Bulletin of the American Physical Society
APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
Session X27: Quantum Computing and Simulation II |
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Sponsoring Units: GQI Chair: Alan Aspuru-Guzik, Harvard University Room: C155 |
Thursday, March 24, 2011 2:30PM - 2:42PM |
X27.00001: Analysis of quantum Monte Carlo dynamics for quantum adiabatic evolution in infinite-range spin systems Jun-ichi Inoue We analytically derive deterministic equations of order parameters such as spontaneous magnetization in infinite-range quantum spin systems obeying quantum Monte Carlo dynamics. By means of the Trotter decomposition, we consider the transition probability of Glauber-type dynamics of microscopic states for the corresponding classical system. Under the static approximation, differential equations with respect to macroscopic order parameters are explicitly obtained from the master equation that describes the microscopic-law. We discuss several possible applications of our approach to disordered spin systems for statistical-mechanical informatics. Especially, we argue the ground state searching for infinite-range random spin systems via quantum adiabatic evolution. [Preview Abstract] |
Thursday, March 24, 2011 2:42PM - 2:54PM |
X27.00002: Ramsey numbers and adiabatic quantum computing Frank Gaitan, Lane Clark The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, only nine Ramsey numbers are currently known, with knowledge of other Ramsey numbers limited to bounds on their possible value. We describe a quantum algorithm for the computation of Ramsey numbers. We show how the problem of computing a Ramsey number can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution (AQE). We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for s $\leq$ 6. We also discuss experimental implementation of an adiabatic quantum computation of R(3,3). [Preview Abstract] |
Thursday, March 24, 2011 2:54PM - 3:06PM |
X27.00003: Two-particle quantum walks applied to the graph isomorphism problem John King Gamble, Mark Friesen, Dong Zhou, Robert Joynt, S.N. Coppersmith We show that an algorithm based on the dynamics of interacting quantum particles is more powerful than the corresponding algorithm for non-interacting particles. Specifically, our algorithm attempts to determine whether two graphs are isomorphic. We focus on strongly regular graphs (SRGs), a class of graphs with particularly high symmetry. By studying the dynamical evolution of two-particle quantum walks on pairs of non-isomorphic SRG's, we show that interacting particles can distinguish non-isomorphic graphs that noninteracting particles cannot. First, we prove that quantum walks of two noninteracting particles cannot distinguish pairs of non-isomorphic SRG's. Next, we demonstrate numerically that two interacting bosons are more powerful, in that their quantum walks distinguish all non-isomorphic pairs of SRGs we tried, including those with up to 64 vertices. Finally, we find a set of operators that determine these evolutions. [Preview Abstract] |
Thursday, March 24, 2011 3:06PM - 3:18PM |
X27.00004: Quantum Walks on Trees with Disorder Steven Jackson, Teng Jian Khoo, Frederick Strauch Quantum walks on trees have the potential for exponential speedup compared to classical algorithms. It has been argued that disorder may limit this potential, due to Anderson localization. We report on an extensive numerical analysis of quantum walks with disorder and find evidence of a localization transition for large disorder, but a quantum-to-classical transition for intermediate disorder. These results suggest that quantum walks may yet retain their speedup for high-dimensional graphs with weak disorder. [Preview Abstract] |
Thursday, March 24, 2011 3:18PM - 3:30PM |
X27.00005: Numerical investigations of quantum walks with hard-core bosons and the graph isomorphism problem Mark Wellons, John Gamble, Eric Bach, Mark Friesen, Robert Joynt, Kenneth Rudinger, Dong Zhou, Susan Coppersmith Gamble et al. investigated quantum walks of two hard-core bosons on a class of highly symmetric graphs called strongly regular graphs (SRGs) and showed that these walks will distinguish nonisomorphic graphs from the same family. However, J. Smith (arXiv:1004.0206) has shown that pairs of nonisomorphic graphs exist that cannot be distinguished by such quantum walks. Here we construct explicit counterexample graph pairs for 2 and 3-particle interacting and non-interacting walks. We also describe an algorithm that, given $k$ particles, generates two graphs indistinguishable by a $k$-boson quantum walk. We find that these indistinguishable graph pairs generated by our algorithm scale in size quadratically with the number of particles. It follows that distinguishing graphs via simulating quantum walks with classical computers will likely require exponential time in the size of the graph, while leaving open the possibility that a quantum computer could distinguish the graphs in polynomial time. [Preview Abstract] |
Thursday, March 24, 2011 3:30PM - 3:42PM |
X27.00006: Simulating Quantum Dynamics On A Quantum Computer Nathan Wiebe, Dominic Berry, Peter Hoyer, Barry Sanders We develop an efficient quantum algorithm for simulating time-dependent Hamiltonian evolution of general input states on a quantum computer. Given conditions on the smoothness of the Hamiltonian, the complexity of the algorithm is close to linear in the evolution time, and therefore is comparable to algorithms for time-independent Hamiltonians. In addition, we show how the complexity can be reduced by optimizing the time steps. The complexity of the algorithm is quantified by calls to an oracle, which yields information about the Hamiltonian, and accounts for all computational resources. In contrast to previous work, which allowed an oracle query to yield an arbitrary number of bits or qubits, we assign a cost for each bit or qubit accessed. This per-bit or per-qubit costing of oracle calls reveals hitherto unnoticed simulation costs. We also account for discretization errors in the time and the representation of the Hamiltonian. We generalize the requirement of sparse Hamiltonians to being a sum of sparse Hamiltonians in various bases for which the transformation to a sparse Hamiltonian may be performed efficiently. [Preview Abstract] |
Thursday, March 24, 2011 3:42PM - 3:54PM |
X27.00007: Preparing Ground States of Many-Body Systems by Simulated Cooling Dvir Kafri, Jacob Taylor Computational problems, such as satisfiability, can be rephrased in terms of the preparation of the ground state of a many-body Hamiltonian. More generally, a quantum simulator could provide information on many-body systems if the ground state can be appropriately prepared. Adiabatic preparation is a common technique for obtaining the ground state of a quantum mechanical system, by slowly varying the system Hamiltonian. A principle disadvantage is that its timing scales with the gap energy of the intermediate Hamiltonian, for which a gap may not be promised, rather than the final Hamiltonian which may be known to be gapped. We present an alternative approach, in which an arbitrary system of qubits is cooled to an effective many-body ground state, through the algorithmic interaction with a small number of ``bath'' qubits. We specify bounds for the parameters of the algorithm, show that cooling time scales with the system's gap, and present simulated results on a frustrated few-spin system. We further discuss possible experimental applications. [Preview Abstract] |
Thursday, March 24, 2011 3:54PM - 4:06PM |
X27.00008: An Open-System Quantum Simulator with Trapped Ions Julio T. Barreiro, Markus Mueller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F. Roos, Peter Zoller, Rainer Blatt The control of quantum systems is of fundamental scientific interest and promises powerful applications and technologies. Impressive progress has been achieved in isolating the systems from the environment and coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled coupling to an environment remains largely unexplored. Here we report the first realization of a toolbox for simulating an open quantum system with up to five qubits. Using a quantum computing architecture with trapped ions, we combine multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate this engineering by the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation. [Preview Abstract] |
Thursday, March 24, 2011 4:06PM - 4:18PM |
X27.00009: Discrete quantum walk on a binary tree Zlatko Dimcovic, Ian Milligan, Dan Rockwell, Robert M. Burton, Thinh Nguyen, Yevgeniy Kovchegov We have recently constructed a framework for quantum walks, based on classical walks with memory. This framework reproduces known walks, while it can be used to build walks in systems that are difficult for current approaches. As our first example of its utility, we study a symmetric discrete quantum walk on the infinite binary tree. For a walk starting from a pure state at a given level in the tree, we compute the amplitude at the root, as a function of time and starting level. The result is strikingly different from the classical case, as its amplitude spans an order of magnitude, with a power law tail, while the classical one decays exponentially. (For example, for a delayed walk this property yields a polynomial vs. exponential speed up over the classical walk, in delay time.) The breadth of the probability peak indicates that any restriction of the extent of the tree, such as a matching tree, sinks or boundaries, would likely yield algorithms superior to classical. The calculation utilizes a variety of analytical techniques (memoried stochastic processes, combinatorics and path counting, transforms, steepest descent, orthogonal polynomials). This study also brings up interesting general questions about quantum processes on such structures. [Preview Abstract] |
Thursday, March 24, 2011 4:18PM - 4:30PM |
X27.00010: Quantum Random Walks of Non-Interacting Bosons on Strongly Regular Graphs Kenneth Rudinger, John King Gamble, Mark Wellons, Mark Friesen, Dong Zhou, Eric Bach, Robert Joynt, S.N. Coppersmith We investigate the quantum dynamics of particles on graphs (``quantum walks"), with the aim of developing quantum algorithms for determining if two graphs are isomorphic and show that there are fundamental differences between the distinguishing power of two-particle and three-particle non-interacting quantum walks. We investigate quantum walks on strongly regular graphs (SRGs), a class of graphs with high symmetry. We show analytically that the two-particle walk always fails to distinguish non-isomorphic members of the same SRG family. We show numerically that the three-boson walk is able to distinguish 99.6\% of 70,712 SRG comparisons made and that this distinguishing power comes from different multiplicities of certain graph substructures in non-isomorphic graphs. We identify certain distinguishing substructures and examine ones that appear in the four-boson walk, discovering they are able to distinguish almost all of the graphs that the three-boson walk failed on. This indicates a positive correlation between number of bosons in the walk and distinguishing power. [Preview Abstract] |
Thursday, March 24, 2011 4:30PM - 4:42PM |
X27.00011: Real-time Simulations of Quantum Spin $\frac{1}{2}$ Particles Coupled to Multiple Spin Baths Marta L. Guerra, M.A. Novotny, Hans De Raedt We present simulations in real time for one and two spin $\frac {1}{2}$ particles coupled to one or more baths of $\frac{1}{2} $-integer quantum spins. The simulations were performed using the algorithm and code of Prof. De Raedt [1,2]. We first simulated one spin coupled to one or two spin-baths with no interactions between the bath spins, as has been calculated theoretically [3]. We find in agreement with [3], that the quantum purity ${\cal P}(t)$ decays in both cases, exponentially for a single bath and algebraically for two baths. We extend these simulations by introducing random interactions between the bath spins in an attempt to reach the asymptotic decay rate at earlier times and for fewer spins in the baths. We also have performed similar studies for two spin $\frac{1}{2}$ quantum particles coupled to one, two, or more spin baths. The time- dependent quantum density matrix and ${\cal P}(t)$, as well as other quantities, are calculated in these simulations.\hfil\break [1] V.V. Dobrovitski and H.A. De Raedt, Phys. Rev. E {\bf 67} 056702 (2003).\hfil\break [2] S. Yuan, M.I. Katsnelson, and H. De Raedt, Phys. Rev. A {\bf 75} 052109 (2007).\hfil\break [3] D.D. B. Rao, H. Kohler and F. Sols, New J. Physicis {\bf 10} 115017 (2008). [Preview Abstract] |
Thursday, March 24, 2011 4:42PM - 4:54PM |
X27.00012: Effects of Decoherence in Quantum Simulations Nayeli Zuniga-Hansen, Mark S. Byrd, Yu-Chieh Chi We investigate the effects of decoherence in quantum simulations by observing the evolution of the system when the Quantum Information Processor is coupled to the environment. We simulate the noise as the interactions between the particles of the processor itself and observe the effects of varying the strength of the couplings. We perform these calculations for different quantum systems and compare the results of those that interact with the environment to the same system when it's completely isolated from it to observe the effects of the noise on the simulation and investigate ways to prevent the adverse effects of the noise. [Preview Abstract] |
Thursday, March 24, 2011 4:54PM - 5:06PM |
X27.00013: Computational codes for simulating the Schr\"{o}dinger equation and the Master equation Nagendra Dhakal, Michael Leuenberger We developed new codes for simulating the Schr\"{o}dinger equation. We compared the codes with the FDTD codes and codes based on Quantum Monte Carlo method in 1, 2 and 3 dimensions. In addition, we simulated the Master equation for the purpose of studying the spatial and time evolution of the decoherence. Our main focus is to investigate the scalability of the codes and we found the Quantum Monte Carlo method is the most suitable for the simulation of the Master equation because it reduces the dimension of the problem to the dimension of Hilbert space, with the benefits of speeding up the process of calculation and at the same time reducing the memory. Our results are important for the implementation of quantum computing, quantum communication, and spintronics. [Preview Abstract] |
Thursday, March 24, 2011 5:06PM - 5:18PM |
X27.00014: Experimental photonic quantum simulation of frustrated Heisenberg spins Philip Walther, Xiao-song Ma, Borivoje Dakic, William Naylor, Anton Zeilinger Quantum simulators are controllable quantum systems that can reproduce the dynamics of the system of interest, which are typically unfeasible for classical computers. The recent developments of quantum technology enable the precise control of individual quantum particles as required for studying complex quantum systems. In particular, quantum simulators capable of simulating frustrated Heisenberg spin systems provide a platform for understanding exotic matter such as high-temperature superconductors. Here we report the analog quantum simulation of arbitrary Heisenberg-type interactions among four spin-1/2 particles. This spin-1/2 tetramer is the two-dimensional archetype system whose ground state belongs to the class of valence-bond states. Depending on the interaction strength, frustration within the system emerges such that the ground state evolves from a localized to a resonating valence-bond state. This spin-1/2 tetramer is created using the polarization states of four photons. The precise single-particle addressability and a tunable measurement-induced interaction allows us to obtain fundamental insights into entanglement dynamics among individual particles by observing the frustration of entanglement, governed by quantum monogamy. [Preview Abstract] |
Thursday, March 24, 2011 5:18PM - 5:30PM |
X27.00015: A realistic topological quantum computation platform using hole-doped semiconductor nanowires and s-wave superconductors Ming Gong, Li Mao, Sumanta Tewari, Chuanwei Zhang We show that two majorana fermions exist at the two ends of a hole-doped semiconductor nanowire that is in proximity contact with an s-wave superconductor. The required experimental parameters (carrier density, g-factor, spin-orbit coupling effect, magnetic field, etc.) for the observation of the Majorana fermions are within the experimentally reachable regime of InSb and InAs nanowires and the mini gap that provides the topological protection for the Majorana zero energy states is of the order of the s-wave superconducting gap. The Majorana zero energy states can be observed through the zero bias peak in the STM signal. The Josephson effects between two nanowire are studied. The proposed model provides a realistic experimental platform for observing non-Abelian statistics and performing topological quantum computation. This work is supported by DARP-MTO (FA955-10-1-0497), and DARPA-YFA (N66001-10-1-4025). [Preview Abstract] |
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