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.

中文翻译：

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量子计算机上的资源高效布尔函数求解器


非线性布尔方程组在广泛的应用中发挥着重要作用。Grover 算法是求解量子计算机上非线性布尔方程组的最著名的量子搜索算法之一。在本文中，我们提出了三种新技术来提高 Grover 算法框架下的效率。W 周期电路构造引入了一种递归思想，在给定固定数量的量子比特的情况下，增加布尔方程的可求解数量。然后，提出了一种贪婪压缩技术来降低 oracle 电路深度。最后，随机 Grover 算法随机选择一个方程子集，在每次迭代时形成一个随机预言机，这进一步减少了电路深度和辅助量子比特的数量。布尔二次方程的数值结果证明了所提出的技术的效率。