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

Abstract

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 restrict this study to the exact ground state, however, the approach can be trivially extended to the inclusion of excited states if the success metric is relaxed. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other (black box) computing paradigm affected by noise.

Degeneracy, degree, and heavy tails in quantum annealing

“…Compared with U 1 instances, S 28 instances are therefore subject to a 28-fold inflation of relative noise, control error, and thermal effects relative to the final (classical) gap when run on DW2. This effect increases for random spin glasses as the classical gap shrinks [7,15], and decreases as excitations from ground state are accepted as viable solutions [9]. This paper demonstrates that even a 5-fold reduction of energy scale significantly degrades DW2X performance on low-degeneracy U 1 instances (see Fig.…”

“…We compare the performance of a D-Wave 2X quantum anealing processor (DW2X) [11] with SA on random ±1 Ising spin glass instances with high local degeneracy and low local degeneracy, where local degeneracy is controlled via parity of qubit connectivity rather than selection of coupling strengths [9,15]. Our results indicate that heavy tails are a consequence of degeneracy in the final target Hamiltonian and a particular implementation of (S)QA wherein all qubits follow an identical annealing schedule.…”

“…Refs. [9,15] avoided the local degeneracy seen in U k instances by drawing coupling strengths from Sidon sets; for example S 28 instances draw couplings from {±28, ±19, ±13, ±8}. Although this construction is effective in reducing local degeneracy, it brings a practical difficulty: Input to DWave processors must be rescaled so that entries of h and J have absolute value at most 1, so S 28 instances must be rescaled by a factor of 1/28.…”

Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions

“…While chaos is an equilibrium phenomena, it is also believed to be related to various non-equilibrium dynamics such as hysteresis, memory and rejuvenation effects [18][19][20][21]. Chaos is also of great relevance for numerical simulations and analog optimization machines [22,23], such as the D-Wave quantum annealers. For example, small temperature perturbations or problem misspecifications could lead to a solution of an entirely different Hamiltonian, especially when the number of spins is large.…”

Enhancing quantum annealing performance for the molecular similarity problem

“…The development of a quantum annealer by D-Wave Systems [3] has initiated a great deal of theoretical and experimental research into the usefulness of the QA approach and its potential supremacy over classical algorithms [4][5][6][7][8][9][10].…”