Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model

TL;DR

This paper introduces a solvable spin system model to analyze quantum annealing bottlenecks, revealing noise amplification effects that impact tunneling rates and success probabilities, supported by both theoretical solutions and empirical simulations.

Contribution

It presents a solvable model of spin systems with bottlenecks, demonstrating noise amplification effects and analyzing their impact on quantum annealing performance.

Findings

Noise amplification scales with the number of qubits $N$.

Success probability at bottlenecks can be close to 50%.

Model predictions are supported by D-Wave 2X simulations.

Abstract

To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits $N$ in the limit that $N\to \infty$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground-state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.