2012 Talk Abstracts
Jonas Anderson, University of New Mexico
Abstract. The discovery of quantum error correction and fault-tolerance were major theoretical breakthroughs on the road towards building a full-fledged quantum computer. Since then thresholds have increased and geometric constraints on the underlying architecture have been added. Homological stabilizer codes provide a method for constructing stabilizer codes constrained to a 2D plane. In this talk I will define and proceed to classify all 2D homological stabilizer codes. I will show that Kitaev's toric code and the topological color codes arise naturally in this classification. I will finally show, up to a set of equivalence relations, that these are the only 2D homological stabilizer codes.
Brian Anderson, University of Arizona
Abstract. Aaron Smith, Brian E. Anderson, Hector Sosa Martinez, Poul Jessen Center for Quantum Information and Control (CQuIC), College of Optical Science and Department of Physics, University of Arizona Carlos Riofrio, Ivan H. Deutsch Center for Quantum Information and Control (CQuIC), Department of Physics and Astronomy, University of New Mexico Quantum systems with Hilbert space dimension greater than two (qudits) provide an alternative to qubits as carriers of quantum information, and may prove advantageous for quantum information tasks if good laboratory tools for qudit manipulation and readout can be developed. We have successfully implemented a protocol for arbitrary quantum state-to-state mapping in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, using only static, radio frequency (rf) and microwave magnetic fields to drive the atomic evolution. This system is controllable given rf and microwave fields with constant amplitude and frequency, and piecewise constant phase modulation. Control waveforms (rf and microwave phases versus time) are found by numerical optimization, and can be designed to work well in the presence of errors in the driving and background magnetic fields. Experimentally, we achieve an average state mapping fidelity of 99% for a sample of randomly chosen target states. To perform quantum state tomography, we drive an ensemble of identically prepared atoms with phase modulated rf and microwave magnetic fields, and simultaneously probe them by coupling an atomic spin observable to the polarization of a near-resonant optical probe field. A measurement of the probe polarization then yields an informationally complete measurement record that can be inverted to obtain an estimate of the unknown quantum state. We have reconstructed the full density matrix for a set of randomly chosen test states, using computer algorithms based either on least squares fitting or compressed sensing. The latter approach reconstructs our test states with an average fidelity above 90%, limited primarily by errors in applied drive fields.
Sergio Boixo, Information Sciences Institute at the University of Southern California
Abstract. A D-Wave One quantum optimizer has been installed at the newly created USC-Lockheed Martin Quantum Computing Center. This chip implements quantum annealing at finite temperature as a computational resource, with 90 working qubits. Quantum annealing is a particularly simple branch of adiabatic quantum computation. We report work in progress on exploring practical applications of quantum annealing in general, and this chip in particular. We will also discuss entanglement tests with realistic numerical simulations of the physical devices implemented in the chip. Some of this work is done in collaboration with Aspuru-Guzik's group at Harvard, and D-Wave.
Kamil Bradler, School of Computer Science, McGill University
Abstract. We construct a class of supersymmetric entangled states which is used as a nonlocal resource in the CHSH game. If the Grassmann-valued degrees of freedom are accessible to measurement using the proposed measurement model then the entangled state is more nonlocal then a maximally entangled two-qubit state. We show that the winning probability reaches at least pwin=0.8641 which is greater than pwin=cos2(pi/8)=0.8536. This value corresponds to an expected value known as Tsirelsons bound and no ordinary quantum-mechanical entangled state can perform better.
Constantin Brif, Sandia National Laboratories
Abstract. External controls are necessary to enact quantum logic operations, and the inevitable control noise will result in gate errors in a realistic quantum circuit. We investigate the robustness of quantum gates to random noise in an optimal control field, by utilizing properties of the quantum control landscape that relates the physical objective (in the present case, the quantum gate fidelity) to the applied controls. An approximate result obtained for the statistical expectation value of the gate fidelity in the weak noise regime is shown to be in excellent agreement with direct Monte Carlo sampling over noise process realizations for fidelity values relevant for practical quantum information processing. Using this approximate result, we demonstrate that maximizing the robustness to additive/multiplicative white noise is equivalent to minimizing the total control time/fluence. Also, a genetic optimization algorithm is used to identify controls with improved robustness to colored noise.
Antoine Browaeys, Institut Optique, CNRS
Abstract. When two quantum systems interact strongly, their simultaneous excitation by the same driving pulse may be forbidden: this is called blockade of excitation. Recently, extensive studies have been devoted to the Rydberg blockade between neutral atoms, which appears due to the interaction induced by their large dipole moments when they are in Rydberg states. This talk will describe our demonstration of the Rydberg blockade between two atoms individually trapped in optical tweezers at a distance of 4 micrometers. The rubidium 87 atoms are prepared in the state |↑〉 = |F =2, M=2〉, and subsequently excited to the Rydberg state 58d3/2, |r〉, by a two-photon transition. A consequence of the blockade mechanism is that the atoms are excited in an entangled state of the form (|r,↑〉 + |↑,r〉) / √2. The signature of the production of this state is the enhanced Rabi frequency of the oscillation of the probability to excite only one of the two atoms, with respect to the Rabi frequency of the excitation of one atom when it is alone. We have then mapped the Rydberg state |r〉 onto a second ground state |↓〉 = |F =1, M=1〉 to generate the Bell state (|↓,↑〉 + |↑,↓〉) / √2. We analyse the amount of entanglement by global Raman rotations on the two atoms. We have measured a fidelity of the two-atom state produced of 0.74. Finally the talk will report our progress on the building of a new setup aiming at entangling a larger number of atoms.
Kenton Brown, Georgia Tech Research Institute
From the earliest days of the field of quantum information, trapped atomic ions have had great potential as qubits. Trapped-ion experiments have demonstrated the individual ingredients believed necessary for scalable quantum information processing, and, for small numbers of ions, many of these ingredients have been combined within the same experimental system. Scaling the capabilities of such test-bed systems to larger numbers of qubits will require a higher level of integration between traps, electronics, optics, and control systems than has been achieved to date. Moreover, calibrating and controlling such a complex system with the necessary speed and accuracy will demand a far greater degree of automation than could be achieved through human intervention.
To explore these challenges, the Quantum Information Systems Group at GTRI has microfabricated several ion traps incorporating 40+ control electrodes, including a long linear trap, a trap with a curved mirror microfabricated onto its surface, an X-junction trap, and a trap with integrated microwave lines. In the linear traps we have loaded long chains with more than 20 resolved ions, while the mirror trap enhanced the collection of ion fluorescence by a factor of 1.8. The junction and microwave traps, when fully tested, should allow us to reorder ions into an arbitrary linear configuration and to perform fast qubit rotations, respectively. Successful operation of these traps necessitates accurate and precise modeling of their electromagnetic properties, so we have developed an in-house method-of-moments simulation package, capable of handling millions of elements, which we use to derive an accurate basis set of micromotion compensation potentials. We are planning an experiment to incorporate in-vacuum DAC electronics alongside a trap chip, all mounted on a single compact circuit board within the vacuum chamber. Finally, we have developed a machine language, known as ?OPCODEs?, that translates high-level schedules directly into experimental operations for our ion traps. The success of OPCODEs relies on automated calibration and control of trap parameters, accurate modeling of the potentials required for compensation, and automated detection of ion positions. I will present our most recent experimental results in these areas.
Orest Bucicovschi, University of California San Diego
Abstract. We investigate the set of achievable values for the three pairwise concurrences of a state of three qubits. We show that it is the intersection of the convex hull of the Roman Steiner surface with the positive octant in the space of concurrences, first for X-states, then for any pure state of three qubits. We further show that the allowable set is the solution of a linear matrix inequality involving three other entanglement invariants. We further consider the extension of this result to mixed states and n qubits, n>=3.
Chris Cesare, Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico
Abstract. Several schemes have been proposed in the literature for performing quantum computations using defects in topological codes. In the color codes, there are three schemes for storing qubits using defects: using single defects tethered to boundaries, using two defects tethered to one another, or using three defects tethered to each other. The three defect approach stands apart as the only known way to retain the transversality property of certain color code gates. As such, one might ask whether there is any relationship between this transversality-preserving encoding and the others, and if there exists a way to convert between them. We demonstrate this relationship by presenting such a method of conversion.
Robert Cook, Center for Quantum Information and Control (CQuIC) and Department of Physics and Astronomy, University of New Mexico
Abstract. Quantum state reconstruction is a fundamental task in quantum information science. The standard approach employs many projective measurements on a series of identically prepared systems in order to collect sufficient statistics of an informationally complete set of observables. An alternative procedure is to reconstruct quantum state by performing weak continuous measurement collectively on an ensemble, while simultaneously applying time varying controls[1,2]. For known dynamics, the measurement history determines the initial state. In current implementations the shot noise of the probe dominates over projection noise so that measurement-induced backaction is negligible. We generalize this to the regime where quantum backaction can play a significant role, even for small numbers of particles. Using the framework of quantum filtering theory, we model the reconstruction of the state of a qubit through collective spin measurement via the Faraday interaction and magnetic field controls, and develop a maximum-likelihood estimate.  A. Silberfarb and I. H. Deutsch, Phys. Rev. Lett. 95, 030402 (2005).  C.A. Riofrio et. al., J. Phys. B: At. Mol. Opt. Phys. 44, 154007 (2011)
Luiz Davidovich, Universidade Federal do Rio de Janeiro
Abstract. The estimation of parameters characterizing dynamical processes is central for science and technology. The estimation error decreases with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). For independent probes, it scales as one over the square root of N. Quantum strategies may improve the precision for noiseless processes, so that it scales as 1/N. For noisy processes, it is not known in general if and when this improvement can be achieved. This talk will introduce some basic aspects of quantum metrology, and present a recent proposal [1,2] of a general framework for obtaining attainable and useful lower bounds for the ultimate limit of precision in noisy systems. This method is applied to estimate precision bounds, which are independent of the initial state of the probes, for lossy optical interferometry and atomic spectroscopy in the presence of dephasing. These bounds capture the main features of the transition from the 1/N to the one over square root of N behavior as N increases. References  B. M. Escher, R. L. de Matos Filho, and L. Davidovich, General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology, Nature Physics vol. 7, 406 (2011).  B. M. Escher, R. L. de Matos Filho, and L. Davidovich, Quantum metrology for noisy systems, Brazilian Journal of Physics, vol. 41, 229 (2011).
Steven Flammia, University of Washington
Abstract. We describe a simple method for certifying that an experimental device prepares a desired quantum state rho. Our method is applicable to any pure state rho, and it provides an estimate of the fidelity between rho and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels. This is joint work with Yi-Kai Liu.
13. Optimal hybrid quantum secret sharing schemes via stabilizer codes and twirling of symplectic structures
Vlad Gheorghiu, Institute for Quantum Information Sciences and Department of Mathematics and Statistics, University of Calgary
Abstract. As recently shown in [quant-ph/1108.5541], any quantum error-correcting code can be converted into a perfect "hybrid" quantum secret sharing scheme by allowing the sharing of extra classical bits between the dealer and the players. An advantage of this scheme is that it allows the players' quantum shares to be of smaller dimension than the dimension of the encoded secret, which is impossible for regular perfect quantum secret sharing protocols. Whenever the underlying quantum error correcting code is a stabilizer code (this being the case for the vast majority of known quantum error-correcting codes), I provide a general scheme of reducing the amount of classical communication required, then prove that my scheme is optimal for the stabilizer code being used. The optimality proof is based on the fact that the correlations between the dealer and the players can be fully described by an "information group" [Phys. Rev. A 81, 032326 (2010)]; the symplectic structure of the information group effectively gives the minimum number of classical bits required. Finally I provide an explicit protocol that achieves this minimum by employing the notion of "twirling" (or scrambling) the information group. The results are general and valid for any stabilizer code. I will illustrate the results by simple examples.
Gilad Gour, Institute for Quantum Information Science
Abstract. In this talk I will show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the global additivity conjecture, makes this result somewhat surprising. In particular, it indicates that the non-additivity of the minimum entropy output is related to a global effect of quantum channels. I will end with few related open problems.
Zhang Jiang, University of New Mexico
Abstract. While unitary transformations are used to describe state evolutions in closed quantum systems, the formalism of quantum operations is the more general approach for open systems. A valid quantum operation has to be completely positive, i.e., the output state for any physical input state, even those entangled with a third party, should also be physical. Often a quantum operation can be described by a Kraus representation. An alternative representation is by a measurement model or ancilla model, which is also called a Stinespring dilation by mathematicians. In an ancilla model, a quantum operation is realized by tracing out the ancilla after a joint unitary is applied on the primary system and the ancilla. Here we answer the following question: given an ancilla model with a particular joint unitary, what are the conditions on the joint unitary so that the ancilla state must be physical, i.e., a density operator, in order that the measurement model gives rise to a valid quantum operation.
Thaddeus Ladd, HRL Laboratories, LLC
Abstract. Electrically defined silicon-based qubits are expected to show improved quantum memory characteristics in comparison to GaAs-based devices due to reduced hyperfine interactions with nuclear spins. Silicon-based qubit devices have proved more challenging to build than their GaAs-based counterparts, but recently several groups have reported substantial progress in single-qubit initialization, measurement, and coherent operation. I will present the recent observation of coherent oscillations in a spin singlet-triplet device built in a Si/SiGe heterostructure, and a measurement confirming that the dephasing time T2* is nearly two orders of magnitude longer than in comparable GaAs devices due to reduced hyperfine effects. Although complete SU(2) control is not yet demonstrated, fully controllable qubits may be enabled using exchange-only operations in Decoherence Free Subsystems (DFS). I will discuss some new control optimizations of the DFS system. Sponsored by the United States Department of Defense. Approved for public release, distribution unlimited.
17. Learning in a variational class of states: efficient tomography method for Matrix Product and Multi Scale Entangled states
Olivier Landon-Cardinal, Université de Sherbrooke
Abstract. Quantum state tomography is essential to benchmark quantum devices but standard techniques fundamentally require a number of experiments and a post-processing effort that scales exponentially with the number of particles. However, by taking advantage of efficient representations of quantum states, such as matrix product states (MPS) or multi-scale entanglement renormalisation ansatz (MERA), we can do exponentially better. Indeed, since those variational classes of states are described by a few parameters, identifying the state amounts to learning those parameters. We describe a method for reconstructing a wide range of states from a small number of efficiently-implementable measurements and fast post-processing, namely all states well-approximated by MPS or MERA states. These variational classes are known to faithfully approximate ground states of local Hamiltonians in 1 dimension. Examples of interest include GHZ, W and cluster states. Our method prevents the build-up of errors from both numerical and experimental imperfections and contains a built-in certification procedure. These ideas extend to learning continuous-time quantum dynamics that are described by local Hamiltonians or Lindbladians. This covers work presented in da Silva, Landon-Cardinal and Poulin, PRL 107, 210404 (2011). It complements the Monte Carlo certification scheme presented in the same paper and independently derived by Flammia and Liu in PRL 106, 230501 (2011). Learning complements the work on certification and is of independent interest.
Jae Hoon Lee, University of Arizona
Abstract. We demonstrate a resonance imaging protocol for optical lattices that enables robust preparation and single qubit addressing of atoms with sub-wavelength resolution. Our setup consists of a 3D optical lattice, and a superimposed long-period (66 lattice sites) 1D ?superlattice? that creates a position dependent shift of the transition frequency between two spin states in the ground manifold. We show that isolated planes of atoms can be prepared by flipping resonant spins with a microwave pulse and removing the remaining non-resonant spins. A second microwave pulses in a translated superlattice subsequently allow us to image these planes with a resolution better than 200 nm. We further show that composite pulse techniques can reduce the sensitivity of the addressing to small variations in the relative position and intensity of the lattices. This robustness is achieved by applying numerically optimized, phase modulated pulses that have a constant atomic response within the region of error. For example, we apply a composite microwave pulse that flips the spin with near unit fidelity for all atoms that are positioned within a target spatial region (e.g., one lattice site), while conserving the spin of the atoms outside of that region (e.g., neighboring lattice sites). Furthermore, with this technique, we show that we are able to implement independent unitaries (single qubit quantum gates) across several adjacent lattice sites with a single composite pulse. Finally, we perform randomized benchmarking, similar to that done by Olmschenk et al., to measure the error per randomized computational gate using composite pulses.
Matteo Mariantoni, Department of Physics and California NanoSystems Institute, University of California, Santa Barbara
Abstract. Superconducting quantum circuits have made significant advances over the past decade, allowing more complex and integrated circuits that perform with good fidelity. We have recently implemented a machine comprising seven quantum channels, with three superconducting resonators, two phase qubits, and two zeroing registers. I will explain the design and operation of this machine, first showing how a single microwave photon |1> can be prepared in one resonator and coherently transferred between the three resonators. I will also show how more exotic states such as double photon states |2> and superposition states |0>+|1> can be shuffled among the resonators as well . I will then demonstrate how this machine can be used as the quantum-mechanical analog of the von Neumann computer architecture, which for a classical computer comprises a central processing unit and a memory holding both instructions and data. The quantum version comprises a quantum central processing unit (quCPU) that exchanges data with a quantum random-access memory (quRAM) integrated on one chip, with instructions stored on a classical computer. I will also present a proof-of-concept demonstration of a code that involves all seven quantum elements: (1), Preparing an entangled state in the quCPU, (2), writing it to the quRAM, (3), preparing a second state in the quCPU, (4), zeroing it, and, (5), reading out the first state stored in the quRAM . Finally, I will demonstrate that the quantum von Neumann machine provides one unit cell of a two-dimensional qubit-resonator array that can be used for surface code quantum computing. This will allow the realization of a scalable, fault-tolerant quantum processor with the most forgiving error rates to date.  M. Mariantoni et al., Nature Physics 7, 287-293 (2011);  M. Mariantoni et al., Science 334, 61-65 (2011). Matteo Mariantoni acknowledges support from an Elings Postdoctoral Fellowship. This work was supported by IARPA under ARO award W911NF-08-1-0336 and W911NF-09-1-0375.
Iman Marvian, Perimeter Institute, Institute for quantum computing
Abstract. Information theory provides a novel approach to the study of the consequences of symmetric dynamics which goes far beyond the traditional conservation laws that are derived from Noether's theorem. For one, these conservation laws are not applicable to dissipative and open systems. Moreover, even in the case of closed system dynamics, the conservation laws do not capture all the consequences of symmetry if the state of the system is not pure, as we will show. Using the information theoretic approach to this problem, we introduce new quantities called asymmetry monotones, such that if the system is closed they are constant of the motion and otherwise, if the system is open, they are always non-increasing. We also explain how different results in quantum information theory can have non-trivial consequences about the symmetric dynamics of quantum systems.
Adam Meier, National Institute of Standards and Technology
Abstract. Randomized benchmarking is a procedure that extracts a "typical" error probability for an experimental quantum computer. This number describes the failure rate of a typical operation in the middle of a long computation and is a worthwhile figure of merit for quantum control demonstrations. I will present a practical, systematic approach to randomized benchmarking of multiple qubits using a recent two-qubit ion trap experiment at NIST as an example. I will also discuss the ways the basic procedure has been extended to reveal information about individual gates.
Morgan Mitchell, ICFO - Institute of Photonic Sciences
Abstract. We describe experiments with highly non-classical states (heralded single photons and NooN states) in interaction with atomic ensembles. Our approach uses ultra-bright cavity-enhanced down-conversion and ultra-narrowband ``interaction-free measurement'' filters. With these we demonstrate heralded single photons that are at least 94 % atom-resonant, with multi-photon contamination below 4%. Also 90% fidelity NooN states, and sensitivity beyond the standard quantum limit in a near-resonant Faraday rotation magnetometer. The potential for highly multi-partite, atom-resonant entanglement using these techniques will also be discussed.
Leigh Norris, University of New Mexico
Abstract. Spin squeezed states have applications in metrology and quantum information processing. While there has been significant progress in producing spin squeezed states and understanding their properties, most spin squeezing research to date has focused on ensembles of qubit spins. We explore squeezed state production in an ensemble of spin f>1/2 alkali atoms (qudits). Collective interactions are achieved through coherent quantum feedback of a laser probe, interacting with the ensemble through the Faraday interaction. This process can be enhanced through further control of the atomic qudits. We control the internal atomic state both before and after the collective interaction. Initial preparation increases the collective squeezing parameter through enhancement of resolvable quantum fluctuations. Qudit control can then be used to map entanglement created by the collective interaction to different pseudo-spin subspaces where they are metrologically useful, e.g., the clock transition or the stretched state for magnetometry. In the latter case, additional internal control can be used to squeeze the individual atoms, further enhancing the total squeezing in a multiplicative manner. The actual squeezing will depend on a balance between the enhanced coupling and decoherence. These considerations highlight the unique capabilities of our platform: we are able to transfer coherences and correlations between subspaces and integrate control tools to explore a wider variety of nonclassical states, with ultimate application in sensors or other quantum information processors.
Jeremy OBrien, University of Bristol
(Session 0: from 1:45pm-2:30pm)
Abstract. Integrated quantum photonics K Aungskunsiri, D Bonneau, J Carolan, E Engin, D Fry, J Hadden, P Kalasuwan, J Kennard, S Knauer, T Lawson, L Marseglia, E Martin-Lopez, J Meinecke, G Mendoza, A Peruzzo, K Poulios, N Russell, A Santamato, P Shadbolt, J Silverstone, A Stanley-Clark, M Halder, J Harrison, D Ho, P Jiang, A Laing, M Lobino, J Matthews, B Patton, A Politi, M Rodas Verde, P Zhang, X-Q Zhou, M Cryan, J Rarity, M Thompson, S Yu, J O?Brien & non-Bristol collaborators Centre for Quantum Photonics, H.H. Wills Physics Laboratory & Department of Electrical and Electronic Engineering, University of Bristol www.phy.bris.ac.uk/groups/cqp Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing , photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2,3]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. ), measurement (eg. ) and other quantum technologies . However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturization and scalability . Here we report high-fidelity silica-on-silicon integrated optical realizations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate . We have demonstrated controlled manipulation of up to four photons on-chip, including high-fidelity single qubit operations, using a lithographically patterned resistive phase shifter . We have used this architecture to implement a small-scale compiled version of Shor?s quantum factoring algorithm , demonstrated heralded generation of tunable four photon entangled states from a six photon input , a reconfigurable two-qubit circuit , and combined waveguide photonic circuits with superconducting single photon detectors . We describe complex quantum interference behavior in multi-mode interference devices with up to eight inputs and outputs , and quantum walks of correlated particles in arrays of coupled waveguides . Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [16,17], diamond [18,19] and nonlinear [20,21] photon sources, fast manipulation of single photons .  T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. OBrien, Nature 464, 45 (2010).  J. L. O?Brien, Science 318, 1567 (2007).  R. Okamoto, J. L. O?Brien, H. F. Hofmann and S. Takeuchi Proc. Natl. Acad. Sci. 108, 10067 (2011)  T. Nagata, R. Okamoto, J. L. O?Brien, K. Sasaki, and S. Takeuchi, Science 316, 726 (2007).  R. Okamoto, J. L. O?Brien, H. F. Hofmann, T. Nagata, K. Sasaki, S. Takeuchi, Science 323, 483 (2009).  J. L. O?Brien, A. Furusawa, and J.Vuckovic, Nature Photon. 3, 687 (2009).  A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O?Brien, Science 320, 646 (2008).  A. Laing, A. Peruzzo, A. Politi, M. R. Verde, M. Halder, T. C. Ralph, M. G. Thompson, and J. L. O?Brien, Appl. Phys. Lett. 97, 211109 (2010)  J. C. F. Matthews, A. Politi, A. Stefanov, and J. L. O?Brien, Nature Photon. 3, 346 (2009).  A. Politi, J. C. F. Matthews, and J. L. O?Brien, Science 325, 1221 (2009).  J. C. F. Matthews, A. Peruzzo, D. Bonneau, and J. L. O?Brien, Phys. Rev. Lett. 107, 163602 (2011)  P. J. Shadbolt, M. R. Verde, A. Peruzzo, A. Politi, A. Laing, M. Lobino, J. C. F. Matthews, J. L. O'Brien, Nature Photon. doi:10.1038/nphoton.2011.283  C. M. Natarajan, A. Peruzzo, S. Miki, M. Sasaki, Z. Wang, B. Baek, S. Nam, R. H. Hadfield, and J. L. O?Brien, Appl. Phys. Lett. 96, 211101 (2010).  A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O?Brien, Nature Comm. 2, 224 (2011)  A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Worhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. O?Brien, Science 329, 1500 (2010)  A. Laing, T. Rudolph, and J. L. O?Brien, Phys. Rev. Lett. 102, 160502 (2009).  X-Q Zhou, TC Ralph, P Kalasuwan, M Zhang, A Peruzzo, BP Lanyon, and JL O?Brien, Nature Comm. 2 413 2011  J. P. Hadden, J. P. Harrison, A. C. Stanley-Clarke, L. Marseglia, Y.-L. D. Ho, B. R. Patton, J. L. OBrien, and J. G. Rarity, Appl. Phys. Lett. 97, 241901 (2010)  L. Marseglia, J. P. Hadden, A. C. Stanley-Clarke, J. P. Harrison, B. Patton, Y.-L. D. Ho, B. Naydenov, F. Jelezko, J. Meijer, P. R. Dolan, J. M. Smith, J. G. Rarity, J. L. O'Brien, Appl. Phys. Lett. 98, 133107 (2011)  C. Xiong, et al. Appl. Phys. Lett. 98, 051101 (2011)  M. Lobino, et al, Appl. Phys. Lett. 99, 081110 (2011)  D Bonneau, M Lobino, P Jiang, CM Natarajan, MG Tanner, RH Hadfield, SN Dorenbos, V Zwiller, MG Thompson, JL O'Brien Phys. Rev. Lett.; arXiv:1107.3476
L. Paul Parazzoli, Sandia National Laboratories
Abstract. We are developing, both theoretically and experimentally, a neutral atom qubit approach to adiabatic quantum computing (AQC). It has been shown in that neutral atoms trapped in optical far off-resonance traps (FORTs) can be used for two-qubit gates using interactions mediated by electric-dipole coupling of a coherently excited Rydberg state. A similar neutral atom system is attractive for this work due to the long-term coherence of the qubit ground states, the potential of multi-dimensional arrays of qubits in FORT traps and the potential for strong, tunable interactions via Rydberg-dressed atoms. If these arrays can be designed to encode a desirable computation into the system Hamiltonian one could use these tunable interactions along with single-qubit rotations to perform an AQC. Taking full advantage of Sandia?s microfabricated diffractive optical elements (DOEs), we plan to implement such an array of traps and use Rydberg-dressed atoms to provide a controlled atom-atom interaction in atomic cesium. We forecast that these DOEs can provide the functions of trapping, single-qubit control and state readout resulting in an important engineering stride for quantum computation with neutral atoms. We will develop this experimental capability to generate a two-qubit adiabatic evolution aimed specifically toward demonstrating the twoqubit quadratic unconstrained binary optimization (QUBO) routine. We are studying the two-qubit QUBO problem to test the immunity of AQC to noise processes in the control interactions as well as dissipation mechanisms associated with the trapping. We are developing our theoretical and experimental capabilities through key collaborations with The University of Wisconsin, NIST and The University of New Mexico.
Heather Partner, Sandia National Labs / University of New Mexico
Abstract. We are developing a low-power, high-stability miniature atomic frequency standard based on trapped 171Yb+ ions.? The ions are buffer-gas cooled and held in a linear quadrupole trap that is integrated into a sealed 10 cm^3, getter-pumped vacuum package, and interrogated on the 12.6 GHz hyperfine transition. We hope to achieve a long-term fractional frequency stability of 10^-14 with this miniature clock. To achieve this exceptional long-term stability, the sensitivity of the clock frequency to magnetic fields must be minimized. Because the ?clock? transition frequency of 171Yb+ depends quadratically on the magnetic field, it is advantageous to operate at a bias field of ~100 mG or below. However, in small-sized ion traps, magnetic field gradients can prevent operation at low fields because of broadening of the clock resonance. This broadening occurs due to the secular motion of the ions in the trap, which in interaction with a spatially varying magnetic field can induce transitions among the Zeeman sublevels of the upper ground state when the Zeeman frequency is close to the secular frequency of the trap, creating a dephasing effect.? Understanding this mechanism for a particular trap geometry as well as taking steps to eliminate background gradients allows us to operate the clock with a much lower bias field in a region below this secular frequency resonance, where we can both minimize broadening and reduce our clock?s sensitivity to magnetic field fluctuations while reducing the overall power required to run the clock.? We have studied these effects in several traps and will discuss these results as well as clock performance. Peter Schwindt, Yuan-Yu Jau, Michael Descour, Lu Fang, Adrian Casias, Ken Wojciechowski, Roy Olsson, Darwin Serkland, Ron Manginell, Matthew Moorman, Robert Boye, John Prestage, Nan Yu, Robert Lutwak, Sheng Chang
Gerardo Paz-Silva, University of Southern California
Abstract. We study the interplay of two well-known open-loop decoherence suppression methods, the Quantum Zeno effect and Dynamical decoupling, with quantum error correction codes. For the first part, the quantum Zeno effect case, we analyze the decoherence suppression induced only by the weak (non-selective) syndrome measurements in every error correction round, i.e. multiple rounds of error correction without the recovery step. We show that there is indeed a suppression effect despite the absence of recovery operations. For the second part, dynamical decoupling, we discuss the use of elements of the code as pulses and show that they provide an advantage over brute force multiqubit dynamical decoupling: they not only generate shorter sequences but impose no additional locality constraints on the noise besides the ones demanded by fault-tolerant models.
Jibran Rashid, Institute for Quantum Information Science at the University of Calgary
We approach stronger that quantum correlations with a new perspective. The nonlocal box model (NLB) allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. Rather than considering a hypothetical box resource, we allow the spatially separated parties Alice and Bob, access to a trusted third party Charlie. Charlie is allowed to communicate with Alice and Bob without allowing communication between Alice and Bob. A natural generalization is to consider the case when Alice and Bob utilize quantum states for communicating with Charlie and he communicates back using quantum states as well.
We model Charlie as a quantum nonlocal box, abbreviated qNLB, which takes as input a joint quantum state and outputs a joint quantum state. A priori, such a model may not obey our non-signalling requirement since any unitary UAB not of the form UA⊗UB allows for signalling. It thus may appear that a quantum generalization of the NLB model would always allow for signalling, but this only holds true if we restrict the maps to be unitary. Quantum nonlocal boxes that satisfy the non-signalling requirement and allow for quantum states as output are possible when we drop the requirement of the box being unitary. Such boxes have previously been studied under the notion of causal maps, completely positive trace-preserving maps, and non-signalling operations. Here we initiate a systematic study of such boxes in terms of nonlocality.
Nonlocality distillation occurs if it is possible for Alice and Bob to concentrate the nonlocality in n copies of an imperfect NLB/qNLB to form a stronger NLB/qNLB. Given the apparent limited distillability of NLBs, we propose a new non-adaptive protocol for nonlocality distillation of qNLBs. As our main result, we show that qNLBs exhibit strictly stronger nonlocality distillation than NLBs, for non-adaptive distillation protocols. We prove our main result by setting up a semi-definite programming framework for analyzing non-adaptive protocols for qNLB distillation. We then use this framework to define and give a protocol for qNLB distillation and show that it asymptotically distills the class of correlated quantum nonlocal boxes to the value 3.098, whereas in contrast, the optimal non-adaptive parity protocol for classical correlated nonlocal boxes asymptotically distills to the value 3.0 (Figure 1). The protocol is also proven to be an optimal non-adaptive protocol for 1, 2 and 3 copies of qNLBs by constructing a matching dual solution for the semi-definite program.
A major component of the research on nonlocality can be linked to identifying a set of restrictions that produce physical theories of varying strength in terms of their correlations. From quantum strategies that violate Bell inequalities to the no-signalling principle, information causality, local quantum measurements and macroscopic locality, one of the goals is to obtain a useful understanding of the conditions that imply quantum correlations. These conditions serve as fundamental physical principles that guide the development of physical theories. One attempt to develop our understanding of the limits on nonlocality is via nonlocality distillation protocols.
The class of correlated NLBs are already known to be asymptotically distillable to a perfect NLB. This is only achieved by an adaptive protocol. In our current work we have shown that even if we restrict out attention to non-adaptive protocols, qNLBs offer improved distillation over NLBs. A generalization of our SDP approach that allows for adaptive protocols may reveal a similar improvement for adaptive protocols. This may imply distillability for correlations that are currently not known to be distillable and at the same time an increased understanding of correlations that violate principles such as information causality.
As a consequence of the work nonlocality distillation we propose a two-pronged approach for classifying correlations which are not known to satisfy the principle of macroscopic locality. We provide numerical evidence that correlations with non-trivial marginals which are not known to satisfy the macroscopic locality principle may be distillable even when corresponding correlations with trivial marginals are not. On the flip side, we argue that if reality does allow correlations that violate the principle, then nonlocality distillation could still be utilized to improve the possibility of detecting such a violation in the lab.
29. Quantum Optical Pulse Shaping, Routing, and Frequency Translation by Four-Wave Mixing in Optical Fiber
Michael Raymer, University of Oregon
Abstract. Our collaboration of U Oregon, Bell Labs, and UC San Diego is developing quantum frequency translation (background-free frequency conversion) of quantum states of light by using four-wave mixing in optical fiber. The involvement of two pump pulses at distinct frequencies leads to useful capabilities not present when using single-pump three-wave mixing. It allows pulse reshaping and routing of quantum optical wave packets, including single-photon states. It also allows translating between nearby frequency channels, opening the possibility of quantum-level wavelength-division multiplexing.
Peter Rose, Carleton College
Abstract. We consider the evolution of Fock states |n> of a harmonic oscillator coupled to a Markovian bath. The master equation in the number basis is an infinite number of coupled, first order differential equations which can be solved analytically at any temperature. Using the negative volume of the Wigner function as a metric of "quantumness", we show that in the absence of environmental coupling, quantumness increases with n, but the presence of any environmental interaction causes high-n states to lose their quantum features more rapidly leading to a time-dependent quantumness peak across the eigenstates. Our results are consistent with recent experiments.
Robert Schoelkopf, Yale University
Abstract. By using the unique properties of quantum physics, such as entanglement and superposition, quantum computers are predicted to be vastly more powerful than their classical counterparts for certain tasks. While some technologies, such as NMR and trapped ions, have succeeded in making and manipulating a handful of quantum bits (qubits), they look quite different from a conventional computer, and there are many obstacles to building large-scale processors. At Yale, we use superconducting circuits to make macroscopic, solid-state qubits which are controlled and measured entirely by a sequence of electronic pulses on wires. These devices have advanced to the point where we can generate and detect highly-entangled states, and perform universal quantum gates. I will describe recent experiments showing two and three qubit entanglement, the operation of Grover?s search algorithm, and the successful realization of simple quantum error correction.
32. Matrix Product States, Projected Entangled Pair States, and the entanglement spectrum of two-dimensional quantum systems
Norbert Schuch, California Institute of Technology
Abstract. Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) provide a description of correlated quantum many-body states from a local perspective. They faithfully approximate ground states of local Hamitonians which makes them powerful numerical tools, while at the same time their ability to explain the global behavior of quantum many-body systems from local properties makes them useful for analytical studies. In my talk, I will give an introduction to Matrix Product States and PEPS as analytical and numerical tools, and illustrate their usefulness by showing how PEPS can be used to establish a full bulk-boundary duality for two-dimensional quantum systems. In particular, PEPS provide an explicit construction relating the entanglement spectrum of a two-dimensional region to the spectrum of a one-dimensional model associated to its boundary, and thereby provide new tools for the analytical and numerical study of boundary models.
Pete Shadbolt, University of Bristol
Rolando Somma, Los Alamos National Laboratory
Abstract. Several problems in science can be solved by preparing a specific eigenstate of some Hamiltonian H. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of H for that eigenstate and the cost of evolving with H for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian H' with the same eigenstate as H but a bigger spectral gap, requiring that constant-time evolutions with H' and H are implemented with nearly the same cost. I will show that a quadratic spectral gap amplification is possible when H satisfies a frustration-free property and construct H' for these cases. This results in quantum speedups for optimization problems. It also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states (PEPS), which play an important role in quantum many-body physics. Defining a suitable black-box model, I will establish that the quadratic amplification is optimal for frustration-free Hamiltonians and that no spectral gap amplification is possible, in general, if the frustration-free property is removed. Interestingly, this results in some limits on the power of some classical methods that simulate quantum adiabatic evolutions.
Robert Spekkens, Perimeter Institute for Theoretical Physics
Abstract. Quantum theory can be thought of as a noncommutative generalization of Bayesian probability theory, but for the analogy to be convincing, it should be possible to describe inferences among quantum systems in a manner that is independent of the causal relationship between those systems. In particular, it should be possible to unify the treatment of two kinds of inference: (i) from beliefs about one system to beliefs about another, for instance, in the Einstein-Podolsky-Rosen or ``quantum steering? phenomenon, and (ii) from beliefs about a system at one time to beliefs about that same system at another time, for instance, in predictions or retrodictions about a system undergoing dynamical evolution or undergoing a measurement. I will present a formalism that achieves such a unification by making use of ?conditional quantum states?, which are noncommutative generalizations of conditional probabilities. I argue for causal neutrality by drawing a comparison with a classical statistical theory with an epistemic restriction. (Joint work with Matthew Leifer)
Frederick Strauch, Williams College
Abstract. I will present a theoretical analysis of methods to synthesize entangled states of two superconducting resonators, and their extension to general unitary operations on resonators as qudits. These methods use experimentally demonstrated interactions of resonators with artificial atoms, and offer efficient routes to generate nonclassical states and processes for high-dimensional quantum systems.
Alexandre Tacla, University of New Mexico
Abstract. We investigate the emergence of three-dimensional behavior in a reduced-dimension Bose-Einstein condensate trapped by a highly anisotropic potential. We handle the problem analytically by performing a perturbative Schmidt decomposition of the condensate wave function between the tightly confined direction(s) and the loosely confined direction(s). The perturbation theory is valid when the nonlinear scattering energy is small compared to the transverse energy scales. Our approach provides a straightforward way, first, to derive corrections to the transverse and longitudinal wave functions of the reduced-dimension approximation and, second, to calculate the amount of entanglement that arises between the transverse and longitudinal spatial directions. Numerical integration of the three-dimensional Gross-Pitaevskii equation for different cigar-shaped potentials and experimentally accessible parameters reveals good agreement with our analytical model even for relatively high nonlinearities. In particular, we show that even for such stronger nonlinearities the entanglement remains remarkably small, which allows the condensate to be well described by a product wave function that corresponds to a single Schmidt term.
James Thompson, JILA
Abstract. I will discuss quantum metrology experiments using large ensembles of cold, trapped atoms and cavity QED. The first portion of the talk will describe conditional spin squeezing of the clock transition of a million Rb atoms, achieved by utilizing the vacuum Rabi splitting as a collective QND meter. The second portion of the talk will describe a Raman laser that operates deep into the superradiant or bad-cavity regime. The system is demonstrated to operate with <1 intracavity photon and with an effective excited state decay linewidth <1 Hz. This model system demonstrates key physics for future active optical clocks that may achieve frequency linewidths approaching 1 mHz due to reduced sensitivity to thermal mirror noise.
Lin Tian, University of California, Merced
Abstract. Light-matter interaction in optomechanical systems can be explored for optical quantum information processing. Here, we present transient and adiabatic schemes for quantum state transfer between optical modes with distinct frequencies via the optomechanical forces. In the transient scheme, red-detuned laser pulses generate state-swappings between the optical and the mechanical modes to achieve the state transfer. In the adiabatic scheme, the cavity dark mode that is immune to the mechanical noise is explored to transfer quantum states. The transfer fidelity for gaussian states can be derived by solving the Langevin equation in the adiabatic limit.
Wim van Dam, University of California, Santa Barbara
Abstract. We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime >2 there are at least p+1 MUBs, which is in contrast with the situation for quantum states defined over the real line R for which only 3 MUBs are known. We comment on the possible reason for the difference regarding MUBs between these two infinite dimensional Hilbert spaces. This is joint work with Alexander Russell. http://arxiv.org/abs/1109.0060
Steven van Enk, University of Oregon
Abstract. The thesis of this talk is that every good experiment (in which the experimentalist knows more or less what she is doing) can be analyzed efficiently, by using so-called information criteria developed for model selection. This holds true even for tomographically complete measurements on many-qubit systems.
Ulrich Warring, NIST Ion Storage Group; National Institute of Standards and Technology
Abstract. In our experiments we employ internal states of trapped and laser-cooled ions as qubits. Typically, laser light is utilized to introduce the coherent coupling between qubits for entangling gates. In recent work we demonstrated microwave near-field control of the qubit states, i.e. single-qubit and entangling two-qubit gates. In this experiment laser light is used only for Doppler cooling, state preparation and state detection, significantly reducing laser power and laser control requirements. Recent experiments on this technique will be reported. In addition we will summarize efforts and progress on benchmarking the fidelity of one- and two-qubit gates, ion transport in multi-zone traps, engineering of Ising-spin interaction with a few hundred ion qubits in a Penning trap, investigations of anomalous heating, and quantum limited metrology. *work supported by IARPA, NSA, ONR, DARPA and the NIST Quantum Information Program.
Stephanie Wehner, Centre for Quantum Technologies, National University of Singapore
Abstract. Even though randomness is an essential resource for many information processing tasks, it is not easily found in nature. The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum state. To tackle this question we here take on the study of quantum-to-classical randomness extractors (QC-extractors). We provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.
Nathan Wiebe, Institute for Quantum Computing
Abstract. We present a new technique that improves the scaling of the error in the adiabatic approximation with respect to the evolution duration, thereby enabling the design of more efficient adiabatic quantum algorithms and adiabatic quantum gates. Our method is conceptually different from previously proposed techniques: it exploits a commonly overlooked phase interference effect that occurs predictably at specific evolution times, suppressing transitions away from the adiabatically transferred eigenstate. Our method can be used in concert with existing adiabatic optimization techniques, such as local adiabatic evolutions or boundary cancellation methods. We perform a full error analysis of our phase interference method along with existing boundary cancellation techniques and show a tradeoff between error-scaling and experimental precision. We illustrate these findings using two examples, showing improved error-scaling for an adiabatic search algorithm and a tunable two-qubit quantum logic gate.
Jian Yang, University of Illinois at Urbana-Champaign
Abstract. The photon plays a critical role in quantum communication and quantum computation. Photon-photon interaction is essential to construct efficient quantum logic gates, but it is typically extremely weak in nonlinear media. Exploiting cavity-quantum dot (C-QD) interactions in the strong coupling regime, we found that photons with ??time-reversed?? line-shapes of the C-QD emissions can excite the system with near-unity efficiency. In this way, photons can acquire strong interactions with each other, which may be useful in a variety of quantum information applications, including quantum non-demolition detectors and constructing high-efficiency quantum logic gates.
Yanbao Zhang, National Institute of Standards and Technology, Boulder
Abstract. Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of statistical p-values, where high violation corresponds to small p-values. We propose a prediction-based ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurement settings and outcomes. It is therefore not subject to the memory loophole [J. Barrett et al., Phys. Rev. A 66, 042111 (2002)]. If the prepared state does not vary in time, the p-values are asymptotically optimal. For comparison, we consider protocols derived from the number of standard deviations of violation of a Bell inequality and from martingale theory [R. Gill, arXiv:quant-ph/0110137]. We find that the p-values of the former can be too small and are therefore not statistically valid, while those derived from the latter are sub-optimal. PBR $p$-values do not require a predetermined Bell inequality and can be used to compare results from different tests of local realism independent of experimental details. This talk is based on the paper [Y. Zhang, S. Glancy, and E. Knill, arXiv:1108.2468, to be published in Phys. Rev. A].