Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session A27: Focus Session: Adiabatic Quantum Computing I |
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Sponsoring Units: GQI Chair: Sergio Boixo, Information Sciences Institute, University of Southern California Room: 329 |
Monday, March 18, 2013 8:00AM - 8:36AM |
A27.00001: Adiabatic Quantum Computation with Neutral Atoms Invited Speaker: Grant Biedermann We are implementing a new platform for adiabatic quantum computation (AQC)\footnote{ E. Farhi, et al. Science \textbf{292}, 472 (2000)} 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,\footnote{S. Rolston, et al. Phys. Rev. A, \textbf{82}, 033412 (2010)}$^,$\footnote{T. Keating, et al. arXiv:1209.4112 (2012)} 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.\\[4pt] In collaboration with Lambert Parazzoli, Sandia National Laboratories; Aaron Hankin, Center for Quantum Information and Control (CQuIC), University of New Mexico; James Chin-Wen Chou, Yuan-Yu Jau, Peter Schwindt, Cort Johnson, and George Burns, Sandia National Laboratories; Tyler Keating, Krittika Goyal, and Ivan Deutsch, Center for Quantum Information and Control (CQuIC), University of New Mexico; and Andrew Landahl, Sandia National Laboratories. [Preview Abstract] |
Monday, March 18, 2013 8:36AM - 8:48AM |
A27.00002: On scalable, universal adiabatic quantum computation Ari Mizel We investigate scalable, universal adiabatic quantum computation. We exhibit a specific Hamiltonian of local one- and two-body interactions for which the ground state (a) yields the correct answer with high probability and (b) is provably fault-tolerant against local excitations. The effects of finite temperature are discussed. [Preview Abstract] |
Monday, March 18, 2013 8:48AM - 9:00AM |
A27.00003: Ground State Spin Logic James Whitfield, Mauro Faccin, Jacob Biamonte Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization. [Preview Abstract] |
Monday, March 18, 2013 9:00AM - 9:36AM |
A27.00004: Experimental signatures of quantum annealing Invited Speaker: Sergio Boixo 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. [Preview Abstract] |
Monday, March 18, 2013 9:36AM - 9:48AM |
A27.00005: Benchmarking the D-Wave adiabatic quantum optimizer via 2D-Ising spin glasses Zhihui Wang, Sergio Boixo, Tameem Albash, Daniel Lidar We present results on benchmarking the D-Wave One quantum optimizer chip using random 2D Ising spin problems. Finding the ground state of the 2D Ising model with randomly assigned local fields and couplings is NP-hard. The chip attempts to find the ground state via quantum annealing, interpolating between a transverse field and the final Ising Hamiltonian. The experimentally obtained final states are checked against exact results and the performance of the chip is characterized by the probability of finding the ground state and the estimated annealing time for finding the ground state with high probability. By analyzing results for 8 to 108 spins, the scaling of the estimated annealing time as a function of the number of spins is compared with the computation time required by classical solvers. The correlation between classical and quantum hardness is also studied. Furthermore, we analyze the correlation between the experimental success probability and the minimum energy gap during the quantum annealing, as well as the interplay between the adiabatic condition and thermalization. [Preview Abstract] |
Monday, March 18, 2013 9:48AM - 10:00AM |
A27.00006: Using coupling strength to tell apart experimental quantum annealing and classical thermalization models Milad Marvian, Sergio Boixo, Tameem Albash, Daniel Lidar Working with a two-qubit Ising Hamiltonian as the target Hamiltonian of quantum annealing implemented on a D-Wave One chip, we study how the qubit-qubit coupling strength affects the probability of finding the ground state. We solve the same problem analytically and numerically using classical thermalization models, and discuss conditions under which the classical prediction for the ground state probability, as a function of coupling strength, differs from the experimental results. For certain reasonable noise models this allows us to tell apart quantum annealing and classical thermalization. [Preview Abstract] |
Monday, March 18, 2013 10:00AM - 10:12AM |
A27.00007: Computational performance and scaling of adiabatic quantum annealing processors Troels Frimodt R{\O}nnow, Sergei Isakov, Dave Wecker, Sergio Boixo, Matthias Troyer We characterise the recent 128 qubit quantum annealing processor, D-Wave One, through investigation of hardness and scaling of ``time-to-solution'' for several thousand realisations of $\pm J$ spin glass problems, ranging from 8 to 108 qubits in size. We compare statistics of the results to classical- and simulated quantum annealing. Within the processors noise and calibration uncertainties, we find that the results generated by the D-Wave One are statistically indistinguishable from results generated by a simulated quantum annealer while significantly different from those of a classical annealer. An intriguing feature is strong bimodal separation of the instances into two categories: hard and easy. This feature is not observed for the classical annealer. Based on the similarities between the simulated quantum annealer and D-Wave One, we make predictions for the 512 qubit processor, D-Wave Two. [Preview Abstract] |
Monday, March 18, 2013 10:12AM - 10:24AM |
A27.00008: Error correction in adiabatic quantum computation Kevin Young, Mohan Sarovar, Robin Blume-Kohout In conventional quantum computing models (e.g. the circuit-model) it is well understood that error suppression techniques by themselves are insufficient for fault-tolerant quantum computing. From a thermodynamic perspective this is because error suppression alone does not provide a mechanism to remove the entropy generated by errors from the encoded system . Since the thermodynamic argument is independent of the computational model it is expected that error suppression alone is insufficient for fault-tolerant quantum computing in the adiabatic quantum computing (AQC) model also. In this talk we provide a scheme for performing error correction for AQC and discuss the differences between our method and those used in quantum circuit model implementations. [Preview Abstract] |
Monday, March 18, 2013 10:24AM - 10:36AM |
A27.00009: Experimental Quantum Error Correction Kristen Pudenz, Daniel Lidar We demonstrate an experimentally implemented quantum error correcting code (QECC) in an adiabatic quantum computation (AQC) setting. In AQC, the computation proceeds by slowly changing the controls of the system to move from an initial Hamiltonian with an easily prepared ground state to a final Hamiltonian whose ground state embodies the solution to the problem. Our QECC is a repetition code in the computational basis, and encodes the final Hamiltonian of the computation. In this way, we provide an energy penalty for excursions outside the codespace which increases as the AQC progresses. We supplement this with classical decoding of the results at the end of the computation, so that the computation may finish in a state other than the ground state and still solve the problem, as long as it stays within the low-lying spectrum of decodable states. We will show experimental results demonstrating that AQCs encoded with our QECC exhibit better success rates than both unencoded and classically encoded versions. [Preview Abstract] |
Monday, March 18, 2013 10:36AM - 10:48AM |
A27.00010: Adiabatic quantum computational properties of Hopf link Omar Shehab Topological quantum computation has recently become an active field of research with a promise of tackling decoherence. Another track of research effort has presented adiabatic quantum computation as a candidate for implementing quantum computers with presently available technologies. We investigate the potential of combining the strengths of both regime. This report conducts adiabatic evolution on low dimensional topological constructs. We study the properties of a Hopf link related to adiabatic quantum computation. The graph and Seifert surface for the link are calculated. The Ising model representing the Hopf link is then derived from the surface. The Edwards-Anderson Hamiltonian is also solved for the Ising model. The associated eigenfunction and eigenvalues are then used to investigate computational problems which can be represented by the ground state of the adiabatic Hamiltonian. We also consider a type II Reidemeister move on the link. The graph and Seifert surface are calculated for the new link. Then the Edwards-Anderson Hamiltonian is solved for the associated Ising model. The constraints of adiabatic evolution are calculated for both cases. Finally, computational problems are investigated which can be represented by the ground state of the adiabatic Hamiltonian. [Preview Abstract] |
Monday, March 18, 2013 10:48AM - 11:00AM |
A27.00011: Symmetry and Controllability for Quantum Spin Networks Xiaoting Wang, Sophie Schirmer, Daniel Burgarth, Peter Pemberton-Ross, Kurt Jacobs Symmetry is found to be an important tool to study the controllability problems in quantum control. Based on quantum spin networks subject to control of a single node by a local potential (Z-control), we have considered the relation of symmetriy and subspace controllability. Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries. For uniformly coupled XXZ chains a characterization of all possible symmetries is derived from Bethe ansatz. Moreover, for uniform Heisenberg and XX chains, basic number theory can be used to prove that the lack of symmetry is equivalent to subspace controllability. On the other hand, symmetries in the Hamiltonian can be classified into two types: the internal and the external symmetries. Based on the external symmetries, we can rigorously prove the subspace controllability in each of the invariant subspaces for both XXZ and XYZ chains, but not for XX or Ising chains. All these results are useful to design the appropriate control strategy when implementing QIP in real physical systems. [Preview Abstract] |
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