# 2011 Talk Abstracts

## 1. Engineering Coherences at Single-Atom Level

Andrea Alberti, Universität Bonn

(Session 3 : Friday from 11:45am-12:15pm)

*Abstract.* We report on our capabilities to coherently control individual neutral Cs atoms in a 1D optical lattice with single site resolution [1,2]. By controlling the atoms through spin-dependent optical potentials we are able to entangle their internal and external degrees of freedom, allowing us to demonstrate 1D quantum walks in real space. Multi-path matter wave interference results in characteristic patterns of coherently delocalized atoms over many lattice sites [3]. In addition, microwave control of atomic motion is used to prepare atoms in predefined motional quantum states, e.g. in the vibrational ground state [4]. Presently we are exploring single-atom interferometry using spatially delocalized atoms in a Mach-Zehnder-like geometry. The atomic wave packets accumulate a relative phase at their respective positions from potential differences, making it a microscopic quantum detector of forces, such as magnetic field gradients or accelerations. Spatial separations over more than 20 sites still yields usable coherent phase evolution. These results lay the basis for interferometric detection of collisional phases and two-atom entanglement generation. [1] M. Karski et al., Imprinting Patterns of Neutral Atoms in an Optical Lattice using Magnetic Resonance Techniques, New J. Phys. 12, 065027 (2010) [2] M. Karski et al., Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging, Phys. Rev. Lett. 102, 053001 (2009) [3] M. Karski et al., Quantum Walk in Position Space with Single Optically Trapped Atoms, Science 325, 174 (2009) [4] L. Förster et al., Microwave Control of Atomic Motion in Optical Lattices, Phys. Rev. Lett. 103, 233001 (2009)

## 2. Making Error Correction Spatially Local

Dave Bacon, University of Washington

(Session 2 : Thursday from 7:30pm-8:00pm)

*Abstract.* In quantum error correction quantum information is encoded across multiple subsystems in such a way that one can diagnose and fix the most likely errors that occur to the system. This error correcting step is achieved by performing a measurement that does not disturb the encoded quantum information but does diagnose what error has occurred on the system. These error diagnosing measurements are often, but not always, of observables that are non-trivial over nearly the entire quantum system containing the encoded quantum information. An example of the contrary case are topological and color quantum codes, where the diagnosing measurements involve only a small number of spatially local subsystems (that is, involve only measurements over a constant sized neighborhood on some D-dimensional lattice.) Here we show how to convert a large class of quantum error correcting codes, all stabilizer codes, into spatially local codes. These codes are subsystem codes derived from measurement based quantum computing and have properties similar to toric and surface codes.

## 3. Confidence intervals for quantum state estimation

Robin Blume-Kohout, Los Alamos National Lab

(Session 10a : Saturday from 4:00pm-4:30pm)

*Abstract.* Quantum state and process tomography -- widely used to validate quantum devices -- typically yield a point estimate. The final result is a single "best guess" for the system's density matrix or process matrix. A point estimator cannot enable reliable fault-tolerant design, for the best that can be said is "The estimate is probably close to the true state." Interval estimators, on the other hand, report a convex region that contains the true state with (guaranteed) high probability. They support rigorous logical statements about the state (or process), which in turn enable fault tolerant designs. In this talk, I'll demonstrate how to design a confidence region estimator with guaranteed success probability, how to describe the result concisely, and how to derive a useful point estimator from it.

## 4. Subsystem and stabilizer quantum codes with spatially local generators

Sergey Bravyi, IBM Watson Research Center

(Session 2 : Thursday from 5:15pm-6:00pm)

*Abstract.* Fault-tolerant quantum computation based on 2D topological quantum codes has received a considerable attention lately since it can be implemented on quantum machines with a geometrically local architecture. To better understand the potential of topological codes we derive upper bounds on the parameters of quantum codes that stem from the spatial locality constraint and find families of codes that achieve these bounds. Our analysis applies to both subspace and subsystem quantum codes. We also discuss topological subsystem codes (TSCs) proposed recently by Bombin. These codes require only the measurement of two-qubit nearest-neighbor operators for error correction. We demonstrate that TSCs can be viewed as generalizations of Kitaev's honeycomb model to 3-valent hypergraphs. This new connection provides a systematic way of constructing TSCs and analyzing their properties. Furthermore, we propose and implement some candidate decoding algorithms for one particular TSC assuming perfect error correction. Our Monte Carlo simulations indicate that this code, which we call the five-squares code, has a threshold against depolarizing noise of at least 2%.

## 5. Pseudo-unitary freedom in the operator-sum representation, positive maps, and quantum error correction

Mark Byrd, Southern Illinois University

(Session 10b : Saturday from 4:00pm-4:30pm)

*Abstract.* A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition. The method of the construction applies to more general maps which need not be completely positive. The OSR is not unique; there is a freedom to choose a different set of operators in the OSR, yet still obtain the same map. Here we show that, whereas the freedom for completely positive maps is unitary, the freedom for maps which are not necessarily completely positive is pseudo-unitary. Those that are genuinely different must therefore differ by the number and type of spectral decomposition. Moreover, our theorem enables us to prove a necessary and sufficient condition for error correcting codes which can correct errors due to maps which are not completely positive.

## 6. Efficient methods for the characterisation of qbit Hamiltonian dynamics

Joshua Combes, Center for Quantum Information and Control, University of New Mexico, USA

(Session 10a : Saturday from 5:00pm-5:30pm)

*Abstract.* We investigate schemes for Hamiltonian parameter estimation of a two-level system using fixed-basis projective measurements. To be concrete we consider two regimes of parameter estimation. Regime I: the coupling of qbit to the environment is negligible. However, due to manufacturing imperfections the strength ω of the Hamiltonian, H=ω σ_{x}/2, is unknown. Regime II: the second and more realistic case is when the qbit is weakly coupled, with strength κ, to a Markovian environment. In this situation both κ and ω must be estimated. We show that it is possible to reduce the total number of measurements required for characterisation in both cases by using measurements that are not uniformly spaced in time.

## 7. Simulating Concordant Computations

Bryan Eastin, Northrop Grumman Corporation

(Session 8 : Saturday from 11:30am-12:00pm)

*Abstract.* A quantum state is called concordant if it has zero quantum discord with respect to any part. By extension, a concordant computation is one such that the state of the computer, at each time step, is concordant. In this talk, I describe a classical algorithm that, given a product state as input, permits the efficient simulation of any concordant quantum computation having a conventional form and composed of gates acting on two or fewer qubits. This shows that such a quantum computation must generate quantum discord if it is to efficiently solve a problem that requires super-polynomial time classically. While I employ the restriction to two-qubit gates sparingly, a crucial component of the simulation algorithm appears not to be extensible to gates acting on higher-dimensional systems.

## 8. Relaxation, thermalization, and a quantum algorithm to prepare Gibbs states

Jens Eisert, University of Potsdam

(Session 8 : Saturday from 1:30pm-2:15pm )

*Abstract.*

This talk will be concerned with recent progress on understanding how quantum many-body systems out of equilibrium eventually come to rest. The first part of the talk will highlight theoretical progress on this question - employing ideas of Lieb-Robinson bounds, quantum central limit theorems and of concentration of measure (1-4). These findings will be complemented by experimental work with ultra-cold atoms in optical lattices, constituting a dynamical "quantum simulator", allowing to probe physical questions that are presently out of reach even for state-of-the-art numerical techniques based on matrix-product states (5). The last part of the talk will sketch how based on the above ideas, a fully certifiable quantum algorithm preparing Gibbs states can be constructed, complementing quantum Metropolis algorithms (6).

(Joint work with C. Gogolin, M. Mueller, T.J. Osborne, A. Flesch, C. Cramer, U. Schollwoeck, I. Bloch, S. Trotzky, Y.A. Chen, A. Riera.)

(1) "Absence of thermalization in non-integrable systems", Phys. Rev. Lett., in press (2011).

(2) "Concentration of measure for quantum states with a fixed expectation value", Commun. Math. Phys., in press (2011).

(3) "A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states", New J. Phys. 12, 055020 (2010).

(4) "Exact relaxation in a class of non-equilibrium quantum lattice systems", Phys. Rev. Lett. 100, 030602 (2008).

(5) "Probing the relaxation of a strongly correlated 1D Bose gas towards equilibrium", submitted to Nature Physics (2011).

(6) "Gibbs states, exact thermalization of quantum systems and a certifiable algorithm for preparing thermal states", submitted to Phys. Rev. Lett. (2011).

## 9. Universal Quantum Computation with Non-Interacting Fermions

David Feder, University of Calgary

(Session 12 : Sunday from 10:30am-11:00am)

*Abstract.* In measurement-based quantum computation, an algorithm proceeds entirely by making measurements on successive qubits comprising some highly entangled 'resource state.' The most well-studied resource state is the cluster state. Much recent work has been done to identify other suitable resource states, and particular effort has been expended on identifying experimentally implementable Hamiltonians that yield resource states as their gapped ground states. We show that for a particular choice of lattice model, the gapped ground state of non-interacting indistinguishable fermions is formally equivalent to a cluster state. Entanglement is a direct consequence of fermionic antisymmetry, and local unitary gates are implemented by turning on a small additional lattice. The quantum information is encoded entirely in the lattice positions of the fermions, rendering it impervious to many sources of decoherence. This suggests that resources for quantum information processing may be generic in Nature.

## 10. Tomography via Compressed Sensing

Steve Flammia, Caltech

(Session 4 : Friday from 3:00pm-3:30pm)

*Abstract.* I will review past results and present current progress on using methods from the theory of compressed sensing to drastically reduce the number of measurements required for quantum tomography. These methods achieve a square root improvement in the number of measurement settings when the state in question is pure. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, can be applied to states that are only approximately pure, and can be extended to process tomography of nearly unitary channels. The acquired data can be used to certify that the state is indeed close to pure, so *no a priori assumptions are needed*.

## 11. Exchange-Only Computation, Leakage Reduction, and Dynamical Decoupling in the Three-Qubit Decoherence Free Subsystem

Bryan Fong, HRL Laboratories, LLC

(Session 2 : Thursday from 8:00pm-8:30pm)

*Abstract.* We describe exchange-only universal quantum computation, leakage reduction, and dynamical decoupling in the three-qubit decoherence free subsystem (DFS). We discuss the angular momentum structure of the DFS, the proper forms for the DFS CNOT and leakage reduction operators in the total angular momentum basis, and new exchange-only pulse sequences for the CNOT and leakage reduction operators. While the search for sequences is performed numerically using a genetic algorithm, the final solutions found are exact, with closed-form expressions. We also show that exchange pulses are sufficient to decouple the three-qubit DFS from its environment and describe bang-bang pulse sequences for decoupling the DFS from its bath. Sponsored by United States Department of Defense.

## 12. Ultracold bosons in 3D double wells: macroscopic superposition of vortex states and the tunneling of atoms carrying vorticity

Miguel-Angel Garcia-March, Colorado School of Mines

(Session 10c : Saturday from 4:00pm-4:30pm)

*Abstract.* M.A. Garcia-March and L.D. Carr We study ultracold bosons in three-dimensional double wells when they are allowed either to condense in single-particle ground states or to occupy excited states. This permits the consideration of angular degrees of freedom on the model, since the second level eigenstates can carry angular momentum. We show that the number of relevant parameters is increased, since new processes, like two-particle hopping between different levels or vortex-antivortex pair creation or annihilation, are considered. We clearly demarcate the new range of dynamical regimes obtained in terms of the new parameters. We show the presence, in the interaction-dominated regimes, of macroscopic superposition states of atoms with non-zero angular momentum. This leads to the study of the dynamics of atoms carrying vorticity while tunneling between wells. Among these new tunneling processes, we find vortex hopping and vortex-antivortex pair superposition along with the sloshing of atoms between both wells.

## 13. Multipartite Entanglement: Classification, Quantification, Manipulation, Evolution and Applications

Gilad Gour, Institute for Quantum Information Science, University of Calgary

(Session 10c : Saturday from 5:30pm-6:00pm)

*Abstract.* Exotic multipartite entangled states plays an important role in a variety of quantum information processing tasks such as conventional and measurement-based quantum computation, quantum error correction schemes, quantum secret sharing, quantum simulations, and in principle in the description of every composite system consisting of more than one subsystem. The amount of information needed to describe N-party quantum system grows exponentially with N, which makes it very difficult and almost impossible to classify multipartite entangled states. In this talk I will show that a new formalism based on the stabilizer group of a given multipartite state, not only makes it possible to classify and quantify the amount of entanglement in multipartite states, but also describes fully the manipulation of multipartite entanglement under separable operations. In particular, I will introduce necessary and sufficient conditions to transform one pure multipartite state to another multipartite state via separable operations. In addition, I will discuss the evolution of multipartite entanglement under noise and decoherence, and its quantification in terms of SL-invariant polynomials. I will end with few applications to quantum secret sharing. Some of the work presented here is based on a joint work with Nolan Wallach.

## 14. Quantum simulation of an antiferromagnetic Ising chain with longitudinal and transverse magnetic fields

Markus Greiner, Harvard University

(Session 3 : Friday from 8:30am-9:15am)

*Abstract.* With single lattice site detection and control, the quantum gas microscope opens new possibilities for quantum simulations. It allows us to study quantum magnetism with ultracold atoms in optical lattices. We experimentally realize an antiferromagnetic Ising chain with longitudinal and transverse magnetic fields, and observe a quantum phase transition from a paramagnetic to an antiferromagnetic state.

## 15. Addressable multi-qubit logic via permutations

Jim Harrington, HRL Laboratories

(Session 10b : Saturday from 4:30pm-5:00pm)

*Abstract.* An important issue when encoding multiple logical qubits into a single code block is identifying how to separately address the different logical qubits. Previous schemes have generally required unpacking of the logical qubits into empty code blocks before computing on them, thus giving up much of the space advantage of these codes. We solve the addressability problem by instead taking advantage of the permutation automorphism structure of the 15-qubit Hamming code, and we present schemes for implementing targeted logical gates with a space efficiency of one-third or two-fifths. This is joint work with Ben Reichardt. Sponsored by United States Department of Defense.

## 16. Quantum simulation with trapped atomic ions

Kihwan Kim, Joint Quantum Institute and University of Maryland

(Session 11 : Sunday from 9:00am-9:30am)

*Abstract.* As Feynman proposed a couple of decades ago, a well-controlled quantum system called a "quantum simulator" can efficiently simulate other interesting and complex quantum systems that are otherwise intractable. For a collection of spins subject to a fully-connected frustrated Ising interaction, current conventional computations can simulate no more than about 20-30 spins. A crystal of trapped ions system is one of most promising quantum systems for the realization of such a quantum simulator. We demonstrate the quantum simulation of a frustrated Ising Hamiltonian in a transverse field with 3 spins [1] and increase the number of spins up to 9 for the case of all ferromagnetic interactions [2]. This is an important benchmark as the system is fast approaching a level where classical simulation will not be possible. In the experiment with up to 9 spins, we observe several technical imperfections such as state detection efficiencies, spontaneous emissions, AC stark shift fluctuations, qubit decoherence of qubits, and heating of motion. We find that these errors do not appreciably affect the observation of the magnetic order while crossing a phase transition from paramagnetism to ferromagnetism as the system size increases. We finally speculate on how this system can be scaled to models that cannot be simulated using classical computers. This research was supported by the DARPA OLE program under ARO contract, IARPA through ARO contract, the NSF PIF Program, the AQUTE program, and the NSF Physics Frontier Center at JQI. [1] K. Kim, et al., Nature 465, 590 (2010). [2] In preparation

## 17. Atom trapping in the evanescent field of a tapered optical fiber: towards cQED with micro-toroids and trapped atoms.

Clement Lacroute, California Institute of Technology

(Session 7 : Saturday from 9:45am-10:15am)

*Abstract.* Authors: C. Lacroute*, D. J. Alton*, K. S. Choi*, A. Goban*, N. P. Stern*, H. J. Kimble* *Norman Bridge Laboratory of Physics MC 12-33, California Institute of Technology, Pasadena, California 91125, USA It has recently been shown that a two-color Far Off-Resonance optical Trap (FORT) could be generated in the evanescent field of a sub-wavelength diameter optical fiber [1]. About 2000 Cs atoms were trapped 200nm away from the fiber surface, with a 50ms lifetime. This is an important result in the context of cavity Quantum Electrodynamics (cQED) with micro-resonators, where a single atom needs to be located a few hundred nanometers away from a dielectric surface to be strongly coupled to the evanescent field of a lithographically patterned waveguide [2]. The two-color FORT consists of the combination of a red-detuned attractive potential and a blue-detuned repulsive potential [1]. The two trapping beams propagate in a sub-wavelength optical fiber, and the resulting evanescent-field potential confines the atoms radially at a distance of a few hundred nanometers from the fiber surface. Azimuthal confinement can be obtained by a right choice of relative polarizations of the trapping beams. Adding a counter-propagating red-detuned beam provides longitudinal confinement by generating a standing wave. We investigate the evanescent electric field and its polarization in the vicinity of the fiber surface, which is found to be spatially varying in all directions on the optical wavelength scale, and is not everywhere linear because of the out-of-phase, non-vanishing longitudinal component of the electric field. Elliptically polarized light can result in a splitting of the atomic Zeeman sub-levels by a so-called fictitious magnetic field [3]. We quantify this splitting for the use of a pair of "magic wavelength" trapping beams that minimize the spread in the atomic polarizabilities for both red and blue detuned light fields [4, 5], and the subsequent spread of the total trapping potential. We will discuss experimental consequences in terms of lifetime and coherence times of the trapped atoms, and the implementation of such a fiber trap in a cQED experiment using micro-toroids. This work is supported by NSF, NSSEFF, DARPA, and the Northrop Grumman Corporation. [1] Vetsch et al., PRL 104(20), pp. 203603 (2010). [2] Aoki et al., Nature 443(12), pp. 671-674 (2006). [3] I. Deutsch and P.S. Jensen, PRA 57(3), pp. 1972-1986 (1998). [4] McKeever et al., PRL 90(13), pp. 133602 (2003). [5] Kien et al., J. Phys. Soc. Jpn. 74, pp. 910-917 (2005).

## 18. Entanglement-Assisted Quantum Error-Correcting Codes when the Ebits of Receiver are not Perfect

Ching-Yi Lai, University of Southern California

(Session 10b : Saturday from 5:00pm-5:30pm)

*Abstract.* The scheme of entanglement-assisted quantum error-correcting (EAQEC) codes assumes that the ebits of the receiver are error-free. In practical situations, errors on these ebits are unavoidable, which diminishes the error-correcting ability of quantum codes. We provide two different schemes to cope with this problem. We first show that any (nondegenerate) standard stabilizer codes can be transformed into EAQEC codes that can correct both errors on the qubits of sender and receiver. These EAQEC codes are equivalent to standard stabilizer codes, and hence the decoding techniques of standard stabilizer codes can be applied. Several EAQEC codes of this type are found to be optimal. In the second scheme, the receiver uses a standard stabilizer code to protect the ebits. The decoding procedure has two stages: decode the ebits of the receiver and then decode the information protected by the EAQEC code. To achieve high channel capacity, the second scheme is preferable, with a good EAQEC code that is not equivalent to any standard stabilizer code, at the cost of more resources at the receiver. Several optimal EAQEC codes not equivalent to any standard stabilizer code are found by the encoding optimization algorithm.

## 19. Quantum Control of the Motional and Internal Degrees of Freedom of Neutral Atoms

Jae Hoon Lee, University of Arizona

(Session 3 : Friday from 10:45am-11:15am)

*Abstract.* Cold trapped atoms provide an excellent platform on which to explore fundamental aspects of quantum information science, due in part to long coherence times and in part to the diverse sets of tools available for quantum manipulation. In this talk we discuss recent experimental progress towards robust quantum control of motional and ground hyperfine states of 133Cs atoms. An essential aspect of quantum information processing in optical lattices is the ability to prepare and address atoms with single-site resolution. In principle this can be done via "resonance imaging", using e. g. a combination of spatially varying light shifts and microwave pulses to change the internal state of atoms at well defined positions. In our current, first generation experiment we superimpose a long-period 1D standing wave on top of our 3D optical lattice, flip the spins of atoms in planes where the light shifted transition frequency matches that of the microwave field, and remove the remaining atoms from the lattice. Using composite pulse techniques we can make this preparation step robust against small variations in the relative position of the lattices. In a separate experiment we explore the use of DC, rf and microwave fields to manipulate the internal quantum state associated with the 16-dimensional ground hyperfine manifold of the Cs atom. Using robust control techniques, we demonstrate quantum state mapping from arbitrary initial to final states with fidelities of 98% or better, in the presence of errors and inhomogeneities in the control fields. We also study successive applications of state mapping waveforms, with the goal of separating qudit initialization and readout errors from state mapping errors, and to reliably measure state mapping fidelities in excess of 99%.

## 20. Superconducting Transition-Edge Sensors Optimized for High-Efficiency Photon-Number Resolving Detectors

Adriana Lita, National Institute Of Standards and Technology (NIST) Boulder

(Session 9 : Saturday from 2:45pm-3:15pm)

*Abstract.* Collaborators: B. Calkins, N. Tomlin, I. Vayshenker, L. A. Pellouchoud, A. J. Miller, S. Nam Ideal single photon detectors for quantum information applications should operate at wavelengths that span visible through infrared with very high quantum efficiency, have photon-number-resolving capabilities, high speed, and very low dark-count rates. Currently no single-photon detector technology is able to provide a detector that achieves all the properties that would make such an ideal detector. Superconducting transition-edge sensors (TESs) however, currently have almost all the required properties, except high speed operation. TESs are microcalorimeters operating at cryogenic temperatures, that have the ability to unambiguously resolve the photon number in a pulse of light and can be optimized for high quantum efficiency from near-ultraviolet to near-infrared with essentially no dark counts. TES optimization for high quantum efficiency at particular wavelengths from near-ultraviolet to near-infrared is achieved by designing multilayer structures that enhance the absorption of light into the active device material, and efficient self-alignment to optical fibers by silicon chip micromachining. We will describe the details of the design of the detectors as well as packaging of the detectors to achieve system detection efficiencies approaching 99%.

## 21. Convex Roof Optimization from Cartan Decompositions

Peter Love, Haverford College

(Session 10c : Saturday from 5:00pm-5:30pm)

*Abstract.* Extension of pure state entanglement measures to mixed states requires optimization over the set of ensembles that realize the density matrix. As discovered independently by Schroedinger, Jaynes and Hughston, Josza and Wooters, all ensembles may be realized by a unitary transformation of an initial ensemble. Hence the convex roof extension of pure state entanglement may be phrased as a problem of optimization on the unitary group. Prior work on this problem has used an Euler-Hurwitz parameterization of the unitary group. In this work, we describe the use of a parameterization based on a pair of Cartan decompositions previously developed in the context of the quantum Shannon decomposition.

## 22. Quantum-enhanced magnetometry and nonlinear metrology with atomic ensembles.

Morgan Mitchell, Institute of Photonic Sciences

(Session 5 : Friday from 4:00pm-4:45pm)

*Abstract.* I will present recent results on quantum metrology combining atomic and quantum-optical systems. Optical magnetometry, which employs an atomic ensemble interacting with an optical beam, is both of considerable practical interest and a good test-bed for quantum metrology with dual quantum systems. With a hot atomic ensemble, we have recently demonstrated a squeezed-light-enhanced rubidium magnetometer, showing the possibility of sub-shot-noise performance in this system. I will also describe an analogous cold atom system which achieves both shot-noise- and projection-noise-limited performance, allowing study of optical magnetometry in a fully-quantum regime. We have recently pushed this cold-atom quantum interface into the nonlinear regime, using spin-dependent optical nonlinearities to perform shot-noise-limited measurements of the ensemble spin. By implementing a non-linear Hamiltonian proposed by Boixo et al. [Phys. Rev. Lett. 101, 040403 (2008)], we demonstrate a sensitivity scaling better than the 1/N "Heisenberg limit" over two orders of magnitude in photon number.

## 23. Improving Quantum Clocks via Semidefinite Programming

Mike Mullan, National Institute of Standards and Technology

(Session 10a : Saturday from 4:30pm-5:00pm)

*Abstract.* The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, as before and after clock queries, we are able to apply arbitrary unitary operations and measurements. Here, we take advantage of this freedom and present a numerical technique designed to increase the accuracy of these clocks by optimizing over these choices of quantum operations. We use a greedy approach, minimizing the phase variance of a noisy classical oscillator with respect to a perfect frequency standard after a single interrogation step; we do not optimize over sequences of interrogations nor over the time of each step. In contrast to prior work, which derived asymptotically optimal strategies under the assumption that all classical oscillator states are equiprobable, we are able to consider the more realistic situation where we have some prior knowledge of the frequency of this oscillator, either from experimental considerations or previous measurements. Additionally, we are able to compare clocks with varying numbers of ions and those subject to multiple, coherent queries. Our technique is based on the semidefinite programming formulation of quantum query complexity, a method first developed in the context of deriving algorithmic lower bounds. The application of semidefinite programming to an inherently continuous problem like that considered here requires discretization; we derive bounds on the error introduced and show that it can be made suitably small. While we can only simulate small systems, many quantum logic clocks, like the highly accurate Al+ optical clock at NIST, use relatively few ions and are therefore natural candidates for the techniques developed here. This work is in collaboration with Manny Knill and Till Rosenband.

## 24. Rapid Adiabatic Passage on a Trapped Ion with a Noisy Laser

Thomas Noel, University of Washington

(Session 11 : Sunday from 9:30am-10:00am)

*Abstract.* We report experimental investigation of rapid adiabatic passage (RAP) in a trapped ^{138}Ba^{+} system. RAP is implemented on the transition from the ^{138}Ba^{+} ground state to a metastable D state by applying a laser at 1.76 μm. We focus on the interplay of laser noise and laser power in shaping the effectiveness of RAP, which has been shown to be a robust tool for state detection of ionic qubits. However, we note that reaching high state transfer fidelity requires a combination of small laser linewidth and large rabi frequency.

## 25. Randomized benchmarking of atomic qubits and differential light shift cancellation in an optical lattice

Steven Olmschenk, Joint Quantum Institute, National Institute of Standards and Technology and University of Maryland Department of Physics

(Session 3 : Friday from 11:15am-11:45am)

*Abstract.* We perform randomized benchmarking on atomic qubits confined in an optical lattice. Single qubit rotations are implemented using microwaves, with a measured average error per gate of 1.4(1) x 10^-4 that is dominated by the decoherence time of the system. A method to extend the coherence time by cancellation of up to 95(2)% of the differential light shift in the ground state of rubidium is also demonstrated. Finally, we discuss how these gate operations might be performed with single-lattice-site addressability for more advanced applications in quantum information.

## 26. Uncertainty, nonlocality, & complementarity

Jonathan Oppenheim, University of Cambridge

(Session 4 : Friday from 1:45pm-2:30pm )

*Abstract.* Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.

## 27. Light shifts of ground-state quantum beats: A consequence of quantum jumps.

Luis Orozco, Joint Quantum Institute, Dept. Physics and National Institute of Standards and Technology, University of Maryland

(Session 7 : Saturday from 9:15am-9:45am)

*Abstract.*

Spontaneous emission in resonance fluorescence is a fundamental process in which an atom loses energy and the dipole emission of radiation is interrupted, with the consequence of damping. This process has been studied under different conditions, and the analysis with two-level atoms has given many insights into the behavior of more complicated atomic structure. The multi-level atom often has ground-state hyperfine and Zeeman structure. This structure allows the manipulation of ultra-cold atoms in areas as different as atomic clocks and quantum information processing. We present a study of ground-state light shifts with weak coherent excitation when the light is quasi-resonant with an electronic excited state of^{85}Rb (within a linewidth). This mechanism is only discernible through the polarization mode selection (drive V, measure H) available in cavity QED and the powerful signals coming from ground-state quantum beats, and correlation measurements on the H mode. The shift requires the presence of spontaneous emission, which generally preserves the ground-state coherence but induces a significant frequency shift with the presence of even a single photon.

Quantum trajectories show that quantum jumps on the driven V mode (pi transitions) that happen in between H detections cause phase shifts on the Larmor precesion. Quantum jumps interrupt the atomic dipole and transfer the differential phase accumulated by the excited state to the ground state. The stochastic process of the quantum jumps produces both a frequency shift, if the phase jumps are small compared to p, and a broadening of the spectral linewidth from the phase diffusion process.

Work performed by David G. Morris, Adres D. Cimmarusti, Luis A. Orozco, Pablo Barberis-Blostein and H. J Carmichael with support from NSF, USA; CONACYT, Mexico; and The Marsden Fund of the Royal Society of New Zealand.

## 28. Quantum information processing with trapped ions at NIST

Christian Ospelkaus, National Institute of Standards and Technology, Boulder

(Session 11 : Sunday from 8:30am-9:00am)

*Abstract.* We discuss experiments towards scalable Quantum Information Processing (QIP) in the Ion Storage Group at NIST Boulder. The architecture we pursue is based on quantum information stored in internal (hyperfine) states of the ions. Laser beams are used to induce both single-qubit gates and multi-qubit gates through the Coulomb interaction between ions held in the same potential well. Transport of ions allows for keeping the number of ions per trap zone small and for individual addressing. We first describe a set of experiments that demonstrate these basic techniques with two qubits in a scalable way to realize a programmable quantum processor. Based on current efforts towards scalable surface-electrode trap arrays, we discuss the integration of the various experimental techniques, for example integrated fiber-optic readout. We also discuss studies on decoherence and efforts to improve the fidelity of entangling operations. Moreover, we explore techniques that go beyond the established scheme of laser-based multi-qubit gates on ions held in a common trap. We demonstrate Coulomb coupling between two ions (mechanical oscillators) held in individual traps separated by 40 μm and observe oscillations of single energy quanta between the two ions. Furthermore, we explore a microwave near-field approach to quantum control. In particular we observe microwave single-qubit rotations with pi times of less than 20 ns, motional sideband transitions, and cooling of the ion motion. These two techniques could open new experimental perspectives for quantum simulation in surface-electrode trap arrays, for novel entangling schemes for QIP, and for precision spectroscopy. In related work our group explores multiqubit entanglement of ions in Penning traps and applications of quantum information protocols to optical atomic clocks. This work has been supported by IARPA, DARPA, NSA, ONR, and the NIST Quantum Information Program.

## 29. Concatenated Stabilizer Dynamical Decoupling

Gerardo Paz, University of Southern California

(Session 2 : Thursday from 8:30pm-9:00pm)

*Abstract.* We show how to integrate concatenated dynamical decoupling (CDD) techniques with quantum error correction (QEC) codes: the two main strategies to protect quantum information from the decoherence induced by unwanted interaction with the environment. It has been shown that CDD can be used as a lower level protection layer against decoherence and improves the effective error rate of a physical gate, provided one assumes certain locality conditions (local bath assumption) [Ng, Lidar, Preskill, arXiv:0911.3202]. The typical CDD protocol uses pulses from a group of non-commuting operators to decouple to arbitrary order, in the language of Magnus expansion, the state one wants to protect from the environment. In this work, in the same spirit as [Lidar, Phys. Rev. Lett. 100,160506 (2008)], we show how decouple a state encoded in some stabilizer QEC code to arbitrary order by applying pulses from the stabilizer group of the QEC code used. We demonstrate the technique for concatenated and non-concatenated QEC codes and show that, in contrast to the CDD case, (i) one can omit the local bath assumption, and (ii) has the freedom of introducing a fixed evolution for the protected quantum state. We show how to decouple a multiqubit state with a non-local system bath to arbitrary order (dictated by the distance of the QEC code).

## 30. Scaling up entanglement in the optical frequency comb: recent experimental progress

Olivier Pfister, University of Virginia

(Session 9 : Saturday from 2:15pm-2:45pm)

*Abstract.* It is known that the set of quantum "quasimodes" defined by the optical frequency comb of a single optical parametric oscillator can be placed, in principle, in a continuous-variable cluster state of arbitrary large size (up to thousands of modes). In this talk we report on our progress towards this goal and towards an intermediate one: the simultaneous generation of multiple sets of quadripartite cluster states.

## 31. Quantum Metropolis Sampling: An algorithm to simulate thermal systems with a quantum computer

David Poulin, Université de Sherbrooke

(Session 8 : Saturday from 10:45am-11:30am)

*Abstract.* The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is intractable for classical computers. Such a machine would have tremendous applications in all physical sciences, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the more fundamental problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibb's states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. In this talk, I will demonstrate that the corresponding quantum problem can be solved by a quantum Metropolis algorithm. This validates the quantum computer as a universal simulator, and proves that the so-called sign problem occurring in quantum Monte Carlo methods can be resolved with a quantum computer.

## 32. General-Purpose Quantum Simulation with Prethreshold Superconducting Qubits

Emily Pritchett, University of Waterloo, Institute for Quantum Computing

(Session 1 : Thursday from 4:45pm-5:15pm)

*Abstract.* We introduce a protocol for the fast simulation of n-dimensional quantum systems on n-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of an n -dimensional real (but otherwise arbitrary) Hamiltonian that is simulated in the n-dimensional single-excitation subspace of the quantum simulator. A time-dependent energy/time rescaling minimizes the simulation time on hardware having a fixed coherence time. We demonstrate how three tunably coupled superconducting phase qubits can simulate a realistic three-channel molecular collision using this protocol. The method makes a class of general-purpose time-dependent quantum simulation practical with today's sub-thershold-fidelity qubits.

## 33. Trapping and Interfacing Cold Neutral Atoms Using Optical Nanofibers

Arno Rauschenbeutel, Institute of Atomic and Subatomic Physics, Vienna University of Technology

(Session 7 : Saturday from 8:30am-9:15am )

*Abstract.* We recently demonstrated that laser-cooled cesium atoms can be simultaneously trapped and optically interfaced with a multi-color evanescent field surrounding an optical nanofiber. The atoms are localized in a one-dimensional optical lattice about 200 nm above the nanofiber surface and can be efficiently interrogated with a resonant light field sent through the nanofiber. This technique opens the route towards the direct integration of laser-cooled atomic ensembles within fiber networks, an important prerequisite for large scale quantum communication schemes. Moreover, it is ideally suited to the realization of hybrid quantum systems that combine atoms with, e.g., solid state quantum devices. Finally, the use of nanofibers for atom trapping allows one to straightforwardly realize interesting trapping geometries which are not easily accessible w! ith freely propagating laser beams.

## 34. The 2D AKLT state is universal for measurement-based quantum computation

Robert Raussendorf, University of British Columbia

(Session 12 : Sunday from 11:00am--11:30am)

*Abstract.* We demonstrate that the two-dimensional AKLT state on a honeycomb lattice is a universal resource for measurement-based quantum computation [1]. Our argument proceeds by reduction of the AKLT state to a 2D cluster state, which is already known to be universal, and consists of two steps. First, we devise a local POVM by which the AKLT state is mapped to a random planar graph state. Second, we show numerically that the connectivity properties of these random graphs are governed by percolation, and that typical graphs are in the connected phase. The corresponding graph states can then be transformed to 2D cluster states by standard techniques. Joint work with Tzu-Chieh Wei and Ian Affleck. An analogous result has been obtained by A. Miyake in [2]. [1] TC Wei, I. Affleck and R.Raussendorf, arXiv:1009.2840, [2] A. Miyake, arXiv:1009.3491

## 35. Quantum Darwinism in an Everyday Environment: Huge Redundancy in Scattered Photons

Jess Riedel, Los Alamos National Laboratory

(Session 10c : Saturday from 4:30pm-5:00pm)

*Abstract.* We study quantum Darwinism---the redundant recording of information about the preferred states of a decohering system by its environment---for an object illuminated by a blackbody. In the cases of point-source, small disk, and isotropic illumination, we calculate the quantum mutual information between the object and its photon environment. We demonstrate that this realistic model exhibits fast and extensive proliferation of information about the object into the environment and results in redundancies orders of magnitude larger than the exactly soluble models considered to date. We also demonstrate a reduced ability to create records as initial environmental mixedness increases, in agreement with previous studies.

## 36. Quantum tomography of the full hyperfine manifold of atomic spins via continuous measurement on an ensemble

Carlos Riofrio, University of New Mexico

(Session 3 : Friday from 9:45am-10:15am)

*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)). In this talk, we present a detailed review of the quantum tomographic algorithm developed by Silberfarb et al. (PRL 95, 030402 (2005)), and study its application to controlling large spin ensembles. In particular, we show reconstruction of states stored in the 16 dimensional ground-electronic hyperfine manifolds (F=3, F=4) of an ensemble of 133Cs atoms controlled by microwaves and radio-frequency magnetic fields and discuss our efforts in the undergoing experimental implementation.

## 37. Towards multi-qubit computing with Rydberg blockade

Mark Saffman, University of Wisconsin Madison

(Session 3 : Friday from 9:15am-9:45am)

*Abstract.* I will summarize recent progress in Rydberg blockade mediated quantum gates and then discuss approaches to developing multi-qubit neutral atom processors. Emphasis wil be placed on multi-qubit gate protocols, and the use of ensemble qubits for single atom loading, and efficient atom-light quantum interfaces.

## 38. An Improved Query for the Hidden Subgroup Problem

Asif Shakeel, University of California at San Diego

(Session 10b : Saturday from 5:30pm-6:00pm)

*Abstract.* An equal superposition query with |0> in the response register is used in the "standard method" of single-query algorithms for the Hidden Subgroup Problem (HSP). Here we introduce a different query, the character query, a generalization of the well-known phase kickback trick. This query maximizes the success probability of subgroup identification under a uniform prior, for the HSP in which the oracle functions take values in a finite abelian group. We then apply our results to the case when the subgroups are drawn from a set of conjugate subgroups and obtain a success probability greater than that found by Moore and Russell.

## 39. Quantum-based Measurements with Superconducting Circuits

Raymond Simmonds, National Institute of Standards and Technology

(Session 1 : Thursday from 4:00pm-4:45pm)

*Abstract.* Over the last decade, superconducting circuits have shown rapid progress in being implemented for quantum-based measurements. This includes the advent of superconducting qubits, high quality-factor resonant electromagnetic cavities, and high-Q mechanical resonators. Combinations of these circuit elements could lead to a quantum information processor, the ability to simulate quantum systems, or quantum-limited measurements. I will discuss efforts at NIST to develop these circuit elements and describe some of our recent experimental results.

## 40. Multi-qubit compensation sequences

Yu Tomita, Georgia Institute of Technology

(Session 10a : Saturday from 5:30pm-6:00pm)

*Abstract.* We discuss our recent work on the multi-qubit compensation sequences [Tomita et al., New J. Phys. 12, 015002 (2010)]. The Hamiltonian control of n qubits requires precision control of both the strength and timing of interactions. Compensation pulses relax the precision requirements by reducing unknown but systematic errors. Using composite pulse techniques designed for single qubits, we show that systematic errors for n-qubit systems can be corrected to arbitrary accuracy given either two non-commuting control Hamiltonians with identical systematic errors or one error-free control Hamiltonian. We also examine composite pulses in the context of quantum computers controlled by two-qubit interactions. For quantum computers based on the XY interaction, single-qubit composite pulse sequences naturally correct systematic errors. For quantum computers based on the Heisenberg or exchange interaction, the composite pulse sequences reduce the logical single-qubit gate errors but increase the errors for logical two-qubit gates.

## 41. Fundamental Quantum Limit to Waveform Estimation

Mankei Tsang, University of New Mexico

(Session 5 : Friday from 4:45pm-5:15pm)

*Abstract.* Quantum noise is now routinely observed in atomic, optical, electrical, and mechanical systems and will impose severe limits to the precision of sensors in the near future. Atomic magnetometers limited by quantum noise have been demonstrated, while optomechanical force sensors, including the gravitational wave detector in LIGO, are expected to reach the so-called standard quantum limit (SQL) within the next few years. Such technological advances have motivated renewed interest in the theoretical quantum limits to sensing. Recent work on such quantum limits focuses on the relatively simple problem of parameter estimation, but in realistic applications, the unknown signal of interest, such as a gravitational wave or a magnetic field, is rarely a parameter constant in time but a continuously varying waveform, in which case no rigorous quantum limit has yet been established. Here we present a rigorous limit to the error of waveform estimation in quantum sensing in the form of a quantum Cramer-Rao bound (QCRB). Unlike the one first derived by Helstrom for parameter estimation, our QCRB shows how the prior information crucial for waveform estimation can be taken into account and is more directly applicable to force sensing and magnetometry applications. As an important example, we calculate the QCRB for optomechanical force sensing, show that the QCRB is in general below the SQL, and demonstrate that the QCRB can be achieved by applying a quantum estimation technique called quantum smoothing to the observations and a quantum noise cancellation technique to the experimental setup, thus proving the optimality of these techniques. Being a rigorously proven and demonstrably achievable limit, our QCRB supercedes the heuristic SQL as the fundamental quantum limit to force sensing. We are thus able to relate the modern theoretical program of quantum metrology, which has so far relied on toy parameter-estimation models, to the classic but more practical studies of continuous quantum measurement theory initiated by Braginsky and others.

## 42. Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function

Wim van Dam, University of California, Santa Barbara

(Session 12 : Sunday from 11:30am-12:00pm)

*Abstract.* This work analyzes the non-stabilizer states and non-stabilizer operations that must be present in any quantum circuit if it is to perform better-than-classical quantum computation. That such a non-stabilizer resource is necessary for universal quantum computation is a consequence of the Gottesman-Knill theorem. In particular, we find states and operations that are maximally non-stabilizer in the sense that they require the highest amount of depolarizing noise to make them become stabilizer states and operations respectively. In doing so we make novel use of a theoretical construction known as the discrete Wigner function (DWF). We find d-level (qudit) states whose negativity (in terms of the DWF quasiprobabilites) is maximal, answering a conjecture of Wootters. We find non-Clifford gates, acting on d-level systems, which require very high amounts (rapidly approaching 100 percent as dimension, d, increases) of depolarizing noise to become decomposable in terms of Clifford gates. In previous literature the convex hull of Clifford gates was called the Clifford polytope. This work describes the qudit version of the Clifford polytope, and bounding inequalities that describe this object are derived using a simple argument. Our results have implications for the question of qudit magic state distillation.

## 43. Faithful squashed entanglement with applications to separability testing and quantum complexity

Jon Yard, Los Alamos National Laboratory

(Session 4 : Friday from 2:30pm-3:00pm)

*Abstract.* Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this talk, I will present a new lower bound for squashed entanglement in terms of the distance to the set of separable states, along with several applications. I will first show how this implies that squashed entanglement is a faithful measure of entanglement, meaning it is positive on a state if and only if it is entangled. The bound also implies a new de Finetti-type bound for quantum states which, in turn, implies a quasipolynomial-time algorithm for deciding if a density matrix is entangled. The best known algorithms for this problem had been exponential. I will also show several applications in quantum complexity theory by giving new multi-prover characterizations of QMA, which is a quantum analog of NP. The bound follows from a sequence of new results about entanglement measures, whose proofs utilize some recent results in quantum information theory. These include an operational interpretation of quantum conditional mutual information as the optimal communication rate in quantum state redistribution, and an operational interpretation of the regularized relative entropy of entanglement as the optimal error rate for hypothesis testing with one-sided error. Another crucial aspect of the proof is the utilization of operationally-motivated norms on bipartite states that quantify distinguishability under local operations and classical communication. This is joint work (arXiv:1010.1750, 1011.2751) with Fernando Brandão and Matthias Christandl.