Experimental demonstration of perturbative anticrossing mitigation using non-uniform driver Hamiltonians

TL;DR

This paper demonstrates experimentally that using non-uniform driver Hamiltonians in quantum annealing can mitigate perturbative anticrossings, improving success probabilities and sampling fairness in a D-Wave system.

Contribution

The study applies a perturbative approximation-based method to physical quantum annealing hardware, showing practical improvements in overcoming anticrossings.

Findings

Increased minimum eigengaps during annealing.

Higher ground state success probabilities.

Reduced biased sampling of degenerate states.

Abstract

Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous theoretical research sought to alleviate such anticrossings by adjusting the transverse driver Hamiltonians on individual qubits according to a perturbative approximation. Here we apply this principle to a physical implementation of quantum annealing in a D-Wave 2000Q system. We use samples from the quantum annealing hardware and per-qubit anneal offsets to produce nonuniform driver Hamiltonians. On small instances with severe perturbative anticrossings, our algorithm yields an increase in minimum eigengaps, ground state success probabilities, and escape rates from metastable valleys. We also demonstrate that the same approach can mitigate biased sampling of degenerate ground states.