounds on query complexity via relaxation and duality (if time permits).

## 5. Quantum communications with a partially coherent beam propagating through the atmosphere

Gennady Berman, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

Collaborators: Gennady P. Berman, Boris M. Chernobrod, and Aleksandr A. Chumak (Los Alamos National Laboratory, Theoretical Division, Los Alamos, NM 87545)

**Abstract**. A new concept of a free-space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km. The photon density operator function is used to describe the propagation of single-photon pulses through a turbulent atmosphere. The effects of statistical properties of photon source and the effects of a random phase screen on the variance of photon counting are studied. A procedure for reducing the total noise is discussed. The physical mechanisms responsible for this reduction are explained.

## 6. Quantum-limited metrology with product states

Sergio Boixo, University of New Mexico

(Session 14: Sunday from 13:00-13:30)

**Abstract**. We study the performance of generalized quantum metrology protocols that involve estimating an unknown coupling constant in a nonlinear k-body Hamiltonian. We obtain the theoretical lower bound on the uncertainty in the estimate of the parameter. For arbitrary initial states, the lower bound scales as 1/n^k, and for initial product states, it scales as 1/n^(k-1/2). We show that the latter scaling can be achieved using simple, separable measurements. We analyze in detail the case of a quadratic Hamiltonian (k=2), implementable with Bose-Einstein condensates. We formulate a simple model, based on the evolution of angular-momentum coherent states, which explains the O(n^(-3/2)) scaling for k=2; the model shows that the entanglement generated by the quadratic Hamiltonian does not play a role in the enhanced sensitivity scaling. We show that phase decoherence does not affect the O(n^(-3/2)) sensitivity scaling for initial product states.

## 7. Quantum information experiments in a Penning ion trap

John Bollinger, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

Collaborators: N. Shiga#, J. J. Bollinger, W. M. Itano NIST, 325 Broadway, Boulder, CO 80305

**Abstract**. A Penning trap uses static magnetic and electric fields to confine charged particles. With static confinement we can form large arrays of trapped ions. In particular we have formed 2-dimensional planar arrays of a few thousand ions and large 3-dimensional arrays of up to 10^{6} ions. In this poster we summarize progress on an initial quantum information experiment involving spin squeezing of a few hundred Be9 ion planar array. We use the ground-state electron spin-flip transition, which in the 4.5 T trap magnetic field has a 124 GHz transition frequency, as the ion qubit. We have realized projection noise limited spectroscopy on this transition, which is a prerequisite for demonstrating spin squeezing. For entangling the ions we plan to use a generalization of the few-ion qubit phase gate developed at NIST to generate an exp{(i\\chi {J_{z}}^2 t)} interaction between all of the ion qubits. Improvements in the frequency stabilization of our 124 GHz source have enabled spin echo coherence times as long as 2 ms. The spin echo coherence time limits the amount of time that can be used to apply the squeezing.

Acknowledgements: #Supported by a DOD MURI program administered by ONR under Grant N00014-05-1-0420.

## 8. Coherent control of resonant cavity length

Douglas Bradshaw, Los Alamos National Laboratory, University of New Mexico

(Session 5: Friday from 18:00-20:00)

**Abstract**. The effective length of an optical resonator filled with a dispersive medium is influenced by the group velocity of the resonating light. The associated effects on cavity properties become most interesting in connection with quantum-coherent manipulations that severely alter the resonating-light\'s group velocity while maintaining its transparency within the medium. We will discuss the implications of magnified, reduced, and negative cavity lengths as made possible through these types of group-velocity modifications.

## 9. Ion Traps for Scalable Quantum Information Processing

Joe Britton, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

Collaborators: J. Britton, J. M. Amini, R. B. Blakestad, C. W. Chou, D. B. Hume, T. Rosenband, S. Seidelin (*), J. H. Wesenberg (**), J. J. Bollinger, K. R. Brown, R. J. Epstein(***), J. P. Home, W. M. Itano, J. D. Jost, C. Langer (****), D. Leibfried, C. Ospelkaus, N. Shiga, A. VanDevender, and D. J. Wineland

**Abstract**. Microfabricated traps for atomic ions are a promising technology for building a scalable quantum information processor. Toward this goal we are investigating several approaches to trap fabrication, characterization and transport in multi-zone structures.

We have expanded upon our single layer gold-on-fused-silica surface electrode trap to include a patterned conducting layer under the trapping electrodes and interlayer vias. The fabrication of this architecture was demonstrated using standard microfabrication techniques and testing is underway. We are also testing a 21-zone doped-silicon surface electrode trap with closest ion-surface separation of 13 microns. In a 18-zone two-layer gold-on-alumina trap we are making tests of ion transport thru an x-junction. Techniques for measuring and minimizing ion micromotion are also discussed.

Acknowledgements: Work supported by IARPA and NIST.

Time and Frequency Division, NIST, Boulder, Colorado 80305, USA

(*) University of Grenoble, France

(**) Oxford University, UK

(***) Arete Associates, Longmont, CO

(****) Lockheed Martin, Huntsville, AL

## 10. Efficient feedback controllers for continuous-time quantum error correction

Brad Chase, University of New Mexico

(Session 4: Friday from 16:00-16:30)

**Abstract**. We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [quant-ph/0511221 (2005)] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.

## 11. A Quantum Kicked Top with Cold Atomic Spins

Souma Chaudhury, University of Arizona

(Session 4: Friday from 17:30-18:00)

**Abstract**. Complexity in classical as well as quantum physics arises through the coupling of multiple degrees of freedom. Recent theoretical studies have shown a connection between the dynamical rate of entanglement generation in a bipartite quantum system and the presence of chaos in the corresponding classical dynamics. In order to explore this and similar questions that lie at the boundary between quantum information science and quantum chaos we have developed a version of the quantum kicked top based on laser cooled atomic spins driven by a pulsed magnetic field and a rank 2 tensor light shift. Among the advantages offered by our system are the ability to prepare arbitrary initial spin states, the ability to precisely implement the desired non-linear dynamics, and the ability to accurately measure the entire spin density matrix and thus obtain accurate snapshots of the evolving quantum state.

We will present results from an experiment that implemented a quantum kicked top for the F=3 hyperfine ground state of Cs. Initial spin states were chosen to overlap with regular or chaotic areas of the classical phase space map, and the resulting spin Husimi distribution measured after each step in a series of 50 kicks. The spin dynamics seen in the experiment agrees closely with the predictions of theory, including dynamical tunneling between regular islands, rapid spreading of states throughout the chaotic sea, and surprisingly robust signatures of classical phase space structures even after many kicks and significant decoherence. As expected, the entanglement generated between electronic and nuclear spin is larger when the corresponding classical dynamics is chaotic, though the difference "while clear" is modest due to the small size of the total spin. Future versions of the experiment may circumvent this limitation by driving the electronic and nuclear spins independently, or by working with the collective spin of an ensemble of atoms.

## 12. Transversality versus universality for subsystem stabilizer codes

Xie Chen, Massachusetts Institute of Technology

(Session 5: Friday from 18:00-20:00)

**Abstract**. Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are transversal, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be universal; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation.

We study the structure of subsystem stabilizer codes in d-dimensional Hilbert space (for d >= 2), and show that a universal set of transversal gates cannot be found for even one encoded qudit. We prove our results in two different ways, by using different kinds of subcodes of the stabilizer. Our results strongly support the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal fault-tolerant computation on additive codes and may be the determining factor for fault tolerance noise thresholds. Furthermore, the proof techniques we employ give a recipe for understanding how and when gates other than standard Clifford operations can be transversal on stabilizer codes.

## 13. Lattice Ion Traps for Quantum Simulation

Rob Clark, Massachusetts Institute of Technology

(Session 5: Friday from 18:00-20:00)

**Abstract**. Two dimensional arrays of trapped ions show great promise for simulating dynamics of interacting spin systems that are intractable on classical computers. We propose a method for constructing such a lattice of ion traps that allows one to control the structure of the lattice, enabling the inclusion of defects, and leads to relatively straightforward fabrication. As a first demonstration of this method, we report stable confinement of ions in a 1 mm-scale lattice trap. Numerical models of the trap potentials are verified by measuring the motional frequencies of trapped strontium ions, and ion-ion repulsion between charged microspheres in neighboring lattice sites is observed. Scaling this interaction to atomic ions, we estimate that ion-ion repulsion should be observable for lattice spacings of about 150 microns. Finally, we discuss progress toward a microfabricated lattice trap in which interactions between atomic ions in different potential wells can be measured.

## 14. A quantum algorithm for finding the modal value

Mark Coffey, Colorado School of Mines

(Session 5: Friday from 18:00-20:00)

Collaborators: Mark W. Coffey and Zachary Prezkuta, Department of Physics, Colorado School of Mines, Golden, CO 80401

**Abstract**. We present a quantum algorithm for finding the most often occurring (or modal) value of a data set. We thereby supplement other algorithms that can determine the mean value or similar quantities. Our algorithm [1] requires the combined use of quantum counting and extended quantum search, and gives a quadratic speed up over the classical situation. For a data list of N elements, each entry an integer in the range [1,d], our method requires O(d N^{1/2}) oracle calls, and further complexity results are described.

[1] to appear in Quantum Information Processing.

Acknowledgements: This work was partially supported by Air Force contract number FA8750-06-1-0001.

## 15. Progress Toward a Cavity-QED Realization of the Dicke Model Quantum Phase Transition

Rob Cook, University of New Mexico

(Session 5: Friday from 18:00-20:00)

**Abstract**. We present progress towards a Cavity-QED realization of the quantum phase transition seen in the Dicke Model Hamiltonian for N>1 spins coupled to a single Bosonic field mode. The implementation is based upon cesium atoms held within a high finesse optical cavity. Cavity-mediated Raman transitions between magnetically detuned Zeeman sublevels provides near critical coupling between a collective pseudo-spin and a quantized cavity mode. Progress has been made in building the necessary infrastructure to collect a million atoms in an intracavity optical lattice, while still maintaining a background pressure of ~1E-10 torr. A tandem vacuum chamber provides a pressure difference of 3 orders of magnitude. A 2D-MOT will funnel atoms from a high pressure chamber into the lower pressure science cell. Current efforts are directed towards a home built tapered amplifier diode laser, to provide at least 500 mW of light for the 2-D MOT.

## 16. Using the cutting edge of matrix product state techniques to slice infinitely large entangled systems down to size

Gregory Crosswhite, University of Washington, Department of Physics

(Session 3: Friday from 15:00-15:30)

**Abstract**. The numerical simulation of quantum systems is inherently very difficult because the presence of entanglement means that one is faced with a state space exponentially large with respect to the number of particles. The only hope one has to get around this is to employ a clever form of representation that approximates quantum states of interest adequately while remaining small enough to be tractable. Matrix product states have garnered much interest over the past decade because they have these properties. In particular, matrix product states make an excellent ansatz for using the variational method to determine properties of the ground state. In my talk, I shall present an algorithm which uses a local direct variational optimization algorithm to obtain a translationally invariant representation of ground states for infinitely large one-dimensional systems.

## 17. Polarons in Bose-Einstein condensates

Fernando Cucchietti, Los Alamos National Laboratory

(Session 13: Sunday from 13:30-14:00)

**Abstract**. I will describe the behavior of impurities in a Bose-Einstein condensate using analogies with the problem of electrons in ionic crystals -- i.e. the "quantum simulation" of condensed-matter polarons using ultra-cold atoms. In the strong coupling regime, the impurities take on a self-localized state that is smaller than the healing length of the condensate. For intermediate to weak coupling, a different variational approach allows us to calculate analytic expressions for the effective mass of the BEC-polarons and its dispersion relation. I will discuss applications of this quantum simulation as well as its experimental viability.

## 18. Quantum Circuits Architecture

Giacomo Mauro D'Ariano, Università di Pavia

(Session 8: Saturday from 13:30-14:15)

**Abstract**. A method method for optimizing quantum circuits architecture is presented. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits, and mathematically corresponds to a generalization of the notions of quantum operation and POVM. The method allows to address novel kinds of quantum processing tasks, such as optimal storing-retrieving and cloning of channels, and optimal quantum circuit board testers.

## 19. Ground States as Resources for Universal Measurement-Based Quantum Computing

Adam G. D'Souza, University of Calgary

(Session 5: Friday from 18:00-20:00)

**Abstract**. Measurement-based quantum computation (MBQC) requires a massively entangled resource state (such as a cluster state) as input. Experimental efforts towards generating such states have typically focused on performing global entangling operations on uncorrelated qubits. As the states that result from this type of procedure are not generally ground states, they are very sensitive to decoherence effects. A more robust resource would be one that is in fact a ground state of some Hamiltonian that exhibits a reasonably large energy gap between the ground state and the various excited states. We discuss the possibility of finding simple two-body Hamiltonians whose ground states are equivalent to resource states for MBQC under stochastic protocols comprised solely of local operations and classical communication.

## 20. On the repulsive Casimir force using metamaterials

Felipe Da Rosa, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

Collaborators: Diego Dalvit (T-13) and Peter Milonni (T-13), Los Alamos National Laboratory

**Abstract**. It has been known for quite some time that Casimir repulsion between a dielectric and a magnetodielectric plate is possible, and the development of metamaterials brought this phenomenon closer to experimental possibilities. The purpose of this work is to discuss as realistically as possible the role that metamaterials play in the Casimir force and bring to the surface some aspects of this issue that were previously never or very little mentioned, such as the typical anisotropy of metamaterials and the presence of a Drude background in its electric permittivity. We also study the Casimir-Polder force between an atom and a metamaterial, since this may be relevant to future experiments.

## 21. Entanglement is an important resource ??!!

Animesh Datta, University of New Mexico

(Session 15: Sunday from 13:30-14:00)

**Abstract**. We attempt at characterizing the correlations present in the quantum computational model DQC1, introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. Although there is little or no entanglement between two parts of this system, it provides an exponential speedup in certain problems. On the contrary, we find that the quantum discord across the most natural split is nonzero for typical instances of the DQC1 circuit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model. This might be a complementary measure for counting resources in quantum information science.

## 22. Barium Ions for Quantum Computation

Matthew Dietrich, University of Washington

(Session 5: Friday from 18:00-20:00)

**Abstract**. We report progress on investigating 137Ba+ as a trapped ion qubit candidate. The hyperfine structure and visible spectrum cooling transitions of 137Ba+ make it an excellent qubit candidate. Here we report trapping 137Ba+ in a linear Paul trap. Cooling is provided by two diode lasers, one at 650 nm and the other at 493 nm is generated by a doubled infrared laser. To create the sidebands necessary for trapping this odd isotope, an EOM is applied to the blue light, while the red is modulated directly using a bias-T on the diode’s operating current. Shelving to the D5/2 state from the ground S1/2 state has been accomplished with a 1.76 micron fiber laser and during qubit readout direct adiabatic rapid transfer will shelve the state with high fidelity. The 1.76 micron fiber laser has been locked to a pressure and temperature stabilized high finesse zerodur cavity. Rabi flops between the ground hyperfine levels will be performed using microwave pulses whose waveforms can be shaped using a homebuilt pulse sequencer. A 400 fs pulsed Ti:sapphire laser is doubled in a single pass of BBO to 455 nm, and can be used for coherent population transfer and single photon production, as well as spectroscopic measurements, using the S1/2 to P3/2 transition.

## 23. Ultra-Low Noise Photon Pair Source in Dispersion Shifted Optical Fiber

Shellee Dyer, National Institute of Standards and Technology

(Session 11: Sunday from 09:45-10:15)

Collaborators: Shellee D. Dyer, Lenson Pellouchoud, and Sae Woo Nam

**Abstract**. Single photon and photon pair sources are important resources for optical quantum information processing. We demonstrate a fiber-based photon pair source in which the photon pairs are generated through four-wave mixing in dispersion shifted fiber (DSF). Previous demonstrations of photon pair generation in DSF were limited by the strong Raman scattering background in the fiber. By cooling the fiber to 4 K, we demonstrate that we can achieve almost complete suppression of the Raman photons, yielding a coincidence-to-accidental ratio larger than 300, exceeding previous best-case results by a factor of 4.

## 24. A graphical description of stabilizer states

Matthew Elliott, University of New Mexico

(Session 9: Saturday from 16:45-17:15)

**Abstract**. Stabilizer states are ubiquitous elements of quantum information theory, as a consequence of both their power and of their relative simplicity. The purpose of this talk is to augment the stabilizer formalism by introducing a graphical representation of stabilizer states. We furthermore demonstrate how Clifford operations, Pauli measurements, and stabilizer codes can be interpreted graphically using this approach.

## 25. A quantum computer can determine who wins a game faster than a classical computer

Edward Farhi, Massachusetts Institute of Technology

(Session 6: Saturday from 08:30-09:15)

**Abstract**. Imagine a game where two players go back and forth making moves and at the end of a fixed number of moves the position is either a win or a loss for the first player. In this case, if both players play best possible, it is determined at the first move who wins or loses. To figure out who will be the winner you need not look at all of the final positions but only at N^{.753} where N is the number of final positions. I will show that with a quantum computer the exponent can be reduced to 1/2. The technique involves quantum scattering theory.

## 26. Ultracompact Generation of Continuous-Variable Cluster States

Steve Flammia, Perimeter Institute

(Session 1: Friday from 10:30-11:00)

**Abstract**. We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum using a multi-frequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO. (PRA 76, 010302 (2007) and arXiv:0710.4980)

## 27. Generation of optical Cat States by squeezed photon subtraction

Thomas Gerrits, National Institute of Standards and Technology

(Session 1: Friday from 09:30-10:00)

Collaborators: Thomas Gerrits, Tracy Clement, Scott Glancy, Sae Woo Nam, Richard Mirin, Manny Knill (National Institute of Standards and Technology, Boulder, CO, 80303)

**Abstract**. Optical Cat States are superpositions of coherent states with opposite phases. Those states may be useful for optical phase measurements, as an interferometer's sensitivity is enhanced compared to a classical interferometer, when the light in both interferometers contains equal mean number of photons and wavelength. Also, in quantum computing they are a fundamental resource of fault-tolerant algorithms. Cat States are very sensitive to decoherence, and as a result their preparation is challenging and can serve as a demonstration of good quantum control. We will present our recent effort in generating and detecting these Cat States. Using a femtosecond laser and a KNbO3 downconversion source we are able to generate non-Gaussian states, which are similar to a Schroedinger Cat State.

## 28. Calibration for Slightly Unbalanced Homodyne Detection

Scott Glancy, National Institute of Standards and Technology, Boulder, Colorado

(Session 5: Friday from 18:00-20:00)

**Abstract**. Homodyne detection is a very useful tool for many modern experiments in quantum optics. In this technique the light mode to be measured interferes with a strong reference beam (called the "local oscillator") at a beam splitter. One then measures the difference between the number of photons arriving from the output ports of the beam splitter. This quantity is proportional to one of the quadratures of the signal mode. By varying the local oscillator phase, one can measure many quadratures and reconstruct the quantum state of the signal mode. Here we describe methods for calibrating a homodyne detector which allow us to compensate for problems such as electronic detector noise, a beam splitter reflectivity different from 1/2, and local oscillator intensity fluctuations.

## 29. Polygamy of entanglement of assistance: duality for monogamy of entanglement

Gilad Gour, Institute of Quantum Information Science

(Session 15: Sunday from 12:30-13:00)

**Abstract**. In contrast to classical multi-partite systems, which can enjoy arbitrary correlations between components, shared entanglement is restricted in a multipartite system. In this talk I will introduce a duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, I will show that the same quantity provides a lower bound for distribution of bipartite entanglement in a multipartite system. I will then show that our results for monogamy of entanglement can be used to establish relations between bipartite entanglement that separate one qubit from the rest vs separating two qubits from the rest.

## 30. Quantum Non-Demolition counting of photons in Cavity QED

Serge Haroche, Ecole Normale Supérieure

(Session 1: Friday from 08:45-09:30)

**Abstract**. Rydberg atoms crossing one by one a high-Q cavity extract information from the field stored in it, without absorbing the photons. The procedure realizes an ideal quantum-non demolition (QND) measurement of light. Initially prepared in a coherent state, the field quickly collapses into a Fock state of well-defined photon number, then undergoes successive jumps towards vacuum due to cavity relaxation. We have checked Planck's law and the predictions of quantum field theory by performing a statistical analysis of thousands of individual quantum trajectories recorded in this way. As the photon number is pinned down to a single value by the QND procedure, the field's phase is blurred. The first stage of this blurring process, induced by a single atom, prepares a photonic Schrödinger cat in the cavity, i.e. a coherent superposition of two field states with different phases. By displacing this cat state in phase space and performing a QND measurement on the translated field, we have reconstructed its Wigner function. It exhibits two classical components and, between them, an interference feature presenting negative parts. which is a signature of the cat state quantum coherence. This interference component vanishes much faster than the decay of the field intensity. This tomographic procedure opens the way to a direct investigation of the decoherence process on cat states containing up to a few tens of photons.

## 31. Practical long distance quantum key distribution

Jim Harrington, Los Alamos National Laboratory

(Session 11: Sunday from 09:15-09:45)

**Abstract**. We implemented a quantum key distribution protocol of phase-encoded BB84 with decoy states in optical fiber, and we achieved secret bits over more than 140 km with high confidence of security against any eavesdropping attack. The protocol included finite statistics effects for decoy state analysis, reconciliation, deskewing, information estimate, and privacy amplification.

## 32. Implementation Of Spin-Based Quantum Operations

Marilyn Hawley, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

**Abstract**. The long-term quantum computer goal is to achieve a large scale, fast, parallel, and easily fabricated QC. Silicon-based solid-state proposals, using nuclear or electron spins of dopants such a phosphorus as qubits, are still attractive because of the long spin relaxation times, scalability, and integratability with existing silicon technology. Our approach is to use a simplified architectural scheme involving multiple aligned duplicate pairs of interacting P spins in silicon to directly address the issue of entangling the spins using NMR and ESR methods and utilizing a optical detection method to determine the states of the spins. The QC device consists of linear arrays of P atoms 35 nm apart that act as qubits entangled through weak exchange interactions. The multiple duplicate copies are spaced far enough apart to ensure that the spins in adjacent QCs do not interact. The duplicate QCs provide enough signal strength above the spectrometer signal-to-noise ratio. The P array created on the surface of a silicon wafer is encapsulated under an isotopically pure homoepitaxial layer to activate the dopant. An external magnetic field splits the degeneracy of spins and a field gradient allows individual spins to be addressed. The 7T external field, field gradient, mm waveguide, and RF coils are housed in a custom designed He3 cryostat equipped with an optical access for the laser beam and collection of the photons emitted during the exciton recombination. The key to controlling the nuclear spin states and interactions is to use the lone P electron spins to control the nuclear spin orientation via a combination of microwave and RF pulses. Excitons, generated in the substrate by a laser beam focused on the sample diffuse to the P sites and are used to probe the state of the spins.

## 33. Black Holes as Mirrors

Patrick Hayden, McGill University

(Session 3: Friday from 13:45-14:30)

**Abstract**. I'll discuss information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and also assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

## 34. Bose-Einstein Condensates in Time-Averaged Optical Dipole Potentials

Kevin Henderson, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

**Abstract**. We are using Rb Bose-Einstein condensates in time-averaged optical dipole potentials to study atom interferometry and the dynamics of quantum phase transitions. The optical potential is generated by rastering a red-detuned (1064 nm, YAG) laser beam using dual acousto-optic modulators independently driven by RF arbitrary waveform generators. Axial confinement is provided by focusing the beam. We are studying the dynamics of a BEC optically trapped in these arbitrary potentials. We characterize the atom loss, heating rate, and coherence time for time-averaged optical dipole traps. We also study the robustness of manipulating multiple BECs in a variety of trapping geometries.

## 35. Progress towards distribution of entanglement in an ion trap array

Jonathan Home, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

**Abstract**. Trapped atomic ions can provide a scalable architecture for large scale quantum information processing, with most of the fundamental building blocks having already been demonstrated. However, the ability to entangle, distribute, and perform subsequent entangling operations on multiple atomic ions has only been demonstrated to a limited extent. We report on progress towards distributing entangled atomic ions in an ion trap array and re-establishing a well defined motional state after distribution. Performing multiple high fidelity multi-ion quantum logic gates requires their collective modes of motion to be well initialized. Moving and separating the qubits can lead to excitation of the motion that needs to be removed before subsequent gate operations. In addition, ambient electric field noise will also contribute to the heating. Using two species ion crystals (24Mg+ and 9Be+) allows for one species to act as a sympathetic cooling ion and one to act as a logical ion qubit. We report on experiments using mixed crystals of 24Mg+ and 9Be+ ions in a multi-zone trap.

## 36. Upper Bounds on the Fault-tolerance Threshold

Mark Howard, University of California, Santa Barbara.

(Session 5: Friday from 18:00-20:00)

**Abstract**. An important question in quantum computing is how much noise can be tolerated by a universal gate set before quantum-computational power is lost. Motivated by the result of Bravyi and Kitaev (Phys. Rev. A 71, 022316), there have been a number of recent papers which provide such bounds, within the framework of a model which presumes perfect Clifford operations. The ability to perform UQC is provided by the addition of a gate from outside the Clifford group. Here we show that gates which have non-zero off-diagonal elements can tolerate dephasing noise of any strength, and provide an explicit distillation algorithm to create a "magic state" which enables universal quantum computation. We also provide threshold expressions for arbitrary unitary gates undergoing depolarizing noise, dephasing noise or both.

## 37. The Optimal Control Landscape for the Generation of Unitary Transformations

Michael Hsieh, Princeton University

(Session 5: Friday from 18:00-20:00)

**Abstract**. The generation of specific unitary transformations is central to a variety of quantum control problems. Given a target unitary transformation, the optimal control landscape is defined as the Hilbert-Schmidt distance between the target and controlled unitary transformation as a function of the control variables. The critical topology of the landscape is analyzed for controllable quantum systems evolving under unitary dynamics over a finite dimensional Hilbert space. It is found that the critical regions of the landscape corresponding to global optima are isolated points, and the local optima are Grassmannian submanifolds. The volumes of the critical submanifolds corresponding to sub-optimal critical values asymptotically vanish in the limit of large Hilbert space dimension. Furthermore, these critical submanifolds have saddlepoint topology, which cannot act as traps when searching for optimal controls. These favorable properties of the local optima suggest that the landscape topology is generally amenable to optimization. The analysis is independent of the particular structure of the system Hamiltonian, except for the assumption of full controllability, and results are universal to the control of unitary transformations of any quantum system.

## 38. Decoherence-free subspaces and incoherently generated coherences

Raisa Karasik, University of California, Berkeley

(Session 14: Sunday from 12:30-13:00)

**Abstract**. A decoherence-free subspace (DFS) is a collection of states that is immune to the dominant noise effects created by the environment. DFS is usually studied for states involving two or more particles and is considered a prominent candidate for quantum memory and quantum information processing.

We present rigorous criteria for the existence of DFS in finite-dimensional systems coupled to the Markovian reservoirs. This allows us to identify a new special class of decoherence free states that relies on rather counterintuitive phenomenon, which we call an “incoherent generation of coherences.” We provide examples of physical systems that support such states.

## 39. A Nuclear Clock

Alex Kuzmich, Georgia Institute of Technology

(Session 2: Friday from 13:00-13:45)

**Abstract**. Th-229 nucleus has an exceptionally low-lying first excited state, 7.5 eV relative to the ground state. As the nuclei are affected less by background electromagnetic fields than atoms, laser excitation of the nuclear transition has been proposed as a basis for an ultrastable clock. In this talk, I will report our progress towards trapping triply ionized Th-229.

## 40. Convexity and Positivity in Quantum Information: Part II

Andrew Landahl, University of New Mexico

(Session 101: Thursday from 16:00-18:00)

**Abstract**. Convex sets and convex cones occur frequently in quantum information theory. For example, normalized density matrices, completely positive maps, separable states, and POVMs all form convex sets. Finding an optimal quantum information processing protocol can often be cast as minimizing a linear function over a compact convex set, a problem for which much is known. This tutorial will cover some of the basic theory of convex sets and optimization over them, and applications to quantum information processing.

The second half of the tutorial will be given by Andrew Landahl and will focus on some concrete applications of semidefinite programming in quantum information:

Outline of Tutorial:

- I. Optimal quantum error correction
- Convexity of quantum process distance measures.
- Optimal optimal encoding and recovery as convex optimization problems.
- Semidefinite program (SDP) formulation for some distance measures.
- Comparison to stabilizer coding.
- Definition of weak coin flipping (WCF).
- Maximum cheating bias in a quantum WCF protocol as an SDP.
- Minimum bias over all quantum WCF protocols as an SDP.
- Why incorporating cheat detection makes problem nonconvex.
- Definition of quantum state discrimination problems.
- Optimal minimum-error state discrimination measurement as an SDP.
- Optimal unambiguous state discrimination measurement as an SDP.
- Optimal "hybrid" state discrimination measurement as an SDP.

## 41. Single-Photon Spin-Orbit Coupling for Cluster State Quantum Computation

Cody Leary, Oregon Center for Optics, University of Oregon

(Session 13: Sunday from 12:30-13:00)

**Abstract**. When a quasi-paraxial photon propagates through a cylindrically symmetric inhomogeneous transparent medium such that the inhomogeneity is slowly varying over the spatial extent of the photon’s transverse electric field, its spin angular momentum s and its orbital angular momentum l are coupled. That is, photons in eigenmodes with the formerly degenerate propagation constant k but different values of s and l undergo splitting in k according to k + k(A + B s l) in the presence of the inhomogeneity. The constants A and B are both small compared to unity and are determined by the properties of the medium. This is photon spin-orbit coupling (SOC). In the case of a multimode step-index optical fiber, this k splitting gives rise to a rotational effect in the transverse spatial field distributions of the higher order fiber modes, in which left (right) circularly polarized modes resembling free-space Hermite-Gauss (H-G) modes rotate clockwise (counterclockwise) as they propagate through the fiber. Due to these rotations, single-photon SOC can be used to exploit the transverse spatial photonic degrees of freedom in order to create cluster states for use in fiber-based linear optical quantum computation. We propose fiber-based spin-orbit fusion gate elements towards the creation of cluster states entangled in H-G mode.

## 42. Progress Towards Microwave Controlled Collisions of Cs Atoms in an Optical Lattice

Jae hoon Lee, University of Arizona

(Session 5: Friday from 18:00-20:00)

Collaborators: Worawarong Rakreungdet, Jae Hoon Lee, Enrique Montano, and Poul Jessen (College of Optical Sciences, University of Arizona, Tucson, AZ)

Brian Mischuck and Ivan Deutsch (Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM)

**Abstract**. Quantum information processing with Cesium atoms in an optical lattice requires successful implementation of both single- and two-qubit quantum gates. Accurate single-qubit control can be achieved with simple or composite microwave pulses, whereas two-qubit logic requires pairwise atom-atom interactions that can be implemented for example via controlled atomic collisions. We are currently working on a proof-of-principle experiment wherein we have developed the ability to drive well-resolved microwave transitions of atomic qubits between spatially separated lattice potential wells associated with different logical basis (spin) states. In the case of Cs, collisional interactions are sufficiently strong that the microwave excitation of one atom from a spin-down to a spin-up well can be significantly affected by the presence of a second atom in a neighboring well of the spin-down lattice. For appropriate lattice parameters a spin-up/down pair will occupy a long range molecular state whose energy can be shifted by a large amount relative to isolated, non-interacting atoms. As a first step we are attempting to observe distinct lines in the microwave spectrum corresponding to excitation of this molecular state. In principle, selective microwave excitation of the molecular transition can then be used as the basis for a controlled-phase interaction and the implementation of a two-qubit quantum gate.

## 43. Novel two-qubit gates for trapped ions

Dietrich Leibfried, National Institute of Standards and Technology, Boulder

(Session 5: Friday from 18:00-20:00)

Collaborators: C. Ospelkaus, D. Leibfried, E. Knill, J. Amini, R. B. Blakestad, , J. Britton, K.R. Brown, J.P. Home, J.D. Jost, C. R. Langer #, A. VanDevender, J. Wesenberg+ and D.J. Wineland

**Abstract**. Atomic ions confined in an array of interconnected traps represent a potentially scalable approach to quantum information processing. The primary task is to scale the system to many qubits while minimizing and correcting errors in the system. In this context, it is desirable to minimize the overhead of laser-beam control in large scale implementations.

It will also be necessary to precisely control the transport of ions in large trap arrays. This ability can be utilized to implement one and two-qubit gates with only global control of the light fields and minimal control of the temporal pulse shape of the fields [1]. Going one step further, the small distance scales involved in microfabricated ion traps could enable the tailoring of local magnetic fields and their gradients to directly drive one- and two-qubit gates between hyperfine ground states, thereby completely avoiding laser fields and their inherent decoherence mechanisms due to spontaneous emission.

[1] D. Leibfried, E. Knill, C. Ospelkaus, and D. J. Wineland, Phys. Rev. A 76, 032324 (2007).

Acknowledgements: *Supported by IARPA and NIST.

+ Current address: Oxford University, UK;

# Current address: Lockheed Martin, Huntsville, AL, USA

## 44. High-Efficiency Tungsten Transition-Edge Sensors in the Near-Infrared

Adriana Lita, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

Collaborators: A. E. Lita [1], A. J. Miller [2], S. Nam [1]

**Abstract**. Single-photon detectors operating at visible and near-infrared wavelengths with high detection efficiency and low noise are a requirement for many quantum-information applications. Detection of visible and near-infrared light at the single-photon level and discrimination between one- and two-photon absorption events place stringent requirements on TES design in terms of heat capacity, thermometry, and optical detection efficiency. We report on the demonstration of fiber-coupled, photon number resolving transition edge sensors with 95% system efficiency at 1550 nm.

Acknowledgements: [1] Optoelectronics Division, NIST, Boulder CO, USA [2] Physics Department, Albion College, MI, USA

## 45. On the accuracy of 2-RDM methods for finding ground state energies

Yi-Kai Liu, California Institute of Technology

(Session 5: Friday from 18:00-20:00)

**Abstract**. One way of computing molecular ground state energies in quantum chemistry is to find the 2-electron reduced density matrix (2-RDM), for instance by variational minimization subject to so-called N-representability conditions. N-representability is a QMA-hard problem, but in practice, simple constraints on the 2-RDM, known as p-positivity conditions, often give surprisingly accurate results. We show that, if the Hamiltonian is band-diagonal (with respect to the basis set of single-electron orbitals), then the p-positivity method gives a constant-factor approximation to the ground state energy in polynomial time.

## 46. Ultracold atoms in a radiofrequency-dressed optical lattice

Nathan Lundblad, National Institute of Standards and Technology

(Session 2: Friday from 11:00-11:30)

**Abstract**. We load cold atoms into an optical lattice dramatically reshaped by the rf dressing of a strongly state-dependent bare lattice. This rf dressing changes the unit cell of the lattice at a subwavelength scale, such that its curvature and topology departs strongly from that of a simple sinusoidal lattice, and in certain limits is ringlike. Such a lattice is generally interesting from a band-structure engineering perspective, and more specifically from a need for lattices that will realize more complicated solid-state analogues. Radiofrequency dressing has previously been performed at length scales from millimeters to tens of microns, but not at the single-optical-wavelength scale. At this length scale significant coupling between adiabatic potentials leads to nonadiabatic transitions, which we characterize. We also investigate the dressing itself by measuring the momentum distribution of the dressed states.

## 47. Trapped-Ion Quantum Simulations of Spin Systems: From Two Qubits to Thousands

Warren Lybarger, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

**Abstract**. Due to the exponential growth of a quantum system\'s state-space with its size, the current technological limit for simulating the evolution of many-quantum-spin systems with classical computers (CC) is 36 spin-$\\frac{1}{2}$ particles. While CC\'s cannot be scaled to meet the exponentially increased demand in computational resources, mapping the Hamiltonians of such problems onto that of a quantum simulator (QS) completely avoids this exponential scaling problem, allowing for efficient simulations of much larger systems. QS may be the first attainable application of quantum information processing, enabling exploration of parts of the phase space not accessible in the original system and possibly providing an exponential speedup of computations for even just a few tens of interacting qubits when compared to CC methods. Following the work of Porras and Cirac [Phys. Rev. Lett. 92, 207901-1 (2004)] we discuss the status of an experiment at Los Alamos for demonstrating a proof of principle QS of an Ising-like spin-spin interaction in a transverse magnetic field. We also discuss a novel architecture for microfabricated ion trap arrays geared toward enabling large scale QS and one-way quantum computing with potentially thousands of ions [arXiv:0711.0233].

## 48. Ion Trap for efficient single Photon-Atom Coupling

Robert Maiwald, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

**Abstract**. Excitation of a single atom by a single photon is a fundamental process of physics, yet fairly inefficient in today\'s realizations. We present the design of a compact ion trap with superior optical access compared to conventional designs that allows for the localization of an ion in the focal point of a deep parabolic mirror. The electrode geometry results in a trapping potential that follows the axial symmetry of the mirror and provides optical access to the ion from almost the entire solid angle. The latter property is essential for efficient coupling of single ions to single photons in free space. The trap design can be adapted for other applications by replacing the mirror by a planar electrode. Using this more general design the ion can still be optically accessed from at least half to over 90% of the solid angle. The generation of a suitable mode-matched, dipole-like excitation pattern is discussed as well. Applications of an efficient light-matter coupling scheme include decoherence studies, quantum repeaters and quantum memories.

## 49. Beyond T_{1}: Measuring Coherence with State and Process Tomography

John Martinis, University of California, Santa Barbara

(Session 101: Thursday from 13:30-15:30)

**Abstract**. The tutorial would review the physics and mathematics behind the metrology of qubit coherence, using specific examples from recent experiments on superconducting qubits.

Outline of Tutorial

- Two-state quantum system
- Time evolution of state with external control
- Simple physical picture of decoherence
- Example: Josephson phase qubit

- I. Qubit basics

_{1}

- - and T

_{2}

- -ology
- T
_{1}, T_{2}, polarization describes memory of practically all qubits - T2 is approximate concept, depends on details
- Why are simple T
_{1}, T_{2}measurements not sufficient? - Density matrix description
- How measured - two methods
- Dynamic errors (to other states) measured to 10
^{-4}via "Ramsey filtering" - Errors in memory storage described by process tomography
- Research issue: going from matrix to "what needs fixing"
- Density matrix description
- How measured from single qubit rotatins
- Experiment to demonstrate entanglement, measure matrix
- Process tomography
- Bell-violation experiment

## 50. Efficient Generation of Large Number-Path Entanglement Using Spontaneous Parametric Down-Conversion

Kevin McCusker, University of Illinois at Urbana-Champaign

(Session 5: Friday from 18:00-20:00)

**Abstract**. We show how a large number-path entangled state (commonly called a N00N state) can be efficiently created using heralded spontaneous parametric down-conversion. The basic procedure is to use a pulsed source incident on a nonlinear crystal to create pairs of linearly polarized photons. One of these photons is detected, and the other is emitted into a polarization insensitive cavity. When the trigger photon is detected, all of the photons in the cavity are rotated by N/180 degrees. After N pairs are created, what remains in the cavity is a N00N state in the left/right polarization basis. This scheme can offer an exponential speed up over methods of creating N00N states using linear optics. We calculate the theoretical performance as a function of the transmission of the cavity, and discuss several other factors limiting overall efficiency.

## 51. A Clifford simulator for modeling fault-tolerance

Adam Meier, National Institute of Standards and Technology

(Session 5: Friday from 18:00-20:00)

Collaborators: K. Costello, B. Eastin, S. Glancy and E. Knill.

**Abstract**. A classical computer is capable of efficiently simulating certain subsets of quantum processes. One such subset, according to the Gottesman-Knill theorem, consists of logical qudit preparation, application of Clifford gates, and measurement in the logical basis which together comprise so-called Clifford circuits. We are writing a Clifford (circuit) simulator with the dual aims of providing a test bed for quantum fault-tolerance techniques and overseeing experimental quantum error-correction. In addition to being asymptotically faster than previous Clifford simulators in many cases of interest, our simulator is being designed to work with qudits of arbitrary size and, eventually, with non-stochastic error models. We present aspects of the design as well as some speed profiles and possible uses for the simulator.

## 52. Optimal Control of Large Spin-Atomic Systems with Coherent Electromagnetic Fields

Seth Merkel, University of New Mexico

(Session 4: Friday from 17:00-17:30)

**Abstract**. Cold atomic systems provide an excellent testing ground for quantum control protocols due to the isolation of these systems from their environment and the availability of high precision fields from the “quantum optics toolbox”. In this talk, we look at a variety of way to control large spins confined to the ground state hyperfine manifold of 133Cs. In particular, we present a scheme for controlling spins coherently using microwaves and rf-magnetic fields and compare this some previous experiments that utilized quasi-static magnetic fields and a nonlinear AC-Stark shift. We look at the requirements for controllability and find state preparations protocols, fields that map a fiducial state to an arbitrary target state, through a simple stochastic search algorithm. Additionally, we show that in this system the ability to easily find state preparation protocols translates into the ability to easily find arbitrary unitary maps.

## 53. Quantum Nondemolition Detection of Photons through an Enhanced Cross-Kerr Interaction

Kevin Mertes, Los Alamos National Laboratory

(Session 5: Friday from 18:00-20:00)

**Abstract**. We describe an experiment currently underway at Los Alamos National Laboratory that aims to demonstrate the quantum nondemolition (QND) measurement of single to several photons through the cross-phase modulation inherent in the giant Kerr nonlinearity theoretically predicted by Schmidt and Imamoglu. Our experiment will overlap three laser beams -- a signal, a probe, and a drive -- within an atomic vapor. The signal beam contains the one to several photons to be nondestructively counted. In the cross-Kerrr interaction, photons within the signal beam impress a phase shift on the probe beam that is proportional to the photon number. The drive beam mediates the interaction in a way that both augments the interaction cross section and minimizes the probe- and signal-beam absorption. To our knowledge, our experimental work will represent the first QND measurement of one to several photons by without recourse to a cavity.

## 54. When a quantum query is no better than a classical one

David Meyer, University of California at San Diego

(Session 6: Saturday from 10:15-10:45)

**Abstract**. We consider a simple generalization of Deutsch's problem in which a single quantum query, rather than solving the problem, provides no more information than a single classical query. This result can be explained by properties of quantum interference, and also follows from results in the early quantum hypothesis testing literature.

## 55. Probing Atomic Interactions of Cs in an Optical Lattice for Quantum Information

Brian Mischuck, University of New Mexico

(Session 5: Friday from 18:00-20:00)

Collaborators: Brian Mischuck, Ivan Deutsch, Worawarong ("O") Rakreungdet,Jae Hoon Lee,Enrique Montano and Poul Jessen

**Abstract**. We study a method to probe the spectrum of interacting Cs atoms in an optical lattice. Transport of the atoms to overlapping wells is achieved through a microwave drive between hyperfine levels in a lin-perp-lin polarization-gradient lattice. The spectral response of pairs of atoms to microwaves can be used to measure the effect of the interactions, even in the presence of a large background of unpaired atoms. Control of such interactions may have applications in quantum information processing such as quantum walks on a lattice and quantum simulations of many-body Hamiltonians.

## 56. The role of state preparation in quantum process tomography

Kavan Modi, University of Texas

(Session 13: Sunday from 12:00-12:30)

**Abstract**. The immense computational power of a quantum computer comes with a cost - the fragility of entangled quantum states from coherence loss. Although decoherence is present in all physical systems, the effect of these logic errors can be eliminated by using error correcting codes provided gate errors fall below a fault tolerance threshold. This threshold depends on system architecture and specific forms of decoherence, but is likely to be in the 10^{-4} range. The measurement of gate fidelity is thus a critical step for implementing fault tolerant quantum computing.

Most experiments determine coherence through T1 and T2 measurements, which gives only a simple description of error process in qubits. A more full and precise measurement is based on density matrix measurements of qubit states, which leads to a description of coherence in terms of state and process tomography. We study the effects of preparation of input states in quantum process tomography experiments. We study two preparation procedures, stochastic preparations and preparations by measurements. We show that for stochastic preparation procedure, linear process maps adequately describe the process. But when linear process maps are obtained from systems initially prepared using von Neumann measurements, they cannot describe the process adequately. We introduce a quadratic process map that can describe the processes initialized by preparation by measurements. I will discuss the consequences of the quadratic map and its properties.

## 57. Optimal control of light storage and retrieval

Irina Novikova, The College of William & Mary

(Session 11: Sunday from 08:30-09:15)

**Abstract**. Mapping of quantum states between light and matter (light storage) using a dynamic form of electromagnetically induced transparency is a topic of great current interest. We demonstrate experimentally a general approach to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media by finding optimal temporal profile for a strong control field or a signal wavepacket. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. These optimization procedures are applicable to a wide range of systems.

## 58. Fault-tolerant holonomic computation on quantum error-correcting codes

Ognyan Oreshkov, University of Southern California

(Session 9: Saturday from 16:15-16:45)

Collaborators: Ognyan Oreshkov, Todd Brun, Daniel Lidar, and Paolo Zanardi

**Abstract**. Holonomic quantum computation is a method of computation that uses non-abelian generalizations of the Berry phase. Due to its geometric nature, this approach is robust against various types of errors in the control parameters driving the evolution. In this study, we propose a scheme for fault-tolerant holonomic computation on stabilizer codes, which combines the virtues of error correction with those of the geometric approach. The scheme implements single-qubit operations on different qubits in the code by adiabatically varying Hamiltonians that are elements of the stabilizer, or in the case of subsystem codes---operators that act on the noisy subsystem. Two-qubit operations between qubits from different blocks require Hamiltonians whose weights are higher by one. Thus for certain codes, like the 9-qubit Shor code or its subsystem versions, it is possible to realize universal fault-tolerant computation using Hamiltonians of weight two and three, which is the optimal Hamiltonian weight for holonomic computation on a system of qubits. We also study the regime in which the adiabaticity condition becomes compatible with the fault-tolerance condition for fast gates on the time scale of the noise. Both conditions can be satisfied for a sufficiently large Hamiltonian strength, or equivalently, for a sufficiently low noise rate. This requires only a constant overhead of resources compared to those needed for fault-tolerant dynamical computation.

## 59. Progress Toward Atomic Magnetometry Beyond the Conventional Heisenberg Scaling

Heather Partner, University of New Mexico

(Session 5: Friday from 18:00-20:00)

Collaborators: Heather L. Partner, Brigette D. Black and JM Geremia (Department of Physics and Astronomy, The University of New Mexico, Albuquerque, New Mexico 87131 USA)

**Abstract**. We describe an atomic magnetometer whose field estimation uncertainty is expected to decrease faster than the conventional Heisenberg (1/N) scaling with the number of atoms in the atomic sample. Our procedure makes use of the effective two-body atomic interactions obtained by double-passing an off-resonant probe laser through the atomic sample during atomic Larmor precession. Performing balanced polarimetry on the transmitted probe field provides a continuous measurement signal that can be used to estimate the value of the magnetic field. We report on numerical simulations of our proposed quantum parameter estimation procedure and describe our ongoing efforts to implement our proposal using room-temperature Cs atoms.

## 60. Preserved information in quantum processes

David Poulin, California Institute of Technology

(Session 12: Sunday from 10:45-11:15)

**Abstract**. I will derive a general structure theorem characterizing the information that can be preserved by a quantum process (CPTP map). This characterization builds on a very simple yet powerful operational definition of the notion of being preserved: a set of quantum states is preserved by a process if the states are as distinguishable before and after the process. This definition encompasses noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes. More generally, I will demonstrate that all such information-preserving structure (IPS) is isomorphic to a matrix algebra. This provides a simple and efficient algorithm for finding all noiseless and unitarily noiseless IPS.

## 61. quantum thermodynamic cycles and quantum heat engines

Haitao Quan, Los Alamos National Laboratory

(Session 15: Sunday from 12:00-12:30)

**Abstract**. In this work, We are trying to make quantum mechanical generation of thermodynamics. our discussion will focus on the so-called quantum heat engines, which use quantum mechanical systems as the working substance. Quantum heat engines have some different properties from their classical counterpart. In order to describe quantum heat engines, we systematically studyisothermal and isochoric processes for quantum thermodynamic cycles. Based on these results the quantum versions of both the Carnot heat engine and the Otto heat engine are defined without ambiguities. We also study the properties of quantum Carnot and Otto heat engines in comparison with their classical counterparts. In addition, we discuss the role of Maxwell\'s demon in quantum thermodynamic cycles. We find that there is no violation of the second law, even in the existence of such a demon, when the demon is included correctly as part of the working substance of the heat engine.

## 62. Enhancing performance of a single-photon source with continuous monitoring

Shesha Raghunathan, University of Southern California

(Session 5: Friday from 18:00-20:00)

**Abstract**. In this work we numerically show that the performance of a single-photon source can be enhanced with continuous monitoring. We analyse a two-level atom ($2LA$) and a three-level atom ($3LA$) whose first excited state is resonantly coupled to the cavity mode of the atom $+$ cavity system. We continuously monitor the excited state/s of the atom and use stochastic master equation (SME) to evolve the system. Integrating the output "current" obtained due to continuous monitoring of the atom, we generate an estimate of $when$ the atom relaxed to its ground state. Since the output ``current\'\' due to monitoring is inherently noisy, we use a well known signal processing technique called affine mean-squared error estimation (AMSEE) to better estimate $when$ the atom relaxed to its ground state. In the parameter regime that we consider in this work, the information regarding $when$ the atom relaxed to its ground state closely follows $when$ a photon leaks out of the cavity. This estimate is thus used to control variable delay at the output of a single-photon source to reduce time-uncertainity of photons leaking out of the cavity, enhancing performance of a single-photon source.

## 63. On measurement-based quantum computation with the toric code states

Robert Raussendorf, University of British Columbia

(Session 8: Saturday from 14:15-14:45)

**Abstract**. We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer by mapping to non-interacting fermions via the planar Ising model.

J-Ref: S. Bravyi and R. Raussendorf, Phys. Rev. A 76, 022304 (2007)

Acknowledgements: Joint work with Sergey Bravyi

## 64. Photoassociation of alkaline earths

Iris Reichenbach, University of New Mexico

(Session 5: Friday from 18:00-20:00)

**Abstract**. Photoassociation on the very narrow clock transitions of alkaline-earth like elements, 1S->3P, allows both the accurate examination of molecular state at large separation, and the manipulation of scattering properties via optical Feshbach resonances. The latter could be used to tailor the scattering properties between different atoms to vastly simplify the construction of quantum gates. We calculate the long-range molecular potentials of alkaline-earth-like elements for photoassociation on the narrow intercombination line, for the first time including hyperfine interactions and the effects of magnetic fields. We investigate the existence of purely long-range bound states, caused by anticrossings induced by the hyperfine interaction.

## 65. Superoperator Dynamics Approach for Identification and Control of Hamiltonian Systems

Ali Rezakhani, University of Southern California Center for Quantum Information Science and Technology

(Session 14: Sunday from 13:30-14:00)

**Abstract**. Characterization and control of open quantum systems are among the fundamental tasks/challenges in quantum physics and quantum information science. In particular, there is much interest in the identification of quantum systems which have unknown interactions with their embedding environment. Quantum process tomography is known to be a general method for characterization of quantum dynamical processes, through an inversion of experimental data obtained from a complete set of state tomographies. In an earlier work we demonstrated that the utilization of quantum error detection techniques leads to the direct estimation of all independent parameters of a superoperator. Motivated by that approach, we now introduce new dynamical equations for superoperators â€“ leading to novel ways for Hamiltonian identification and control of open quantum systems. As an application, we show that this method could lead to efficient identification of certain properties of some sparse Hamiltonians. We also briefly discuss some possible applications to open-loop/learning control of Hamiltonian systems.

## 66. Continuous Measurement Quantum State Reconstruction in an Almost Decoherence-Free Protocol

Carlos Riofrio, University of New Mexico

(Session 5: Friday from 18:00-20:00)

**Abstract**. Quantum state reconstruction techniques based on weak continuous measurement have the advantage of being fast, accurate, and almost non-perturbative. Moreover, they have been successfully implemented in experiments on large spin systems (PRL 97, 180403 (2006)). The performance of these techniques is generally limited by decoherence, however, as controlling optical fields lead to spontaneous emission. In this poster, an application of the reconstruction algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)) is presented for the reconstruction of quantum states stored in the ground-electronic hyperfine manifolds (F=3, F=4) of an ensemble of 133Cs atoms controlled by microwaves and radio-frequency magnetic fields. This system is advantageous in the sense that its evolution only depends on the dynamics of the ground state, giving as a result an almost decoherence-free protocol.

## 67. Quantum walk on a circle in phase space via superconducting circuit

Barry Sanders, University of Calgary

(Session 8: Saturday from 14:45-15:15)

**Abstract**. We show how a quantum walk, with a single walker and controllable decoherence, can be implemented for the first time in a quantum quincunx created via superconducting circuit quantum electrodynamics (QED). Two resonators are employed to provide simultaneously fast readout and controllable decoherence over a wide range of parameters. The Hadamard coin flip is achieved by directly driving the cavity, with the result that the walker jumps between circles in phase space but still exhibits quantum walk behavior over 15 steps.

## 68. Open-Access Micro Optical Cavities on Atom Chips

Peter Schwindt, Sandia National Laboratories

(Session 5: Friday from 18:00-20:00)

**Abstract**. We are developing high-finesse, open-access optical cavities to achieve strong atom-photon coupling in small mode volume cavities. Such devices are essential for quantum computers and networks based on neutral atoms as the qubits. One mirror of the optical cavity is formed by a hemispherical void etched into a Si wafer and the other mirror is the coated tip of an optical fiber. In this way, the optical axis is normal to the plane of the atom chip. In parallel, we are fabricating high quality atom chips using Al conductors in multilayer structures to form magnetic traps and guides for neutral atoms. We are working to integrate the optical cavity and Al conductor processes to form an integrated atom chip. We will present details on the design, fabrication, and characterization of the conductors and optical cavities and on our efforts to develop an experiment to test our atom chips with cold atoms.

## 69. PT-Symmetric Quantum Evolution and Logic

Torey Semi, Colorado School of Mines

(Session 5: Friday from 18:00-20:00)

Collaborators: Mark W. Coffey, Torey Semi (Department of Physics, Colorado School of Mines, Golden, Colorado)

**Abstract**. There has been much recent interest in PT-symmetric quantum mechanics (QM) as an alternative formulation of quantum theory. We investigate the potential of this formulation for quantum computation and simulation.

PT-symmetric QM replaces the usual postulate that a system’s Hamiltonian must be Hermitian. It argues instead that the Hamiltonian can be symmetric with respect to combined parity and time-reversal and, for certain parametric regions, still produce real eigenvalues and maintain unitary time evolution. Besides being of fundamental interest, this approach allows for a fresh perspective on many QM applications.

It is known that for one-qubit PT-symmetric systems the evolution time from an initial state to a final state can be made arbitrarily small. We report on applying PT-symmetric Hamiltonians for two-qubit systems to quantum logic.

## 70. Optimal Measurements for Quantum Control in the Regime of Strong Feedback

Alireza Shabani, University of Southern California

(Session 5: Friday from 18:00-20:00)

**Abstract**. We consider the feedback control of an arbitrary (N-dimensional) quantum system, in the regimes of good control and strong feedback. Under the minimal constraints that the strength of the measurement is limited, we obtain the measurement strategy that achieves locally optimal control. That is we obtain the measurement that optimizes the control objective for each infinitesimal time-step. This measurement is partially, but not fully, unbiased with respect to the system state. We compare the performance of the resulting feedback algorithm to more pedestrian algorithms in which the measurement is fixed during feedback.

## 71. Resources and decoherence in qubit metrology

Anil Shaji, University of New Mexico

(Session 12: Sunday from 11:15-11:45)

**Abstract**. In quantum parameter estimation, accuracies that beat the standard quantum limit can be obtained by using the quantum properties of the probes and by modulating the nature of the interaction between the probe and the measured system. When qubits are used to construct a quantum probe, it is known that initializing n qubits in an entangled state, rather than in a separable state, can improve the measurement uncertainty by a factor of $1/\\sqrt{n}$. It is also known that if the interaction between the probe and the measured system involves $k$-qubit couplings then the best possible scaling of the measurement uncertainty is $1/n^k$ for a probe initialized in an entangled state and $1/n^{k-1/2}$ for a probe initialized in a product state. We investigate how the measurement uncertainty is affected when the individual qubits in a probe are subjected to decoherence in measurement schemes involving both linear and nonlinear couplings. In the face of such decoherence, we regard the rate $R$ at which qubits can be generated and the total duration $\\tau$ of a measurement as fixed resources, and we determine the optimal use of entanglement among the qubits and the resulting optimal measurement uncertainty as functions of $R$ and $\\tau$.

## 72. Kinetics of Quasiparticle Tunneling in a Pair of Superconducting Charge Qubits

Matthew Shaw, University of Southern California / NASA Jet Propulsion Lab

(Session 5: Friday from 18:00-20:00)

**Abstract**. We directly observe the statistics of non-equilibrium quasiparticle tunneling in a pair of charge qubits based on the single Cooper-pair box. Incoherent tunneling processes are a significant problem in single-charge devices, which must be engineered away for applications in quantum computing. We measure the odd-to-even and even-to-odd transition rates as a function of temperature, and interpret these results using a kinetic theory. At short times and low temperatures, the odd-to-even transitions are found to deviate from a simple Poisson process, in accordance with the theory. Furthermore, at low temperatures the odd-to-even transition rate is found to decrease with temperature, implying that the low-temperature quasiparticles are out of thermal as well as chemical equilibrium.

## 73. Engineering coherent quantum states in superconducting systems

Raymond Simmonds, National Institute of Standards and Technology

(Session 7: Saturday from 10:45-11:30)

**Abstract**. Wouldn't it be great to custom design your own individual quantum systems, then connect them up in interesting arrangements and play around with quantum mechanics? Recently, we have taken the first step towards creating and controlling quantum information using superconducting circuits. We have observed for the first time a coherent interaction between two superconducting “atoms” (quantum bits or qubits) and an LC cavity formed by a ~7 mm long coplanar waveguide resonant at ~9 GHz. When either qubit is resonant with the cavity, we observe the vacuum Rabi splitting of the qubit's spectral line. In a time-domain measurement, we observe coherent vacuum Rabi oscillations between either qubit and the oscillator. Using controllable shift pulses, we have shown coherent transfer of a arbitrary quantum state. We first prepare the first qubit in a superposition state, then this state is transferred to the resonant cavity and then after a short time, we transfer this state into the final qubit. These experiments show that developing custom designed quantum systems on chip is possible, opening up new possibilities for studying quantum mechanics and information science.

## 74. Using Quantum Control to Measure and Null Background Magnetic Fields in Cold Atom Experiments

Aaron Smith, University of Arizona

(Session 5: Friday from 18:00-20:00)

**Abstract**. Quantum control of atomic spins requires precise control of the total magnetic field acting on the spins. This makes accurate nulling of the (generally time dependent) background magnetic field one of the most important limiting factors of a real-world control experiment. We have devised a convenient method to use the atoms themselves as an in situ probe, combining spin-echo techniques and polarization spectroscopy to generate a highly sensitive signature of a desired component of the field. This allows us to quickly measure three orthogonal components of the total field with a resolution of a few tens of µG in a bandwidth of ~1kHz, and to apply the inverse of the measured field with three sets of Helmholz coils driven by arbitrary waveform generators. The resulting background field is typically less than ~50µG, an overall reduction of about one order of magnitude compared to the uncompensated AC field in our laboratory.

## 75. Quantum Simulated Annealing

Rolando Somma, Perimeter Institute

(Session 13: Sunday from 13:00-13:30)

**Abstract**. During the last years it has been shown that if a large quantum computer existed today, certain problems could be solved with them much more efficiently than their classical counterparts. Some of these problems include the quantum simulations of physical systems. In this talk I will show how quantum computers can be used to simulate and compute properties of classical systems in equilibrium. In particular, I will present a quantum algorithm that simulates annealing processes, where the (quantum) annealing rate greatly outperforms other classical methods like Markov chain Monte-Carlo based algorithms.

## 76. Entanglement and Verification

Steven van Enk, University of Oregon

(Session 101: Thursday from 10:00-12:00)

**Abstract**. Besides giving a general and simple introduction to bipartite entanglement, the main idea of the tutorial is to illustrate the differences between the theory and practice of entanglement verification.

Outline of Tutorial:

- I. Bipartite entanglement:
- Definition
- Convex sets
- LOCC
- Entanglement monotones
- Why do we need entanglement anyway?
- Entanglement in infinite dimensions
- Convex sets and entanglement witnesses
- Optimal & nonoptimal witnesses
- Bell inequality violations as a nonoptimal witness
- a priori
- Heralded
- a posteriori
- What could possibly go wrong?
- Criteria for entanglement verification
- Security of quantum key distribution as guideline
- Filtering data
- Assumptions about generated state
- Assumptions about measurements

## 77. Hitting time for the continuous quantum walk

Martin Varbanov, University of Southern California

(Session 5: Friday from 18:00-20:00)

**Abstract**. The hitting (stopping) time for the case of continuous quantum walks is defined. The walk is measured randomly according to a Poisson process with a fixed measurement rate. This allows us to derive an explicit formula for the hitting time and explore its depends on the measurement rate. In the two limits of the measurement rate going to 0 or infinity the hitting time diverges, where the second limit is representative of the quantum Zeno effect. Several conditions for existence of infinite hitting times are explored

## 78. Generic local distinguishability and completely entangled subspaces

Jon Walgate, Perimeter Institute for Theoretical Physics

(Session 3: Friday from 15:30-16:00)

**Abstract**. The geometry of Hilbert space entails many necessary and generic properties of quantum systems. In fact, expressing quantum information theoretic questions in geometric terms can transform apparently complex problems into exceedingly simple results. We present an example - a theorem concerning subspaces of projective Hilbert space with immediate and surprising consequences for entanglement and local state distinguishability.

A subspace of a multipartite Hilbert space is completely entangled if it contains no product states. Such subspaces can be large with a known maximum size, S, approaching the full dimension of the system, D. We show that almost all subspaces with dimension less than or equal to S are completely entangled, and then use this fact to prove that n random pure quantum states are unambiguously locally distinguishable if and only if n does not exceed D-S. This condition holds for almost all sets of states of all multipartite systems, and reveals something unexpected. The criterion is identical for separable and for nonseparable states: entanglement makes no difference.

Acknowledgements: Joint work with Andrew Scott, see arXiv:0709.4238

## 79. Quantum Computer Simulations of Time Dependent Hamiltonians

Nathan Wiebe, University Of Calgary

(Session 5: Friday from 18:00-20:00)

**Abstract**. In 1982, Feynman suggested a quantum computer would efficiently simulate quantum systems and illustrated this concept with Heisenberg chains (Int. J. Theor. Phys, 21, 467), which are difficult to solve on a classical computer. Since then a number of sophisticated quantum simulation schemes have been created to simulate time independent Hamiltonians, but to date only simplistic simulation schemes have been proposed for simulating time dependent Hamiltonians.

In this talk I will present a sophisticated quantum algorithm that can simulate the evolution of a sufficiently smooth and sparse time dependent Hamiltonian, which uses a number of gate operations that is comparable to the best known simulation schemes for time independent Hamiltonians. Applications of this algorithm to simulating Hamiltonian based quantum computing schemes in the circuit model (such as adiabatic quantum computing) will also be discussed.

## 80. Quantum Convolutional Coding with Entanglement Assistance

Mark Wilde, University of Southern California

(Session 9: Saturday from 15:45-16:15)

**Abstract**. We have recently developed quantum convolutional coding techniques for both entanglement distillation and quantum error correction. These techniques assume that the two parties participating in the communication protocols possess prior shared entanglement. Using these methods, we can import arbitrary classical binary or quaternary convolutional codes for use in quantum coding, with no requirement that these codes be self-orthogonal. Moreover, high-performance classical convolutional codes lead to high-performance quantum convolutional codes. We explicitly show how a convolutional entanglement distillation protocol operates, and how to encode and decode a stream of quantum information in an entanglement-assisted quantum convolutional code.

## 81. A general quantum algorithm for knot and link polynomials

Jon Yard, Los Alamos National Laboratory

(Session 6: Saturday from 09:15-9:45)

**Abstract**. In this talk, I will present a quantum algorithm for approximating topological invariants of knots and links coming from Markov traces on centralizer algebras of quantum groups. The method is based on a general formalism for efficiently implementing, on a quantum computer, representations of braid groups associated with path algebras. The general framework presented accommodates known quantum algorithms for approximately evaluating the Jones and HOMFLYPT polynomials - which arise from Markov traces on Temperley-Lieb and Hecke algebras associated to deformations of unitary groups. The framework also allows one to approximately evaluate the Kauffman polynomial invariants which arise from Markov traces on Birman-Wenzl-Murakami algebras associated to deformations of the orthogonal and symplectic groups. Time permitting, I will also comment on the cases in which approximating the Kauffman polynomial is a universal quantum algorithm which solves a Promise-BQP-complete problem.

Acknowledgements: This is joint work with Cris Moore (University of New Mexico, Santa Fe Institute).

## 82. Codeword Stabilized Quantum Codes

Bei Zeng, Massachusetts Institute of Technology

(Session 14: Sunday from 12:00-12:30)

**Abstract**. Quantum error correction codes play a central role in quantum computation and quantum information. While considerable understanding has now been obtained for a broad class of quantum codes, almost all of this has focused on stabilizer codes, the quantum analogues of classical additive codes. However, such codes are strictly suboptimal in some settings---there exist nonadditive codes which encode a larger logical space than possible with a stabilizer code of the same length and capable of tolerating the same number of errors. There are only a handful of such examples, and their constructions have proceeded in an ad hoc fashion, each code working for seemingly different reasons.

We present a unifying approach to quantum error correcting code design, namely, the codeword stabilized quantum codes, that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. In addition to elucidating nonadditive codes, this unified perspective promises to shed new light on additive codes as well. Our codes are described by two objects: First, the codeword stabilizer that can be taken to describe a graph state, and which transforms the quantum errors to be corrected into effectively classical errors. And second, a classical code capable of correcting the induced classical error model. With a fixed stabilizer state, finding a quantum code is reduced to finding a classical code that corrects the (perhaps rather exotic) induced error model.

We use this framework to generate new codes with superior parameters ((n,K,d)) to any previously known, the number of physical qubits being n, the dimension of the encoded space K, and the code distance d. In particular, we find ((10,18,3)) and ((10,20,3)) codes. We also show how to construct encoding circuits for all codes within our framework.

## 83. Quantifying nonlocality in states and experiments

Yanbao Zhang, University of Colorado-Boulder

(Session 5: Friday from 18:00-20:00)

Collaborators: E. Knill, K. Coakley and S. Glancy.

**Abstract**. We consider the use of statistics to quantify experimental evidence against local realism. We base the quantification on measures related to the Kullback-Leibler (KL) divergence, as suggested by W. van Dam, P. Grunwald and R.Gill [arXiv:quant-ph/0307125]. Optimal measurement settings and states can be obtained by maximizing the KL divergence of the experimental statistics predicted by quantum mechanics from the best local realistic model. We performed the maximization for the CHSH and GHZ tests and found results consistent with the results of W. van Dam, P. Grunwald and R.Gill. The advantage of statistical quantifications of non-locality is that they can be applied to the case of any number of parties, measurement settings and measurement outcomes, in which case useful Bell-type inequalities are hard to find.