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arXiv · 2310.05013

Resource Efficient Boolean Function Solver on Quantum Computer

Xiang Li·Hanxiang Shen·Weiguo Gao·Yingzhou Li
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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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Xiang Li, Hanxiang Shen, Weiguo Gao, Yingzhou Li. 2023-10-08. Resource Efficient Boolean Function Solver on Quantum Computer. https://doi.org/10.22331/q-2024-10-10-1500

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