We present the implementation of Grover’s algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation and bitwise exclusive or. Our implementation provides the means to assess with precision the scaling of the number of gates and depth of a full-fledged quantum circuit designed to find the preimages of a given hash digest. The detailed construction of the quantum oracle shows that the presence of AND gates, OR gates, shifts of bits and the reuse of the initial state along the computation require extra quantum resources as compared with other hash functions based on modular additions, XOR gates and rotations. We also track the entanglement entropy present in the quantum register at every step along the computation, showing that it becomes maximal at the inner core of the first action of the quantum oracle, which implies that no classical simulation based on tensor networks would be of relevance. Finally, we show that strategies that suggest a shortcut based on sampling the quantum register after a few steps of Grover’s algorithm can only provide some marginal practical advantage in terms of error mitigation.

我们介绍了在量子模拟器中执行Grover算法的算法，以对两个缩放的哈希函数的原像执行量子搜索，其设计仅使用模块化加法，字旋转和按位异或。我们的实现提供了一种方法，可以精确地评估门的数量和成熟的量子电路的深度的缩放比例，该成熟的量子电路旨在查找给定哈希摘要的原像。量子oracle的详细构造表明，与其他基于模块加法，XOR门和旋转的哈希函数相比，与门，或门，位的移位以及初始状态在计算中的重复使用与其他哈希函数相比，需要额外的量子资源。 。我们还跟踪计算过程中每一步量子寄存器中存在的纠缠熵，这表明它在量子先知的第一个作用的内在核心处变得最大，这意味着基于张量网络的经典模拟将不相关。最后，我们表明，在采取格罗弗算法几步后，基于对量子寄存器进行采样的方法提出了一种捷径，该策略仅能在减少错误方面提供一些边际的实际优势。