Boosting quantum annealing performance through direct polynomial unconstrained binary optimization

TL;DR

This paper demonstrates that formulating optimization problems as polynomial unconstrained binary optimization (PUBO) instead of quadratic (QUBO) can significantly reduce qubit requirements and potentially exponentially speed up quantum annealing, enhancing resource efficiency.

Contribution

It introduces the use of PUBO formulations for quantum annealing, showing advantages in qubit savings and scaling, with empirical evidence suggesting exponential speedup potential over QUBO.

Findings

PUBO formulations reduce qubit requirements.

PUBO can lead to exponentially faster annealing times.

Different 3-SAT instances show varying hardness levels.

Abstract

Quantum annealing aims at solving optimization problems of practical relevance using quantum-computing hardware. Problems of interest are typically formulated in terms of quadratic unconstrained binary optimization (QUBO) Hamiltonians. However, many optimization problems are much more naturally formulated in terms of polynomial unconstrained binary optimization (PUBO) functions of higher order. As we show with various problem examples, leveraging the PUBO formulation can bring considerable savings in terms of required number of qubits. Moreover, in numerical benchmarks for the paradigmatic 3-SAT problem, we find scenarios where the scaling of the minimum energy gap during the optimization sweep differs significantly, suggesting the possibility of an exponentially faster annealing time when using the PUBO as compared to the QUBO formulation. This advantage persists even when considering the overhead caused by the higher-order interactions necessary for PUBO cost Hamiltonians. As an interesting side effect, the analysis on minimum energy gaps of different 3-SAT instance generators reveals different degrees of hardness, which will be of interest also for classical benchmark calculations. Our findings show a promising path to improving the resource efficiency and sweeping speed of quantum annealing protocols on both analog and digital platforms, which are important prerequisites when aiming at solving larger optimization problems with relevance to industry.