Resource Efficient Boolean Function Solver on Quantum Computer

• URL: http://arxiv.org/abs/2310.05013v3
• Date: Tue, 24 Sep 2024 09:10:10 GMT
• Title: Resource Efficient Boolean Function Solver on Quantum Computer
• Authors: Xiang Li, Hanxiang Shen, Weiguo Gao, Yingzhou Li,
• Abstract summary: Grover's algorithm is one of the best-known quantum search algorithms in solving the nonlinear equation system on quantum computers. We propose three novel techniques to improve the iteration efficiency under Grover's framework.
• Score: 7.833656237685403
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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