  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.
