System-level Figure of Merit

This section introduces the different figures of merit employed to evaluate quantum computers at a system-level. Some figure of merti are system-dependent while others can be used on any system.

System independent figure of merit

Minimum distinguishability cost

The minimum distinguishability cost is a figure of merit introduced in the AppQSim benchmark suite by E. Granet et al. [1].

Let’s consider a fixed size circuit composed of n_g gates. Let \(t\) the ideal expectation value of this circuit, \(m\) the obtained expectation value from the quantum computer, \(\sigma^2\) the variance of the ideal expectation value, the aim is to compute the optimal number of shots S such that: \(\frac{(t-m)^2}{\sigma^2}*S = 0.997\)

The final distinguishability score is then: \(S = n_g * S\)

References

1. [1]E. Granet and H. Dreyer, “AppQSim: Application-oriented benchmarks for Hamiltonian simulation on a quantum computer,” Physical Review Research, vol. 7, no. 4, p. 043146, 2025.