Accelerating Grover Adaptive Search: Qubit and Gate Count Reduction Strategies with Higher-Order Formulations

TL;DR

This paper introduces higher-order binary formulations for Grover adaptive search that significantly reduce qubit and gate counts, enhancing efficiency for binary optimization problems.

Contribution

It presents novel strategies involving polynomial factorization and order reduction to improve GAS performance and resource efficiency.

Findings

Reduced qubit and gate requirements for GAS.

Enhanced convergence performance of GAS.

Applicable to general combinatorial optimization problems.

Abstract

Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this paper, we propose higher-order binary formulations that can simultaneously reduce the numbers of qubits and gates required for GAS. Specifically, we consider two novel strategies: one that reduces the number of gates through polynomial factorization, and the other that halves the order of the objective function, subsequently decreasing circuit runtime and implementation cost. Our analysis demonstrates that the proposed higher-order formulations improve the convergence performance of GAS by both reducing the search space size and the number of quantum gates. Our strategies are also beneficial for general combinatorial optimization problems using one-hot encoding.