EQUAL: Improving the Fidelity of Quantum Annealers by Injecting Controlled Perturbations

Abstract

Quantum Annealers (QAs) are single-instruction quantum machines that can only sample from the ground state of an energy function, called Hamiltonian. To execute a program, the problem is cast to a Hamiltonian, embedded on the hardware, and a single quantum machine instruction (QMI) is run. Noise and imperfections in hardware result in sub-optimal solutions on QAs even if the QMI is run for thousands of trials. Owing to the limited programmability of QAs, users execute the same QMI for all trials. This subjects all trials to a similar noise profile throughout the execution, resulting in a systematic bias. We observe that systematic bias leads to sub-optimal solutions and cannot be alleviated by executing more trials or using existing error-mitigation schemes. To address this challenge, we propose EQUAL (Ensemble QUantum AnneaLing). EQUAL generates an ensemble of QMIs by adding controlled perturbations to the program QMI. When executed on the QA, the ensemble of QMIs steers the program away from encountering the same bias during all trials and thus, improves the quality of solutions. Our evaluations using the D-Wave 2000Q machine show that EQUAL bridges the difference between the baseline and the ideal by an average of 14% (and up to 26%), without requiring any additional trials. EQUAL can be combined with existing error mitigation schemes to bridge further the difference between the baseline and ideal by an average of 55% (and up to 68%).