Firas Hamze

Erratum: Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines

Recently, a programmable quantum annealing machine has been built that minimizes the cost function of hard optimization problems by adiabatically quenching quantum fluctuations. Tests performed by different research teams have shown that, indeed, the machine seems to exploit quantum effects. However experiments on a class of random-bond instances have not yet demonstrated an advantage over classical optimization algorithms on traditional computer hardware. Here we present evidence as to why this might be the case. These engineered quantum annealing machines effectively operate coupled to a decohering thermal bath. Therefore, we study the finite-temperature critical behavior of the standard benchmark problem used to assess the computational capabilities of these complex machines. We simulate both random-bond Ising models and spin glasses with bimodal and Gaussian disorder on the D-Wave Chimera topology. Our results show that while the worst-case complexity of finding a ground state of an Ising spin glass on the Chimera graph is not polynomial, the finite-temperature phase space is likely rather simple: Spin glasses on Chimera have only a zero-temperature transition. This means that benchmarking optimization methods using spin glasses on the Chimera graph might not be the best benchmark problems to test quantum speedup. We propose alternative benchmarks by embedding potentially harder problems on the Chimera topology. Finally, we also study the (reentrant) disorder-temperature phase diagram of the random-bond Ising model on the Chimera graph and show that a finite-temperature ferromagnetic phase is stable up to 19.85(15)% antiferromagnetic bonds. Beyond this threshold the system only displays a zero-temperature spin-glass phase. Our results therefore show that a careful design of the hardware architecture and benchmark problems is key when building quantum annealing machines.

Importance of explicit vectorization for CPU and GPU software performance

Much of the current focus in high-performance computing is on multi-threading, multi-computing, and graphics processing unit (GPU) computing. However, vectorization and non-parallel optimization techniques, which can often be employed additionally, are less frequently discussed. In this paper, we present an analysis of several optimizations done on both central processing unit (CPU) and GPU implementations of a particular computationally intensive Metropolis Monte Carlo algorithm. Explicit vectorization on the CPU and the equivalent, explicit memory coalescing, on the GPU are found to be critical to achieving good performance of this algorithm in both environments. The fully-optimized CPU version achieves a 9x to 12x speedup over the original CPU version, in addition to speedup from multi-threading. This is 2x faster than the fully-optimized GPU version, indicating the importance of optimizing CPU implementations.

Fast Computational Methods for Visually Guided Robots

This paper proposes numerical algorithms for reducing the computational cost of semi-supervised and active learning procedures for visually guided mobile robots from O(M3to O(M), while reducing the storage requirements from M2to M . This reduction in cost is essential for real-time interaction with mobile robots. The considerable speed ups are achieved using Krylov subspace methods and the fast Gauss transform. Although these state-of-the-art numerical algorithms are known, their application to semi-supervised learning, active learning and mobile robotics is new and should be of interest and great value to the robotics community. We apply our fast algorithms to interactive object recognition on Sony’s ERS-7 Aibo. We provide comparisons that clearly demonstrate remarkable improvements in computational speed.

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here, we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem-an Ising spin glass-on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other computing paradigm affected by noise.

Self-Avoiding Random Dynamics on Integer Complex Systems

This article introduces a new specialized algorithm for equilibrium Monte Carlo sampling of binary-valued systems, which allows for large moves in the state space. This is achieved by constructing self-avoiding walks (SAWs) in the state space. As a consequence, many bits are flipped in a single MCMC step. We name the algorithm SARDONICS, an acronym for Self-Avoiding Random Dynamics on Integer Complex Systems. The algorithm has several free parameters, but we show that Bayesian optimization can be used to automatically tune them. SARDONICS performs remarkably well in a broad number of sampling tasks: toroidal ferromagnetic and frustrated Ising models, 3D Ising models, restricted Boltzmann machines and chimera graphs arising in the design of quantum computers.

Investigating the performance of an adiabatic quantum optimization processor

Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard Ising spin glass instance class with up to 128 binary variables. Using parameters obtained from a realistic superconducting adiabatic quantum processor, we extract the minimum gap and matrix elements using high performance Quantum Monte Carlo simulations on a large-scale Internet-based computing platform. We compare the median adiabatic times with the median running times of two classical solvers and find that, for the considered problem sizes, the adiabatic times for the simulated processor architecture are about 4 and 6 orders of magnitude shorter than the two classical solvers’ times. This shows that if the adiabatic time scale were to determine the computation time, adiabatic quantum optimization would be significantly superior to those classical solvers for median spin glass problems of at least up to 128 qubits. We also discuss important additional constraints that affect the performance of a realistic system.

High-performance Physics Simulations Using Multi-core CPUs and GPGPUs in a Volunteer Computing Context

This paper presents two conceptually simple methods for parallelizing a Parallel Tempering Monte Carlo simulation in a distributed volunteer computing context, where computers belonging to the general public are used. The first method uses conventional multi-threading. The second method uses CUDA, a graphics card computing system. Parallel Tempering is described, and challenges such as parallel random number generation and mapping of Monte Carlo chains to different threads are explained. While conventional multi-threading on central processing units is well-established, GPGPU programming techniques and technologies are still developing and present several challenges, such as the effective use of a relatively large number of threads. Having multiple chains in Parallel Tempering allows parallelization in a manner that is similar to the serial algorithm. Volunteer computing introduces important constraints to high performance computing, and we show that both versions of the application are able to adapt themselves to the varying and unpredictable computing resources of volunteers’ computers, while leaving the machines responsive enough to use. We present experiments to show the scalable performance of these two approaches, and indicate that the efficiency of the methods increases with bigger problem sizes.

Robust Parameter Selection For Parallel Tempering

This paper describes an algorithm for selecting parameter values (e.g. temperature values) at which to measure equilibrium properties with Parallel Tempering Monte Carlo simulation. Simple approaches to choosing parameter values can lead to poor equilibration of the simulation, especially for Ising spin systems that undergo

Erratum: Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines (Phys. Rev. X 4, 021008 (2014))

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A Performance Comparison of CUDA and OpenCL

-order phase transitions. However, starting from an initial set of parameter values, the careful, iterative respacing of these values based on results with the previous set of values greatly improves equilibration. Example spin systems presented here appear in the context of Quantum Monte Carlo.