2013 Talk Abstracts

Unitary Transformations in a Large Hilbert Space

Brian Anderson, University of Arizona

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 implemented a protocol for arbitrary unitary transformations in the 16 dimensional hyperfine ground manifold of Cesium 133 atoms, using phase modulated rf and microwave magnetic fields to drive the atomic evolution. Our phase modulation waveforms are designed numerically using a variant of the highly efficient GRAPE algorithm. The fidelity of the resulting transformations is verified experimentally through randomized benchmarking, which indicates an average fidelity better than 97% across a sample of random unitaries. Our toolbox for quantum control is in principle applicable for a broad class of physical systems, such as large spins or anharmonic oscillators.

Squeezing of Spin Waves in Atomic Ensembles

Ben Baragiola, Center for Quantum Information and Control, University of New Mexico

(Session 10: Saturday from 2:00 - 2:30)

Squeezing the collective spin of an atomic ensemble via QND measurement is based on the interaction between a cloud of atoms and a laser probe. When the shot noise resolution of the laser probe is below the projection noise fluctuations of the atoms, the resulting backaction can reduce the uncertainty for a collective atomic observable. Most current models of this process rely on idealized one-dimensional plane wave approximations of the underlying light-matter interaction, which are not appropriate for describing a real system consisting of a cigar-shaped cold atomic cloud in dipole trap interacting with a probe laser. We extend such models from first principles to include spatial dependence of both the light and of the atomic ensemble and apply it to QND spin squeezing for large-spin alkali atoms. The model includes spin waves, diffraction, paraxial modes, and optical pumping, derived by a full master equation description. We find that to optimally mode-match for spin squeezing one must consider not only collective scattering into the forward modes of the field, but also the effects of local decoherence from spatially-varying diffuse photon scattering. Surprisingly, in certain circumstances such local decoherence can be less destructive to spin squeezing than previously thought from phenomenological models.

Adaptive gate-set tomography

Robin Blume-Kohout, Sandia National Laboratories

(Session 7a: Friday from 4:00 - 4:30)

Quantum information hardware needs to be characterized and calibrated. This is the job of quantum state and process tomography, but standard tomographic methods have an Achilles heel: to characterize an unknown process, they rely on a set of absolutely calibrated measurements. Many technologies (e.g., solid-state qubits) admit only a single native measurement basis, and other bases are measured using unitary control. So tomography becomes circular -- tomographic protocols are using gates to calibrate themselves! Gate-set tomography confronts this problem head-on and resolves it by treating gates relationally. We abandon all assumptions about what a given gate operation does, and characterize entire universal gate sets from the ground up using only the observed statistics of an [unknown] 2-outcome measurement after various strings of [unknown] gate operations. The accuracy and reliability of the resulting estimates depend critically on which gate strings are used, and benefits greatly from adaptivity. We demonstrate gate-set tomography and quantify the accuracy with which the individual gates can be estimated.

Experimental signatures of quantum annealing

Sergio Boixo, University of Southern California, Information Sciences Institute

(Session 11: Saturday from 3:30 - 4:00)

Quantum annealing is a general strategy for solving optimization problems with the aid of quantum adiabatic evolution. How effective is rapid decoherence in precluding quantum effects in a quantum annealing experiment, and will engineered quantum annealing devices effectively perform classical thermalization when coupled to a decohering thermal environment? Using the D-Wave machine, we report experimental results for a simple problem which takes advantage of the fact that for quantum annealing the measurement statistics are determined by the energy spectrum along the quantum evolution, while in classical thermalization they are determined by the spectrum of the final Hamiltonian only. We establish an experimental signature which is consistent with quantum annealing, and at the same time inconsistent with classical thermalization, in spite of a decoherence timescale which is orders of magnitude shorter than the adiabatic evolution time. For larger and more difficult problems, we compare the measurements statistics of the D-Wave machine to large-scale numerical simulations of simulated annealing and simulated quantum annealing, implemented through classical and quantum Monte Carlo simulations. For our test cases the statistics of the machine are - within calibration uncertainties - indistinguishable from a simulated quantum annealer with suitably chosen parameters, but significantly different from a classical annealer.

Quantum simulation and many-body physics with hundreds of trapped ions

John Bollinger, National Institute of Standards and Technology

(Session 1: Thursday from 8:30 - 9:15)

Many different quantum information protocols have been demonstrated with small linear chains of ions in rf (Paul) traps. I will describe our efforts to extend some of the techniques developed with small linear chains of ions to larger two-dimensional crystals of hundreds of ions formed in a Penning trap [1]. Our qubit (or spin) is the 124 GHz electron spin-flip transition in the ground state of Be+ in the 4.5 Tesla magnetic field of the trap. We control the spins with an effective transverse magnetic field obtained with 124 GHz microwaves [2]. By employing spin-dependent optical dipole forces, we engineer long-range Ising interactions (both ferromagnetic and anti-ferromagnetic) between the ion qubits [3]. We benchmark the interactions through measurements of mean-field spin precession [4]. I will describe the types of Ising interactions we can readily implement and discuss the prospects for simulating the transverse Ising model with hundreds of qubits. [1] T. Mitchell, J. J. Bollinger, D. Dubin, X. Huang, W. M. Itano, and R. Baughman, Science 282, 1290 (1998). [2] M. J. Biercuk, H. Uys, A. P. VanDevender, N. Shiga, W. M. Itano, and J. J. Bollinger, Quantum Information and Computation 9, 920 (2009). [3] K. Kim, M.-S. Chang, R. Islam, S. Korenblit, L.-M. Duan, and C. Monroe, Phys. Rev. Lett. 103, 120502 (2009). [4] J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, Nature 484, 489 (2012).

Instantaneous Quantum Circuits for Ising Models

Gavin Brennen, Macquarie University

(Session 1: Thursday from 10:15 - 11:00)

Statistical Mechanics has provided us with straightforward recipes to compute various physical quantities that can be experimentally probed on an interacting many-body system. But more often than not, the application of these recipes is computationally inefficient, as can be seen from very idealised systems. It may be expected that quantum algorithms could help in this regard. I will describe a scheme for measuring complex temperature partition functions of Ising models which, through appropriate Wick rotations, can be analytically continued to yield estimates for real ones. Notably, the kind of state preparations and measurements involved in this application can in principle be made "instantaneous", i.e. independent of the system size or the parameters being simulated. The estimation error is analysed numerically and analytically and shown to be compatible with prior art using larger depth quantum circuits. Also I'll describe some results on when the algorithm yields approximation scales with multiplicative rather than additive error which could have application in other contexts as well. Finally the dual problem concerning the BQP-hardness of computing partition functions for classical ferromagnetic and consistent Ising models in 2D a high but not perfect accuracy will be described.

Exploring adiabatic quantum computing trajectories via optimal control

Constantin Brif, Sandia National Laboratories

(Session 6a: Friday from 2:00 - 2:30)

Adiabatic quantum computation (AQC) employs a slow change of the Hamiltonian, which helps keeping the system in the instantaneous ground state. When the evolution time is finite, dynamic trajectories corresponding to different forms of time-dependent control function(s) will result in different degrees of adiabaticity (quantified as the average ground state population during evolution). We employ optimal control methods to search for control functions that achieve the target final state while simultaneously maximizing the degree of adiabaticity. Exploring properties of optimal AQC trajectories in model systems elucidates dynamic mechanisms that minimize unwanted excitations from the ground state.

Magic state distillation with noisy Clifford gates

Peter Brooks, California Institute of Technology

(Session 7b: Friday from 5:00 - 5:30)

A promising method for achieving universal fault-tolerant quantum computation is to supplement Clifford operations, which are sufficient for error correction but not a universal basis, with copies of certain single-qubit states called magic states. High-fidelity copies of these states can be prepared from noisy copies using state distillation protocols which use only Clifford gates. This process can proceed to arbitrarily high fidelity, assuming that the Clifford gates are perfect. In practice, imperfect Clifford operations will both reduce the efficiency of distillation and limit the achievable fidelity of the distilled state. This will be particularly relevant to quantum computation where the noise from Clifford operations is substantial, which will likely be the case with early demonstrations of fault-tolerant quantum computing. Recently, a number of interesting proposals have been made for more efficient state distillation protocols which use fewer ancillas to achieve a given error rate. We analyze and compare the efficiency and success probability for magic state distillation under these various proposals, taking into account the presence of imperfect Clifford operations.

Quantum Technology Taken to its Limits

Tommaso Calarco, University of Ulm

(Session 2: Thursday from 3:45 - 4:30)

The full power of quantum coherence has not yet been tapped for everyday technological applications. The exquisite level of control of current atomic physics experiments may enable this, for instance in the field of quantum communication and quantum computing - but scalable quantum information processing requires extremely precise operations. Quantum optimal control theory allows to design the evolution of realistic systems in order to attain the best possible performance that is allowed by the laws of quantum mechanics. I will present a range of its applications to a variety of quantum technologies, and discuss its use in probing the ultimate limits to the speed, fidelity and size of the corresponding quantum processes.

Quantum Control: A Circuit-Based Classification

Carlton Caves, University of New Mexico

(Session 2: Thursday from 2:15 - 2:45)

Control of the behavior of quantum systems, to make them do what we want them to do, instead of just what comes naturally, is fundamental to quantum information science. I will discuss a classification scheme that divides control and feedback techniques into three types: measurement-based control and feedback; coherent control and feedback; and quantum (noncommutative) control and feedback. The classification is based on how these techniques are represented in quantum-circuit diagrams and will be illustrated by examples.

Accurate quantum Z rotations with less magic

Chris Cesare, Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico

(Session 7b: Friday from 4:30 - 5:00)

We present quantum protocols for executing arbitrarily accurate pi/2^k rotations of a qubit about its Z axis. Unlike reduced instruction set computing (RISC) protocols which use a two-step process of synthesizing high- fidelity "magic" states from which T = Z(pi/4) gates can be teleported and then compiling a sequence of adaptive stabilizer operations and T gates to approximate Z(pi/2^k), our complex instruction set computing (CISC) protocol distills magic states for the Z(pi/2^k) gates directly. Replacing this two-step process with a single step results in substantial reductions in the number of gates needed. The key to our construction is a family of shortened quantum Reed-Muller codes of length 2^(k+2)-1, whose distillation threshold shrinks with k but is greater than 0.85% for k <= 6. CC was supported in part by the Laboratory Directed Research and Development program at Sandia National Laboratories. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Cavity-enhanced non-demolition measurements for atom counting and spin squeezing

Zilong Chen, JILA and Department of Physics, University of Colorado at Boulder

(Session 10: Saturday from 2:30 - 3:00)

Cavity-enhanced probing of an atomic ensemble is an important tool for precision metrology. In particular, high resolution, non-destructive atom counting increases measurement or sensing bandwidth, and mitigates noise aliasing (Dick effect) in an atomic sensor. Achieving high resolution atom counting while preserving coherence can generate conditionally spin squeezed states that has phase sensitivity below the standard quantum limit. In recent years, there has been much interest in cavity-enhanced measurements for the above metrological applications. We consider fundamental measurement imprecision and scalings for cavity-enhanced measurements. As a particular example, we will discuss fundamental squeezing limits in Rb-87 for the clock and stretched hyperfine transitions, taking into account the multilevel structure. We will also discuss our experimental squeezing on the Rb-87 clock transition and give an outlook on current efforts to squeeze using the Rb-87 cycling transition. References: [1] Zilong Chen, Justin G. Bohnet, Joshua M. Weiner, Kevin C. Cox, and James K. Thompson, arXiv:1211.0723 [2] Zilong Chen, Justin G. Bohnet, Shannon R. Sankar, Jiayan Dai, and James K. Thompson, Phys. Rev. Lett. 106, 133601 (2011)

Is building a superconducting quantum computer actually feasible?

Andrew Cleland, University of California - Santa Barbara

(Session 4: Friday from 8:30 - 9:15)

There has recently been tremendous progress in the performance of superconducting quantum circuits, especially in single qubit T1 and T2 coherence times, as well as in quantum measurement. Simple implementations of quantum algorithms have also been demonstrated. Are these advances sufficient to consider actually building a quantum computer? I will argue that the answer is (probably) affirmative, although such an effort would still be faced with many challenges, including how to achieve high-fidelity tune-up, control, and measurement of large numbers of qubits. A highly fault-tolerant approach is also needed; I will describe the surface code architecture, which provides what may be the most fault-tolerant scheme that includes topologically-protected logical operations. I will outline the basic principles and operation of this scheme, as well as prospects for the medium and long-term future of this area of research.

Graph Equitable Partitioning in Quantum Many-Body Physics

David Feder, University of Calgary

(Session 7c: Friday from 4:00 - 4:30)

The Hamiltonian for bosonic and fermionic particles hopping on lattices can be interpreted as the adjacency matrix of an undirected, weighted graph, usually with self-loops. The properties of these quantum many-body systems can therefore be analyzed in terms of graph theory. For example, the simple graph for non-interacting distinguishable particles is the Cartesian product of each particle's adjacency matrix; if these particles become indistinguishable, the graph 'collapses' via a graph equitable partition. Under various circumstances, equitable partitioning can allow for a more efficient determination of the eigenstates (and therefore the properties) of physically interesting quantum many-body systems. I will focus in particular on the ground states of the Bose and Fermi Hubbard models.

Minimax quantum tomography: the ultimate bounds on accuracy

Chris Ferrie, Center for Quantum Information and Control, University of New Mexico

(Session 7a: Friday from 4:30 - 5:00)

There are many methods for quantum state tomography (e.g., linear inversion, maximum likelihood, Bayesian mean...). But none of them is clearly "the most accurate" for data of finite size N. Even the upper limits on accuracy are as yet unknown, which makes it difficult to say that a given method is "accurate enough". We address this problem here by (i) calculating the minimum achievable error for single-qubit tomography with N Pauli measurements, (ii) finding "minimax" estimators that achieve this bound, and (iii) comparing the performance of known estimators.

Adiabatic Quantum Computation with Neutral Cesium

Aaron Hankin, University of New Mexico

(Session 11: Saturday from 4:00 - 4:30)

We are implementing a new platform for adiabatic quantum computation (AQC) [1] based on trapped neutral atoms whose coupling is mediated by the dipole-dipole interactions of Rydberg states. Ground state cesium atoms are dressed by laser fields in a manner conditional on the Rydberg blockade mechanism [2,3], thereby providing the requisite entangling interactions. As a benchmark we study a Quadratic Unconstrained Binary Optimization (QUBO) problem whose solution is found in the ground state spin configuration of an Ising-like model. [1] E. Farhi, et al. Science 292, 472 (2000) [2] S. Rolston, et al. Phys. Rev. A, 82, 033412 (2010) [3] T. Keating, et al. arXiv:1209.4112 (2012)

Quantum many-body problems for identical particles: The (anti-)symmetrized n-fold product states.

Zhang Jiang, University of New Mexico

(Session 7c: Friday from 4:30 - 5:00)

Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number N. As a consequence, one needs an exponentially large number of parameters merely to record an arbitrary state, not to say calculating its time evolution. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on N or is proportional to N, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new set of states, which constitute a natural generalization of the product-state ansatz. Our state of N=d× n identical particles is derived by symmetrizing the n-fold product of a d-particle quantum state. The quantum correlations of that d-particle state thus spread out to any two of the N particles. For fixed d, the parameter space of our states does not grow with N. Several properties of our states will be discussed, including the one- and two-particle reduced density matrices, multi-particle correlations, and advantages over the product ansatz. Although our states were initially proposed for bosons, we also briefly discuss its fermion correspondence and applications.

Local topological order inhibits thermal stability in 2D

Olivier Landon-Cardinal, Universite de Sherbrooke

(Session 7c: Friday from 5:00 - 5:30)

We study the robustness of quantum information stored in the degenerate ground space of a local, frustration-free Hamiltonian with commuting terms on a 2D spin lattice. On one hand, a macroscopic energy barrier separating the distinct ground states under local transformations would protect the information from thermal fluctuations. On the other hand, local topological order would shield the ground space from static perturbations. Here we demonstrate that local topological order implies a constant energy barrier, thus inhibiting thermal stability. Joint work with David Poulin. arXiv:1209.5750

Using a mechanical resonator to catch, store, and release propagating microwave fields

Konrad Lehnert, University of Colorado

(Session 5: Friday from 10:30 - 11:15)

Micro-mechanical resonators are an established technology for processing classical signals. The field of quantum micro-electromechanics seeks to use these resonators to process signals in an essentially quantum way. For example, it may be possible to use these resonators as long-lived memories, storing quantum information on a chip in the form of mechanical vibration. In this talk, I will describe our progress in this endeavor. In particular, we are now able to transfer coherent states between propagating microwave fields and a mechanical resonator. Furthermore we can directly observe the decay of the resonator state and estimate a quantum coherence time. Finally, we can perform our state transfer protocol using coherent states with an average energy of one photon, allowing us to estimate the fidelity of a mechanical resonator used as a quantum memory.

Quantum Measurements Constrained by Symmetry

Leon Loveridge, University of British Columbia

(Session 7a: Friday from 5:00 - 5:30)

The Wigner-Araki-Yanase (WAY) theorem prescribes limitations to quantum measurements under the constraint of a particular symmetry: that of an additive conserved quantity on the Hilbert space of the system and measuring apparatus. Any observable not commuting with such a quantity does not admit accurate and repeatable measurements. For example, a WAY constraint is known to inhibit the implementability of qubit operations if angular momentum conservation is to be respected. Furthermore, it has been shown recently that the WAY theorem extends in many respects to position measurements obeying momentum conservation. They key to achieving measurements with high accuracy is to allow the measuring apparatus to become large, quantified by the spread of the conserved quantity in its initial state. I'll review these results with specific reference to WAY constraints in quantum information processing, highlighting the important roles of the repeatability of the measurement and another often neglected condition: that the observable representing a pointer also commutes with the conserved quantity (called the Yanase condition). With this in mind, I'll briefly discuss how WAY-type restrictions occur in the alternative framework of quantum reference frames, where similar behaviour is observed, and present some new results in this context.

Quantum degenerate Bose and Fermi dipolar gases of dysprosium realized

Mingwu Lu, Stanford University

(Session 6b: Friday from 2:00 - 2:30)

Advances in the quantum manipulation of ultracold atomic gases are opening a new frontier in the quest to better understand strongly correlated matter. By exploiting the long-range and anisotropic character of the dipole-dipole interaction, we hope to create novel forms of soft quantum matter, phases intermediate between canonical states of order and disorder. Our group recently created Bose and Fermi quantum degenerate gases of the most magnetic element, dysprosium, which should allow investigations of quantum liquid crystals. We present details of recent experiments that created the first degenerate dipolar Fermi gas as well as the first strongly dipolar BEC in low field. BECs of Dy will form the key ingredient in novel scanning probes using atom chips. We are developing a Dy cryogenic atom chip microscope that will possess unsurpassed sensitivity and resolution for the imaging of condensed matter materials exhibiting topologically protected transport and magnetism.

Distinguishing Hyperentangled Bell States with Linear Evolution and Local Measurement

Theresa Lynn, Harvey Mudd College

(Session 9: Saturday from 11:00 - 11:45)

A measurement of the entangled state, or Bell state, of two particles is essential to numerous protocols in quantum communication, such as quantum teleportation, entanglement swapping, and quantum dense coding. I will discuss limits on Bell-state distinguishability for an apparatus that uses linear evolution and local measurement (LELM). For two identical particles entangled in n qubit variables, I present a simple proof that, of the 4^n hyper-entangled Bell states, 2^(n+1)-1 can be distinguished with LELM. This result generalizes well-known results for n =1,2, and gives us physical intuition with which to understand those limits. I will also discuss extensions beyond the case of qubit variables.

Self-consistent quantum process tomography

Seth Merkel, IBM Watson Research Center

(Session 7a: Friday from 3:30 - 4:00)

Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We will show that the standard approach of process tomography fails in the case where the states and measurement operators used to interrogate the system are generated by gates that have some systematic error, a situation all but unavoidable in any practical setting. These errors cannot be compensated for by statistical oversampling or through increasing the number of measurement settings. We present an alternative method for tomography to reconstruct an entire library of gates in a self-consistent manner where the essential new ingredient is to define a likelihood function that treats the gates used for preparation and measurement on equal footing with the gate being reconstructed. We compare this new method of tomography to standard process tomography in both simulation and experiments on superconducting circuits.

Single photon optomechanics

Gerard Milburn, The University of Queensland

(Session 5: Friday from 11:15 - 12:00)

The emerging field of quantum optomechanics combines quantum optics and new fabrication techniques to control the quantum state of macroscopic mechanical resonators. These systems are an example of a new kind of engineered quantum system in which supra-atomic, hybrid systems are engineered to have the desired quantum functionality. They have application to metrology and sensing and may enable new experiments at the quantum-classical boundary. I will give an overview of optomechanics and discuss some specific models. These include; single photon optomechanics, quantum entanglement in optomechanical networks and quantum-limited readout of phonon jumps.

Relying more on a classical computer during quantum computation

Akimasa Miyake, Center for Quantum Information and Control, University of New Mexico

(Session 1: Thursday from 11:00 - 11:30)

It seems inevitable that a quantum computer functions with the aid of a classical computer in that the latter plays roles of an external controller as well as an interface to us. While such a hybrid structure may have been discussed in the context of quantum control and quantum error correction, we could ask whether it is possible to "replace" part of quantum computation more actively by this classical side-processor in case it is classically tractable? We pay attention to so-called quantum matchgates, which are a class of one- and two-qubit gate operations with certain algebraic constraints and occur ubiquitously in simulating fermionic quantum many-body systems. Since polynomial-sized quantum matchgate circuits can be efficiently classically simulatable, here we attempt to invent a model of quantum-classical hybrid computation where the contribution of matchgates are taken care of by the classical computer in between other quantum computation.

Ultrafast Spin-Motion Entanglement in Single Atomic Qubits

Jonathan Mizrahi, Joint Quantum Institute, University of Maryland

(Session 6b: Friday from 2:30 - 3:00)

We experimentally demonstrate entanglement between the spin and motional degrees of freedom of a trapped ion on a timescale of 15 ns. This entanglement is create by extracting single pulses from a picosecond mode-locked laser, which are then split into short pulse trains. By tuning the spectrum of this pulse train appropriately, the ion can receive a spin-dependent kick, in which the spin states receive momentum kicks in opposite directions. Pairs of these momentum kicks can then be used to create an interferometer, in which the motional wavepacket is split and recombined. This technique should open the door to ultrafast, scalable entangling gates whose speed are not limited by the trap frequency.

Long-lived, radiation-suppressed superconducting quantum bit in a planar geometry

David Pappas, National Institute of Standards and Technology

(Session 6b: Friday from 1:30 - 2:00)

We present a superconducting qubit design that is fabricated in a 2D geometry over a superconducting ground plane to enhance the lifetime. The qubit is coupled to a microstrip resonator for readout. The circuit is fabricated on a silicon substrate by the use of low loss, stoichiometric titanium nitride for capacitor pads and small, shadow-evaporated aluminum/aluminum-oxide junctions. We observe qubit relaxation and coherence times (T1 and T2) of 11.7 0.2 s and 8.7 0.3 s, respectively. Calculations show that the proximity of the superconducting plane suppresses the otherwise high radiation loss of the qubit. A significant increase in T1 is projected for a reduced qubit-to-superconducting plane separation.

Lyapunov exponents across the quantum-classical transition

Arjendu Pattanayak, Carleton College

(Session 6c: Friday from 2:00 - 2:30)

Abstract: We calculate quantum lyapunov exponents for identical noise quantum trajectories for the damped driven double-well Duffing oscillator across a range of parameters, specifically as a function of effective hbar (=beta) as well as the system damping parameter Gamma. We demonstrate the recovery of the classical Lyapunov exponent in the limit of beta to 0. In general Lyapunov exponents decrease (chaos decreases) as beta increases (as the system becomes more quantal). However, we identify the following surprises: (a) Regions of anomalous increase of chaos (Lyapunov exponents increasing with beta); (b) Regions of anomalous 'quantum-induced' onset of chaos (Lyapunov exponent going from negative to positive with increasing beta); and (c) Regions of incomplete correspondence for values of Gamma where the classical system has windows of regularity embedded in a larger chaotic parameter regime. For these last regions, the classical results are not recovered for the smallest beta we can computationally access (beta =0.003). We discuss the meaning and consequences of these results, as well as prospects for experimental verification.

Quantum Control and Fault-tolerant quantum computing

Gerardo Paz Silva, University of Southern California

(Session 6a: Friday from 2:30 - 3:00)

Quantum control (QC) and the methods of fault-tolerant quantum computing (FTQC) are two of the cornerstones on which the hope for a quantum computer rests. However QC methods do not generally scale well with the size of the system, and it is not known how their performance is hindered when integration with FTQC methods, especially considering these demand a large system size overhead, is attempted under realistic noise models. Here we study this problem using dynamical decoupling in the bang-bang limit as a toy model, with a non-Markovian noise where interactions decay with distance, and show that there exists a (reasonable) regime of the norms of the relevant Hamiltonians, in which dynamical decoupling protected gates provide an advantage over the bare gate implementation. This is a first step towards showing that QC protocols designed for a small set of qubits can be extended to larger sets without a significant loss of performance, as long as the noise model behaves reasonably well.

Hypercubic cluster entanglement in the optical frequency comb

Olivier Pfister, University of Virginia

(Session 7b: Friday from 4:00 - 4:30)

Based on our continuing collaboration with Nicolas Menicucci for the theory, we describe a highly nontrivial planned expansion of our previous experimental demonstration of the entanglement of the optical frequency comb into 15 independent quadripartite continuous-variable cluster states (first reported at SQuINT). We will show how multiple hypercubic graph states can be experimentally generated in the optical frequency comb of a few optical parametric oscillators, all of which are considerably simpler than in our previous proposals and experiments.

Entanglement of two superconducting qubits in a three-dimensional architecture via monochromatic two-photon excitation

Stefano Poletto, IBM T.J. Watson Research Center, Yorktown Heights, NY, US

(Session 4: Friday from 9:15 - 9:45)

The superconducting qubit approach for the realization of a quantum processor is a promising candidate because of its compatibility with silicon microfabrication techniques. The coherence times of superconducting devices have continuously improved in the previous decade, with the most noticeably enhancement recently obtained by placing the qubit inside a three-dimensional waveguide cavity. I will present a novel implementation of a two-qubit three dimensional architecture using superconducting qubits, and I will describe a new gate for the direct generation of maximally entangled Bell states. The gate employs the forbidden two-photon 00 - 11 transition, made bright by the interaction between non computational energy levels. A microwave drive tuned to this transition induces Rabi-like oscillations between the ground and doubly excited state via the Bell basis, allowing the generation of entangled states.

Quantum Simulation of Frustrated Spin Models with Trapped Ions

Phil Richerme, Joint Quantum Institute

(Session 1: Thursday from 9:15 - 9:45)

Frustration, or the competition between interacting components of a network, is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses, and spin ices. We study frustrated antiferromagnetic interactions within a fully-connected transverse-field Ising model using a linear chain of 10+ trapped Yb-171+ ions. The Ising interactions are generated via phonon-mediated spin-dependent laser forces, with the form and range of such interactions controlled by manipulation of laser frequencies and trap voltages. State-dependent fluorescence imaging of the ions allows measurement of spin correlation functions as the antiferromagnetic interaction range is increased, revealing increasing amounts of frustration in the system. We are also investigating the nature of spin ordering in an Ising model with both transverse and axial magnetic fields and Kibble-Zurek-like dynamics within the spin system that may be difficult to calculate classically. This work was supported by grants from the U.S. Army Research Office with funding from IARPA, the DARPA OLE program, and the MURI Hybrid Quantum Circuits program; and the NSF Physics Frontier Center at JQI. Co-authors: R. Islam, C. Senko, W.C. Campbell, S. Korenblit, J. Smith, A. Lee, and C. Monroe.

Schrödinger cat state spectroscopy with trapped ions

Christian Roos, Institute for Quantum Optics and Quantum Information

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

Trapped and laser-cooled ions have excellent properties for high-precision spectroscopy. By quantum logic spectroscopy, ions whose internal state cannot be detected easily can be read out via a second ion species trapped together with the spectroscopy ion. I will discuss the use of geometric phases for a particular type of quantum logic spectroscopy that can be used to detect the absorption or emission of single photons with high detection efficiency. By preparing a Schrödinger cat state of a two-ion crystal where the ions's motion is entangled with the internal states of the logic ion, a photon scattered by the spectroscopy ion manifests itself by a geometric phase that can be subsequently read out via the logic ion. This measurement scheme is applied to a mixed ion crystal of two calcium isotopes.

When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?

Asif Shakeel, Haverford College, Haverford, PA.

(Session 7c: Friday from 3:30 - 4:00)

Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned quantum cellular automata) represent an interesting subclass of QCA. Prior work on QCA has investigated the relationship between these two classes of models. We establish necessary and sufficient conditions for unbounded, finite Quantum Cellular Automata (QCA) (finitely many active cells in a quiescent background) to be Quantum Lattice Gas Automata. We define a local condition that classifies those QCA that are QLGA, and we show that there are QCA that are not QLGA.

A real-space renormalization method with applications to frustration-free Hamiltonians

Rolando Somma, Los Alamos National Laboratory

(Session 1: Thursday from 11:30 - 12:00)

We present a numerical method based on real-space renormalization that outputs the exact ground space of Hamiltonians that satisfy a frustration-free property. The complexity of the method is polynomial in the degeneracy of the ground space. We apply the method to obtain the full ground space of spin-1/2 models on a square lattice much more efficiently than methods based on exact diagonalization.

Weak Measurement, Uncertainty Relationships, and Tradeoffs in Experimental Quantum Measurement

Aephraim Steinberg, University of Toronto

(Session 10: Saturday from 1:15 - 2:00)

I will discuss several ongoing projects which investigate quantum measurement, its limitations, and the range of strategies available. In particular, I will describe an experiment using weak measurements and ideas from cluster-state quantum computing to demonstrate a violation of Heisenberg's proposed relationship between measurement precision and measurement disturbance; and work investigating the use of weak-value amplification for measuring nonlinear optical phase shifts at the single-photon level. If time permits, I will also discuss ongoing work investigating the optimal choice of separable or entangled states for tasks ranging from phase estimation or magnetometry to process tomography to detection of decoherence.

Robust entanglement generation via optomechanical quantum interface

Lin Tian, University of California, Merced

(Session 6c: Friday from 2:30 - 3:00)

Entanglement is a powerful source for studying quantum effects in macroscopic objects and for quantum information processing. Here, we will show that robust entanglement at distinct frequencies can be generated in optomechanical systems where strong light-matter interaction has recently been demonstrated. Due to quantum interference, the contribution of the mechanical noise to the two-mode squeezing process can be effectively suppressed in a way similar to electromagnetically induced transparency. Given the entanglement schemes and our previous schemes on quantum wave length conversion, the optomechanical interface can serve as a building block for quantum network.

Quantum state stabilization with engineered quasi-local Markovian dissipation

Lorenza Viola, dartmouth College

(Session 2: Thursday from 1:30 - 2:15)

Harnessing dissipation is a goal of increasing significance for quantum control. In this context, characterizing Markovian evolutions which admit a desired pure state as their unique asymptotically stable state is both relevant for a system-theoretic understanding of open-system stability properties and potentially useful for dissipative quantum state preparation. In this talk, I will focus on addressing under which conditions a multip-artite qubit system can be driven to a desired pure entangled state by a Lindblad dynamics that obeys suitably defined "quasi-locality" constraints. I will first present a necessary and sufficient linear-algebraic criterion for the simplest scenario where the target system is drift-less and quasi local stabilization is possible for arbitrary initial states solely based on dissipative control resources. If the required conditions are not met, I will further address whether the control objective may be achieved conditional upon initialization in a proper subspace and/or by additionally exploiting Hamiltonian control. Applications to engineering entangled states of physical interest and explicit schemes for synthesizing the required controls will be discussed.

Quantum Coherence in Biology

Birgitta Whaley, UC Berkeley

(Session 12: Saturday from 4:30 - 5:15)

Recent years have seen mounting evidence for the existence of dynamical phenomena in biological systems that involve coherent quantum motion, requiring us to revise the long standing view of quantum effects in biology being restricted to understanding of molecular energetics, stability and kinetics. I shall review the considerable evidence that quantum coherent electronic dynamics contributes to the extremely efficient light-harvesting stage of photosynthesis, then present theoretical studies that analyze the nature of this coherence, its relation to the non-local quantum correlations characteristic of entanglement, and possible functional role for long range unidirectional energy transport.

Quantum Control and Simulation Using Product Formulas for Exponentials of Commutators

Nathan Wiebe, Institute for Quantum Computing

(Session 6a: Friday from 1:30 - 2:00)

This work provides a new recursive method for systematically constructing product formula approximations to exponentials of commutators, giving approximations that are accurate to arbitrarily high order. These formulas are very useful for introducing or suppressing interaction terms in quantum systems, a point that I will illustrate by using our formulas to implement the toric code using only two-body interactions. By presenting an algorithm for quantum search using evolution according to a commutator, I will also show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. I then conclude by showing that our product formulas can be used to improve the scaling of the complexity of certain quantum simulation algorithms with the error tolerance, in the black box setting. This work was done in collaboration with Andrew Childs at the Institute for Quantum Computing.

Trapped-ion quantum information processing experiments at NIST*

Andrew Wilson, National Institute of Standards & Technology

(Session 8: Saturday from 9:15 - 9:45)

We report experiments towards scalable quantum information processing with laser-cooled trapped ions. Quantum information is stored in internal(hyperfine ground) states of ions and gate operations are performed with laser and microwave fields. We describe efforts to implement a recently proposed two-qubit gate [1] which incorporates continuous dynamical decoupling. In one experiment, the ions involved in the two-qubit gate are confined in different potential wells - an architecture that may have applications in quantum simulation. In addition, we briefly summarize recent efforts to increase the speed at which multiple two-qubit gate operations can be performed, and to reduce motional heating in surface-electrode traps. This includes demonstrations of a fast laser-cooling scheme based on Electromagnetically-Induced-Transparency (EIT), a method for rapid transport of ions between confinement zones in a micro-fabricated trap, and an in situ surface-cleaning treatment that reduces electric-field noise. *This work is supported by IARPA, ARO, ONR, DARPA and the NIST Quantum Information Program. [1] A. Bermudez et al., Phys. Rev. A 85, 040302(R) (2012)

Superposition, entanglement, and raising Schroedinger's cat.

David J. Wineland, National Institute of Standards and Technology

(Session 12: Saturday from 10:15 - 11:00)

Entanglement is the defining feature of quantum mechanics, and has application in quantum key distribution (QKD) and other quantum technologies. The strongest (and strangest) form of quantum correlation arising from entanglement is Bell-nonlocality [1] (the violation of Bell inequalities at a distance), which lies behind the theoretical possibility of device independent (DI) QKD [2]. The existence of quantum nonlocality of a weaker sort, however, goes back much further than Bell, to the seminal 1935 papers [3] of Einstein, Podolsky and Rosen (EPR) and Schrödinger. The latter coined the term "steering" for the EPR effect, viz. the ability of Alice, by her choice of measurement, to remotely prepare different types of quantum states for Bob, when they share entanglement. EPR-steering has since been formalized as a quantum information task [4], allowing the development of powerful new tests of this phenomenon: EPR-steering inequalities [5]. Just as for Bell inequalities, experimental violations of EPR-steering inequalities may be criticized if they rely upon a fair sampling assumption, as this opens the "detection loophole". For Bell nonlocality, closing this loophole requires both parties' detectors to have high efficiency; for EPR-steering Bob's detector is explicitly trusted [4], so only Alice's efficiency matters. Recently, we have demonstrated for the first time, in three separate experiments, EPR-steering using distant entangled qubits, with no detection loophole [6]. In the first of these, Alice's heralding efficiency was as high as 62% (that is, the probability of Alice seeing a photon given that Bob sees a photon is 62%). This allowed a demonstration using only two settings per side, in the same configuration as standard QKD. The significance of this is that we have shown [7] that there is a more secure version of standard QKD, in which only one detector (Bob's) need be trusted, while Alice's detector and the entanglement source remain untrusted. We call this 1-sided (1s) DI-QKD, as opposed to fully DI-QKD in which no devices need be trusted. For maximally entangled states, 1sDI-QKD is possible with a heralding efficiency for Alice of only 66% [7], while the best known fully DI-QKD scheme [7] requires both Alice and Bob to have heralding efficiencies (if equal) of over 91%. In Ref. [8] we also apply steering to suggest experiments to try to rule out all objective pure-state dynamic models, such as quantum jumps [9] or quantum diffusion [10], for an atom. Our proposed tests, using a strongly driven two-level atom, do not rely upon any special preparation of the atom or field. Our best test (using homodyne detection and a complicated adaptive photo-detection scheme) requires an efficiency of only 58%, and a simpler test (using just homodyne detection) only 73%. REFERENCES [1] J. S. Bell, Physics (N.Y.) 1, 195 (1964). [2] A. Acín et al., Phys. Rev. Lett. 98, 230501 (2007). [3] A. Einstein, B. Podolsky, N. Rosen, Phys. Rev. 47, 777 (1935); E. Schrödinger, Proc. Camb. Phil. Soc. 31, 555 (1935). [4] H. M. Wiseman, S. J. Jones, A. C. Doherty, Phys. Rev. Lett. 98, 140402 (2007). [5] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, M. D. Reid, Phys. Rev. A. 80, 032112 (2009). [6] D. H. Smith et al., Nature Communications 3, 625 (2012); B. Wittmann, et al., New J. Phys. 14, 053030 (2012); A. J. Bennet et al., Phys. Rev. X (in press, 2012). [7] C. Branciard et al. Phys. Rev. A (Rapid Comm.) 85, 010301(R) (2012). [8] H. M. Wiseman and J. M. Gambetta, Phys. Rev. Lett. 108, 220402 (2012). [9] N. Bohr, Phil. Mag. 26, 1 (1913); A. Einstein, Physikalische Zeitschrift 18, 121 (1917). [10] N. Gisin and I. C. Percival, J. Phys. A 25, 5677 (1992).

Loophole-free steering for quantum cryptography and for testing the subjectivity of atomic quantum jumps

Howard Wiseman, Griffith University

(Session 9: Saturday from 10:15 - 11:00)

Nonlinear Quantum Search

Thomas Wong, UC San Diego

(Session 7b: Friday from 3:30 - 4:00)

Abrams & Lloyd (1998) showed that a nonlinear quantum theory could lead to unreasonable computational power, solving NP-Complete problems in polynomial time. To do so, they used a hard nonlinearity, which led to dynamics in which 0 amplitude for some state was an unstable fixed point, and thus extremely susceptible to noise. Instead, we consider a physically motivated, softer nonlinearity of the Gross-Pitaevskii type, which leads to dynamics that are only marginally unstable at 0. We show that with such a nonlinearity the unstructured search problem can be solved in constant time. Our algorithm, however, requires increasingly precise time measurement with increasing problem size, N, but since solving the problem more slowly reduces the necessary measurement precision, the resource requirements can be jointly optimized to scale as N1/4. This is a significant, but not unreasonable, improvement over the N1/2 scaling of Grover's algorithm. We conclude by considering the implications of such nonlinear dynamics arising as an approximation to the quantum evolution of multiple particles, and we arrive at a quantum information-theoretic argument for the number of particles needed for the Gross-Pitaevskii equation to accurately describe the linear, multi-particle dynamics of a Bose-Einstein condensate. This is joint work with David Meyer.

On the structure of symmetric quantum measurements

Jon Yard, Microsoft Research Station Q

(Session 6c: Friday from 1:30 - 2:00)

A central problem in quantum information theory is to understand the apparent existence, for any finite quantum system, of highly-symmetric optimal quantum measurements known as SIC-POVMs. These measurements correspond to finite sets of equiangular complex vectors of the maximal possible size. Much evidence points to the existence of SIC-POVMs obtained from orbits of finite Heisenberg groups, which are proved to exist for about 20 dimensions and which have been found numerically up to around dimension 60. In this talk, I will show how the mathematics of class field theory can explain the group-theoretic structure inherent to these known examples while offering predictions for their structure in arbitrary dimensions.