Evaluation of Quantum Machines by Combining Gate Expressivity, Entanglement Capability, and Fidelity Metrics

The design space of current quantum computers has become expansive, with no technology or architecture clearly asserting themselves as the only viable candidate. From this fact, a clear question arises: "How well can a particular machine represent a given a quantum algorithm?''. This paper explores and analyzes generic fidelity models that directly compare the performance of two quantum machines for a given algorithm. This procedure allows us to evaluate the trade off between gate expressivity, entanglement capability, and fidelity. Utilizing a bottom-up synthesis technique, we run these models on a wide range of quantum algorithms, and show that the decision boundaries between machines differ greatly with respect to the incoming algorithm. We see that for several low-entanglement gates such as the ₄√ (CNOT) and √(ISWAP) are able to offer similar performance to maximum entangling gates at similar gate fidelities for important circuits such as TFIM, QFT, and QAE. On the other hand, high expressibility gates such as the B Gate seem to offer limited advantage across many circuits. We offer insight into these differences by looking at the underlying structures that appear at the unitary level and how they vary by gate set.