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.
@article{arxiv.2208.09914,
title = {An Implementation of the Quantum Verification of Matrix Products Algorithm},
author = {Elton Pinto},
journal= {arXiv preprint arXiv:2208.09914},
year = {2022}
}