What is the Computational Value of Finite Range Tunneling?

TL;DR

This paper demonstrates that finite range tunneling in quantum annealing provides significant computational advantages over classical algorithms like simulated annealing and quantum Monte Carlo, especially for problems with tall, narrow energy barriers.

Contribution

The study provides empirical evidence that finite range tunneling offers a substantial speedup in quantum annealing compared to classical and emulated quantum algorithms, and discusses implications for future hardware design.

Findings

Quantum annealer outperforms simulated annealing by up to 10^8 times on specific problems.

Quantum annealer is up to 10^8 times faster than optimized Quantum Monte Carlo simulations.

For certain classical problems, quantum-inspired algorithms scale better than simulated annealing.

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 $\sim 10^8$ 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 $\sim 10^8$ 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.