Resource Efficient Boolean Function Solver on Quantum Computer

TL;DR

This paper introduces three innovative techniques to enhance the efficiency of solving nonlinear boolean equations on quantum computers using Grover's algorithm, focusing on circuit depth, qubit usage, and recursive problem scaling.

Contribution

It presents a recursive W-cycle circuit, a greedy compression method, and a randomized oracle approach to improve quantum boolean solver performance.

Findings

Numerical results show improved efficiency in solving boolean quadratic equations.

The techniques reduce circuit depth and qubit requirements.

The methods enable solving larger boolean systems with fewer resources.

Abstract

Nonlinear boolean equation systems play an important role in a wide range of applications. Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear boolean equation system on quantum computers. In this paper, we propose three novel techniques to improve the efficiency under Grover's algorithm framework. A W-cycle circuit construction introduces a recursive idea to increase the solvable number of boolean equations given a fixed number of qubits. Then, a greedy compression technique is proposed to reduce the oracle circuit depth. Finally, a randomized Grover's algorithm randomly chooses a subset of equations to form a random oracle every iteration, which further reduces the circuit depth and the number of ancilla qubits. Numerical results on boolean quadratic equations demonstrate the efficiency of the proposed techniques.