Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session R15: Hybrid Quantum-classical Algorithms and Quantum Simulation |
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Sponsoring Units: DQI Chair: Robin Blume-Kohout, Sandia National Laboratories Room: LACC 304C |
Thursday, March 8, 2018 8:00AM - 8:12AM |
R15.00001: Detector Readout of a Transverse Field Ising model Alessandro Monteros, Lin Tian Reliable detection of the many-body correlations in quantum simulators is a key element in analog quantum simulation. However, in finite systems, the detector backaction can affect the detector readout of the simulators significantly. Here we examine the backaction of a cavity detector on two simulators: a single qubit and a transverse field Ising model. We find that the successful extraction of the correlators of the quantum simulators relies on the validity of the Wick's theorem for the coupling operators. We also analyze the conditions for the Wick’s theorem to be approximately valid for the transverse field Ising model. [1] L. Tian, I. Schwenk, and M. Marthaler, arXiv:1612.07419. [2] I. Schwenk, J.-M. Reiner, S. Zanker, L. Tian, J. Leppaekangas, M. Marthaler, arXiv:1701.02683. |
Thursday, March 8, 2018 8:12AM - 8:24AM |
R15.00002: The Fermi-Hubbard Model for Universal Quantum Computation Jiawei Ji, David Feder Quantum circuits based only on matchgates are able to perform non-trivial (but not universal) quantum algorithms. Because matchgates can be mapped to non-interacting fermions, these circuits can be efficiently simulated on a classical computer. One can perform universal quantum computation by adding any non-matchgate parity-preserving gate, implying that interacting fermions are natural candidates for universal quantum computation within the circuit model. Most work to date has focused on Majorana fermions, which are difficult to realize in the laboratory. We instead explore both spinless (spin-polarized) and spin-1/2 fermions within the context of matchgate circuits, investigating interactions within a family of Fermi-Hubbard Hamiltonians, to obtain experimentally realizable conditions under which interacting fermions are able to perform universal quantum computation. |
Thursday, March 8, 2018 8:24AM - 8:36AM |
R15.00003: Many-Body-Localization Transition in Matchgate-Dominated Quantum Circuits Adrian Chapman, Akimasa Miyake We demonstrate the application of new technical tools for characterizing the many-body-localization transition in quantum circuits. Namely, we examine the behavior of the out-of-time-ordered (OTO) correlator, a four-point correlation function between two local observables, one of which is time-evolved. We are able to extend the number of qubits for which this quantity may be classically evaluated efficiently by decomposing universal quantum circuits into matchgate circuits, which describe free-fermion evolution, together with non-matchgates describing fermion interactions. For circuits composed only of matchgates, there exists a simulation technique for the OTO correlator which scales efficiently in the number of qubits, and exponentially with the number of interaction gates when extended to computational universality. Nevertheless, we find that for sufficiently weak interactions, this quantity may be efficiently approximated using perturbation theory. This allows us to numerically characterize the many-body localization transition in a regime which has so-far remained unexplored. |
Thursday, March 8, 2018 8:36AM - 8:48AM |
R15.00004: Quantum Many Body Hamiltonians stored symbolically in polynomial memory Benjamin Commeau, Sanguthevar Rajasekaran, Gayanath W. Fernando, R. Matthias Geilhufe The quantum many particle Hamiltonian contains many undiscovered new physics, however remains intractable due to its large size. Traditional methods of storing these Hamiltonians in memory will consume exponential amount of memory. If we want to simulate N particles, where each particle can only occupy two states, then the numerical size of the Hamiltonian stored in traditional sparse matrix form will consume O(2^{N}) number of bits. The largest computer we can build is limited by the number of atoms in the observable universe. If every atom in the observable universe is assigned one bit of memory storage, then the maximum number of particles that can be simulated is 270. A typical unit cell simulated in materials science can contain from 100 to 1000 electrons. This illustrates the need for a better method for quantum many particle simulations. We will present a numerical method of storing the quantum many particle Hamiltonian in polynomial memory and still retain useful diagonalization tools for polynomial computation time. |
Thursday, March 8, 2018 8:48AM - 9:00AM |
R15.00005: Characterization of quantum circuit properties in hybrid quantum-classical algorithms Panagiotis Barkoutsos, Andreas Woitzik, Filip Wudarski, Andreas Buchleitner, Ivano Tavernelli Recent advances in hybrid quantum-classical algorithms allow us to find the ground state of Hamiltonians for quantum chemistry and optimization problems. This can be achieved by searching the full Hilbert space via the sequential application of single-qubit rotations and entanglement blocks (multi-qubit gates). First results [Kandala et al., Nature 549, 242–246] indicate that the high dimensionality of the molecular Hilbert space enforces us to use a large number of entanglement blocks. In this way, we reach a critical circuit depth for state of the art quantum architectures with limited coherence times, which imposes important restrictions for near-term applications. In order to reduce the number of gate operations, we investigate different entanglement schemes and evaluate their properties by means of a set of descriptors that includes concurrence, site occupation, and convergence efficiency. We discuss the scalability of these approaches, the cost of their implementation in near future quantum devices, and the computational advantage of their application in variational quantum eigensolver optimizers. |
Thursday, March 8, 2018 9:00AM - 9:12AM |
R15.00006: Investigations of the Quantum Alternating Operator Ansatz Eleanor Rieffel, Stuart Hadfield, Zhihui Wang, Bryan O'Gorman, Davide Venturelli The next few years will be exciting as prototype universal quantum processors emerge, enabling implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation, and which have the potential to significantly expand the breadth of quantum computing applications. Here, we present investigations of the Quantum Alternating Operator Ansatz [1], an extension of the framework defined by Farhi et al. [2] in their Quantum Approximate Optimization Algorithm, including design criteria, mappings of specific problems [1], compilation to near-term hardware [3], and early results. |
Thursday, March 8, 2018 9:12AM - 9:24AM |
R15.00007: QAOA Performance Benchmarks using Max-Cut Jonathan Ward, Johannes Otterbach, Gavin Crooks, Nicholas Rubin, Marcus da Silva The Quantum Approximation Optimization Algorithm (QAOA) is an algorithm proposed to solve combinatorial optimization problems such as Max-Cut on near-term quantum computing hardware. In this talk we present benchmark data comparing the performance of QAOA in solving the Max-Cut problem with the performance of its classical counterpart, the Goemans-Williamson algorithm. With a simulator of an N-qubit quantum computer we use QAOA to approximate Max-Cut solutions for all N-vertex fully connected graphs up to N=8 and compare the distribution of the derived approximation ratios with the cited typical approximation ratio obtained with the Goemans-Williamson algorithm. We investigate the dependency of QAOA performance on multiple parameters and determine the percentage of graphs for which QAOA outperforms the Goemans-Williamson bound. |
Thursday, March 8, 2018 9:24AM - 9:36AM |
R15.00008: XY vs X mixer in Quantum Alternating Operator Ansatz for optimization problems with constraints Zhihui Wang, Nicholas Rubin, Eleanor Rieffel Quantum Approximate Optimization Algorithm,[1] further generalized as Quantum Alternating Operator Ansatz (QAOA),[2] is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace.[2,3] Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian. |
Thursday, March 8, 2018 9:36AM - 9:48AM |
R15.00009: Improving operator averaging in hybrid algorithms with approximate N-representability constraints Nicholas Rubin, Jarrod McClean, Ryan Babbush The two most well known hybrid classical/quantum algorithms require calculating expected values of Pauli operators by repeated state preparation and measurement. Accelerating the operator averaging step correlates directly with accelerating the total algorithm runtime. We propose the use of approximate N-representability constraints as a set of conditions for reconstructing marginals generated with noise from measurement. These techniques take the form of projections onto the set of N-representable two-electron reduced density matrices (2-RDMs) enforcing non-negativity of the marginal, particle number conservation, and the appropriate magnetization of the targeted Fermionic state prepared on the quantum resource. We present the performance of the N-representability inspired 2-RDM reconstruction procedures on marginals mimicking real measured data. For small systems, the projection techniques give a significant reduction in the number of samples required for operator averaging to a given precision. |
Thursday, March 8, 2018 9:48AM - 10:00AM |
R15.00010: Solid-state NMR implementation of quantum reservoir computing Makoto Negoro, Keisuke Fujii, Kohei Nakajima, Kosuke Mitarai, Masahiro Kitagawa Reservoir computing is a framework for computation using a neural network (the reservoir), where the internode transition is not trained but instead linear readout weight is trained. Recently a quantum counterpart of reservoir computing was proposed. Here, we implement quantum reservoir computing with nuclear spin qubits as network nodes. Our ensemble qubit system is comprised of 1H and 13C spins in l-alanine-1,13C diluted into a single crystal of l-alanine-2H7. The qubit state is transited with the dipole-dipole interactions. Data input is represented by the phase of NMR pulse sequence. 13C spin state is read out by NMR signal. In this talk, we show the results and discuss the scalability of the architecture. |
Thursday, March 8, 2018 10:00AM - 10:12AM |
R15.00011: Using an Optical Parametric Amplifier as a Noiseless Attenuator Richard Brewster, James Franson Heralded noiseless attenuators, in conjunction with noiseless amplifiers, have been shown to reduce the amount of decoherence a quantum state experiences when it travels through a lossy channel. Here, we introduce a novel noiseless attenuator that can be constructed by appropriate heralding on an optical parametric amplifier. This heralded parametric attenuator is somewhat surprising but it is a direct consequence of post-selecting on vacuum in the idler mode of the device. |
Thursday, March 8, 2018 10:12AM - 10:24AM |
R15.00012: NMRCloudQ: A Quantum Cloud Experience on a Nuclear Magnetic Resonance Quantum Computer Bei Zeng As of today, no one can tell when a universal quantum computer with thousands of logical quantum bits (qubits) will be built. At present, most quantum computer prototypes involve less than ten individually controllable qubits, and only exist in laboratories for the sake of either the great costs of devices or professional maintenance requirements. Cloud-based quantum computing is anticipated to be the most useful and reachable form for public users to experience with the power of quantum. As initial attempts, IBM Q has launched influential cloud services on a superconducting quantum processor in 2016, but no other platforms has followed up yet. Here, we report our new cloud quantum computing service -- NMRCloudQ (http://nmrcloudq.com), where nuclear magnetic resonance, one of the pioneer platforms with mature techniques in experimental quantum computing, plays as the role of implementing computing tasks. Our service provides a comprehensive software environment preconfigured with a list of quantum information processing packages, and aims to be freely accessible to either amateurs that look forward to keeping pace with this quantum era or professionals that are interested in carrying out real quantum computing experiments in person. |
Thursday, March 8, 2018 10:24AM - 10:36AM |
R15.00013: Quantum phase estimation with noisy qubits Thomas O'Brien, Barbara Terhal We study how well small noisy quantum phase estimation circuits can estimate the ground-state energy of a Hamiltonian given an input 'starting' state with some overlap with the ground-state. We describe how one can estimate the ground-state energy from a series of quantum phase estimation experiments by an optimized and computationally feasible Bayesian analysis which includes a scalable modeling of the noise. We focus on quantum phase estimation experiments which consist of multiple rounds, each round coupling to a single ancilla qubit, which gradually project the input state onto a single eigenstate. To demonstrate the robustness and accuracy of our protocol, we numerically assess its performance for a few qubits, randomly picked Hamiltonians and starting states, on a simulation of superconducting quantum computing hardware. We show that the estimate of the ground-state energy and the classically-calculated variance of the posterior distribution of ground-state energies captures the uncertainty in learning the ground-state energy well. |
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