What is the Computational Value of Finite-Range Tunneling?

Abstract

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%success-probability that is ∼ 10 8 times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to ∼ 10 8 times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

Degeneracy, degree, and heavy tails in quantum annealing

“…As for why U 5 1 instances show more of a heavy tail than U 3 1 instances, the cause is unknown but we provide one possible explanation: U 5 1 instances contain more active couplers inside each unit cell of the Chimera graph, which may lead to the development of 1 instances show comparable tails at large R (low success probability) for DW2X and SA. For U 4 1 instances, the DW2X results show the same characteristic heavy tail seen for SQA in Ref.…”

“…Fig. 13 shows performance scaling on U 3 1 , U 4 1 , U 5 1 , and U 6 1 instances. These results suggest that several threads of research that probed for computational advantage in U 6 1 problems [2, 9, 10] might be more successfully directed towards U 3 1 problems.…”

“…The recent development of quantum annealing (QA) processors has spurred research into how to construct input instances-Ising spin instances-that might confirm or refute any purported computational advantage conferred by such hardware [1][2][3][4][5][6][7][8][9][10]. These recent works have proposed various important considerations such as error sensitivity, thermal hardness [10], ground state degeneracy, consistency of energy scale across a random ensemble [6,7], potential barrier shape [4,5], and the existence of classical phase transitions [8].…”

“…These recent works have proposed various important considerations such as error sensitivity, thermal hardness [10], ground state degeneracy, consistency of energy scale across a random ensemble [6,7], potential barrier shape [4,5], and the existence of classical phase transitions [8]. In parallel to this line of research is the consideration of suitable performance metrics for exact and approximate optimization [9,11,12].…”

Quantum Associative Memory with Quantum Neural Network via Adiabatic Hamiltonian Evolution

“…In fact, Dwave Systems Inc. has developed a quantum processor composed of 512 qubits [1], [2], and this achievement could be a breakthrough for the development of quantum computing architectures. Hence, quantum annealing (QA) [3], which is the quantum version of simulated annealing [4] and is realized via adiabatic Hamiltonian evolution, has been demonstrated, although the range of application was restricted [5]. On the other hand, the development of new algorithms is still necessary for practical applications, despite the fact that a small number of powerful quantum algorithms have been proposed [6], [7].…”