Grover Adaptive Search for Constrained Polynomial Binary Optimization

TL;DR

This paper presents an efficient oracle construction for Grover Adaptive Search to solve constrained polynomial binary optimization problems, demonstrating potential quadratic speed-up with simulations and real quantum hardware experiments.

Contribution

It introduces a novel method for constructing efficient oracles for GAS in CPBO problems, including QUBO, applicable to higher-degree polynomials and constraints.

Findings

Demonstrated potential quadratic speed-up in portfolio optimization QUBO.

Developed efficient oracle construction methods for GAS.

Validated approach with simulations and real quantum hardware experiments.

Abstract

In this paper we discuss Grover Adaptive Search (GAS) for Constrained Polynomial Binary Optimization (CPBO) problems, and in particular, Quadratic Unconstrained Binary Optimization (QUBO) problems, as a special case. GAS can provide a quadratic speed-up for combinatorial optimization problems compared to brute force search. However, this requires the development of efficient oracles to represent problems and flag states that satisfy certain search criteria. In general, this can be achieved using quantum arithmetic, however, this is expensive in terms of Toffoli gates as well as required ancilla qubits, which can be prohibitive in the near-term. Within this work, we develop a way to construct efficient oracles to solve CPBO problems using GAS algorithms. We demonstrate this approach and the potential speed-up for the portfolio optimization problem, i.e. a QUBO, using simulation and experimental results obtained on real quantum hardware. However, our approach applies to higher-degree polynomial objective functions as well as constrained optimization problems.