We present a space-efficient implementation of the quantum verification of matrix products (QVMP) algorithm and demonstrate its functionality by running it on the Aer simulator with two simulation methods: statevector and matrix product state (MPS). We report circuit metrics (gate count, qubit count, circuit depth), transpilation time, simulation time, and a proof of Grover oracle correctness. Our study concludes that while QVMP can be simulated on moderately sized inputs, it cannot scale to a degree where we can observe any quantum advantage on current quantum hardware due to circuit depth and qubit count constraints. Further, the choice of simulation method has a noticeable impact on the size of the transpiled circuit which slows down development.

翻译：我们提出了对矩阵产品量子核查(QVMP)算法的空间高效实施,并通过使用两种模拟方法在Aer模拟器上运行来展示其功能:州和矩阵产品状态(MPS),我们报告电路测量(门数、qubit 计数、电路深度)、移转时间、模拟时间以及格罗佛或甲骨骼正确性的证据。我们的研究结论是,虽然QVMP可以模拟中度大小的输入,但无法达到我们能够观察到由于电路深度和qubit 计数限制而使当前量子硬件在量子上的任何优势的程度。此外,模拟方法的选择对加速发展的转动电路的大小有明显的影响。