Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass

TL;DR

This paper investigates how nonstoquastic Hamiltonians can enhance quantum annealing performance on Ising spin glasses, showing they outperform stoquastic ones on harder instances, especially as system size increases.

Contribution

It demonstrates that nonstoquastic Hamiltonians can significantly improve quantum annealing success rates on complex spin glass problems, particularly for difficult instances.

Findings

Nonstoquastic Hamiltonians outperform stoquastic ones on harder instances.

Performance advantage persists with increasing system size.

Frustration in nonstoquastic Hamiltonians may be key to their effectiveness.

Abstract

We study the role of Hamiltonian complexity in the performance of quantum annealers. We consider two general classes of annealing Hamiltonians: stoquastic ones, which can be simulated efficiently using the quantum Monte Carlo algorithm, and nonstoquastic ones, which cannot be treated efficiently. We implement the latter by adding antiferromagnetically coupled two-spin driver terms to the traditionally studied transverse-field Ising model, and compare their performance to that of similar stoquastic Hamiltonians with ferromagnetically coupled additional terms. We focus on a model of long-range Ising spin glass as our problem Hamiltonian and carry out the comparison between the annealers by numerically calculating their success probabilities in solving random instances of the problem Hamiltonian in systems of up to 17 spins. We find that, for a small percentage of mostly harder instances, nonstoquastic Hamiltonians greatly outperform their stoquastic counterparts and their superiority persists as the system size grows. We conjecture that the observed improved performance is closely related to the frustrated nature of nonstoquastic Hamiltonians.