Resource Efficient Boolean Function Solver on Quantum Computer
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.
Cite
@article{arxiv.2310.05013,
title = {Resource Efficient Boolean Function Solver on Quantum Computer},
author = {Xiang Li and Hanxiang Shen and Weiguo Gao and Yingzhou Li},
journal= {arXiv preprint arXiv:2310.05013},
year = {2024}
}