Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session G38: Focus Session: Novel Architectures and Implementations |
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Sponsoring Units: GQI Chair: Jarrod McClean, Harvard University Room: 212B |
Tuesday, March 3, 2015 11:15AM - 11:27AM |
G38.00001: Quantum Simulation: Classical Algorithms Versus Analog Simulators Jonathan Moussa An emerging near-term application for quantum devices is the use of physical qubits without error correction to directly implement many-body Hamiltonians of interest. Such analog quantum simulators may be easier to control and measure than other physical realizations of a Hamiltonian. They have the potential to overcome fundamental limitations of approximate classical algorithms for simulating quantum systems, particularly their real-time dynamics. We compare the behavior of noisy analog quantum simulators operating under several different noise models with several standard classical algorithms including matrix product states. Also, we assess the performance of a new classical algorithm based on approximate state reconstruction through entropy maximization constrained by known expectation values. These tests are based on a finite Heisenberg spin chain both with and without a localizing random field and initialized to either equilibrium, near-equilibrium, or non-equilibrium states. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories. [Preview Abstract] |
Tuesday, March 3, 2015 11:27AM - 11:39AM |
G38.00002: Repulsive interactions in Bose-Einstein condensates accelerate quantum search via quantum walk David Feder, Breanne Hannaford The quantum search algorithm allows a distinct element in an $N$-element database to be located in a time that scales as $\sqrt{N}$, proved to be optimal. In the quantum walk approach to the search problem, a single quantum walker can locate a marked vertex on several graphs at the optimal time scaling. Unfortunately, the quantum walk on the physical case of two- and three-dimensional square lattices fails to improve on the $N$ scaling for a classical search. Particles with linear dispersion have been shown to improve the performance, with the time scaling as $\sqrt{N}\log(N)$ and optimal, respectively. We show that Bose-Einstein condensates (BECs) with on-site repulsive interactions, whose (Bogoliubov) quasiparticle excitations are characterized by a linear dispersion relation at long wavelengths, accelerate the quantum search on these regular lattices. The performance in three dimensions approaches the optimal time scaling, indicating that interacting BECs in optical lattices that are widely realized today can implement an efficient and genuinely interesting quantum algorithm. [Preview Abstract] |
Tuesday, March 3, 2015 11:39AM - 11:51AM |
G38.00003: Universal SU(d) holonomic quantum computing with cat-qudits Victor V. Albert, Stefan I. Krastanov, Chao Shen, Zaki Leghtas, Ren-Bao Liu, Mazyar Mirrahimi, Robert J. Schoelkopf, Liang Jiang We present a holonomic computation scheme with engineered dissipation of a multi-photon process, a generalization of the driven dissipative 2-photon process studied in [1]. The engineered $d$-photon process can stabilize a $d$-dimensional steady state manifold spanned by $d$ coherent states. Universal control is achieved with two types of non-Abelian holonomic gates [2]. The first type consists of adiabatically moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second type consists of adiabatically colliding two coherent states, resulting in a unitary evolution with coherent population transfer between those two components. We outline a way to realize the $d=2$ case using circuit QED. \newline\newline [1] M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, New J. Phys. {\bf 16}, 045014 (2014). \newline [2] A. Carollo, M. Santos, and V. Vedral, Phys. Rev. Lett. {\bf 96}, 020403 (2006). [Preview Abstract] |
Tuesday, March 3, 2015 11:51AM - 12:03PM |
G38.00004: Entangling quantum gates using extended Hilbert space Dmitry Solenov Quantum information is traditionally represented in qubits, which are set entangled by quantum gates as prescribed by algorithms. Multi-state quantum bits (qudits) have also been considered to facilitate algorithm development. Here we explore the potential of additional quantum states available during entangling operations. Unlike in the concept of a qudit, the higher-energy states we consider do not belong to each qubit, but may naturally span over several physical qubit systems. We demonstrate that utilization of such states in an entangling operation involving multiple qubits can lead to significant reduction of its overall time. Such states, which naturally occur in a system of superconducting qubits coupled to a cavity mode, can potentially enable reduction of complexity class of some multi-qubit operations. [Preview Abstract] |
Tuesday, March 3, 2015 12:03PM - 12:15PM |
G38.00005: The spin-2 AKLT state on the square lattice is a universal resource for quantum computation Tzu-Chieh Wei, Robert Raussendorf Universal quantum computation can be driven by local measurement only, provided a suitable entangled state is used. The family of graph states of spin-1/2 entities, including the cluster state as a special case, have been extensively studied. Examples of universal states include graph states on square, honeycomb, and triangular lattices, as well as some faulty square lattices. As of present, it is an open question to characterize all possible universal resource states. Are there any other families of states with different entanglement structures than the graph-state family that can also provide universal resource? We have investigated the family of two-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) states and identified that many states in this family indeed can serve as universal resource. Similar to graph states, AKLT states can be defined on any graph, but their spin magnitude depends on the coordination number. Here, we report that the spin-2 AKLT state on the square lattice is a universal resource for quantum computation. The enabling elements include (1) a generalized measurement that converts a five-level local Hilbert space (spin-2) to a two-level one (spin-1/2), and (2) an analytic formula for the probability distribution for any given outcome of the measurement. [Preview Abstract] |
Tuesday, March 3, 2015 12:15PM - 12:27PM |
G38.00006: Quantum Circuit Complexity of Random Singlet Phases Noah Bray-Ali We use quantum circuit complexity to characterize the entanglement of random singlet phases in one-dimension. Random singlet phases are infinite-randomness fixed points of the strong-disorder renormalization group. They arise in strongly-correlated, quantum many-body systems of bosons, fermions, or anyons, and have long-range entanglement. We compute the depth of the local quantum circuit required to generate the random singlet phase and find that it scales as a super-linear, universal power of the system size. [Preview Abstract] |
Tuesday, March 3, 2015 12:27PM - 12:39PM |
G38.00007: An Efficient Construction of a Matrix Product State for a Free Fermion Ground State Matthew Fishman, Steven White Here we present an efficient and numerically stable procedure for creating the Matrix Product State of a pure fermionic Gaussian state, such as the ground state of a quadratic Hamiltonian. The algorithm produces a minimal number of nearest neighbor gates that, when applied to a product state, forms the many-body ground state. We will cover the procedure for both number conserving Hamiltionians as well as more general parity conserving Hamiltonians, where we will utilize the formalism of Majorana modes. Comparisons to previous methods and applications will be discussed. [Preview Abstract] |
Tuesday, March 3, 2015 12:39PM - 12:51PM |
G38.00008: What constitutes a resource state for measurement-based quantum computation? Eleanor Rieffel, Howard Wiseman Support for universal measurement-based quantum computation (MBQC) is a sufficient condition for states to be considered resources for MBQC, but seems too strong as a necessary condition given known classes of MBQCs that appear to give an advantage over classical computing but which are not universal. We propose some minimal criteria that states must meet in order to be considered resource states for MBQC. We introduce (PRA 89, 032323 (2014)) the notion of inherently measurement-based computations, and give a series of necessary conditions for families of MBQCs to be considered inherently measurement-based. We propose that for a state to be considered a resource for MBQC it must, at minimum, support a family of MBQCs that is inherently measurement-based. Using these criteria, we explain why discord-free states cannot be resources for MBQC, in spite of claims to the contrary. We conclude with some open questions. [Preview Abstract] |
Tuesday, March 3, 2015 12:51PM - 1:27PM |
G38.00009: Shortcuts to Adiabaticity in Quantum Many-Body Systems Invited Speaker: Adolfo del Campo The nonadiabatic dynamics of a many-body system driven through a quantum critical point leads unavoidably to the formation of excitations, in agreement with the Kibble-Zurek mechanism. A way out of this scenario relies on the use of shortcuts to adiabaticity, where the formation of excitations is suppressed by assisting the dynamics with auxiliary multiple-body nonlocal interactions. We propose an alternative scheme which circumvents practical challenges to realize shortcuts to adiabaticity in mesoscopic systems by tailoring the functional form of the auxiliary counterdiabatic interactions. A driving scheme resorting in few-body short-range interactions is shown to generate an effectively adiabatic dynamics. \\[4pt] [1] A. del Campo, W. H. Zurek, Int. J. Mod. Phys. A 29, 1430018 (2014) \\[0pt] [2] A. del Campo, M. M. Rams, W. H. Zurek, Phys. Rev. Lett. 109, 115703 (2012)\\[0pt] [3] H. Saberi, T. Opatrný, K. Mølmer, A. del Campo, Phys. Rev. A 90, 060301(R) (2014)\\[0pt] [4] A. del Campo, K. Sengupta, arXiv:1409.8301 (2014) [Preview Abstract] |
Tuesday, March 3, 2015 1:27PM - 2:03PM |
G38.00010: Quantum algorithms, quantum field theory, and computational complexity Invited Speaker: Keith Lee Quantum field theory provides the framework for the Standard Model of particle physics and plays a key role in physics. However, calculations are generally computationally complex and limited to weak interaction strengths. I'll describe an extension of our quantum algorithm for computing relativistic scattering amplitudes in scalar quantum field theories to fermionic theories. The algorithms run in polynomial time and thus achieve exponential speedup over known classical methods. One of the motivations for this work comes from computational complexity theory. Ultimately, we wish to know what is the computational power of our universe. Studying such quantum algorithms probes whether a universal quantum computer is powerful enough to represent quantum field theory; in other words, is quantum field theory in BQP? Conversely, one can ask whether a given quantum field theory can implement a universal quantum computer; is quantum field theory BQP-hard? I'll describe our approach to addressing the question of BQP-hardness. [Preview Abstract] |
Tuesday, March 3, 2015 2:03PM - 2:15PM |
G38.00011: Are Qubits Fundamentally Flawed for General-purpose Quantum Computing? Cheng-Hsiao Wu When two qubits are employed for the addition operation of two bits, it is not the superposition of 4 states that are relevant for the quantum computing. Rather, it is the 4 symbolic substitution rules derived after collapsing the two qubits. Thus general-purpose quantum paralleling computing is rule-based, not logic-gate based. This is a great departure. The quantum processor (US patent 8,525,544) contains 4 instructions and stores two data. The flaws of qubit concept are explained. Internal coupling (the entanglement) and external coupling (the readouts) must be integrated as one system. The quantum computing architecture is thus in cellular automata with one such processor in each cell. When the cell-to-cell interconnections are altered, a ``new kind of science'' appears and explained. Reversible quantum computing is not as stringent as the unitary operation implies. [Preview Abstract] |
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