An Implementation of the Quantum Verification of Matrix Products Algorithm

TL;DR

This paper implements and tests a space-efficient quantum verification algorithm for matrix products using simulators, highlighting current hardware limitations and the impact of simulation methods on circuit complexity.

Contribution

It provides a practical implementation of QVMP, compares simulation techniques, and evaluates scalability and hardware constraints.

Findings

QVMP can be simulated on moderate inputs but not scaled to demonstrate quantum advantage.

Simulation method choice significantly affects circuit size and development speed.

Current hardware limitations prevent observing quantum advantage with QVMP.

Abstract

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.