A Quantum Volume Metric for Qudit Quantum Computers

Qudit-based quantum computers, such as the high-Q superconducting radio frequency
resonator cavities being pursued by the SQMS Center hosted at Fermilab, may provide
computational advantages relative to qubit-based machines for some problems. However,
the novel system’s hardware and software will present different errors that must be
understood and mitigated, along with other unforeseen inefficiencies across the entire stack.
It is essential to benchmark these qudit platforms against existing systems. We propose such
a benchmark by generalizing the qubit-based quantum volume metric to qudit devices. In
particular, we show that the performance depends on the available gateset used to compile
unitary operations, as well as realistic noise sources.