Average-computation benchmarking for local expectation values in digital quantum devices

Abstract

As quantum devices progress towards a quantum advantage regime, they become harder to benchmark. A particularly relevant challenge is to assess the quality of the whole computation, beyond testing the performance of each single operation. Here we introduce a scheme for this task that combines the target computation with variants of it, which, when averaged, allow for classically solvable correlation functions. Importantly, the variants exactly preserve the circuit architecture and depth, without simplifying the gates into a classically-simulable set. The method is based on replacing each gate by an ensemble of similar gates, which when averaged together form space-time channels [P. Kos and G. Styliaris, Quantum 7, 1020 (2023)]. We introduce explicit constructions for ensembles producing such channels, all applicable to arbitrary brickwork circuits, and provide a general recipe to find new ones through semidefinite programming. The resulting average computation retains important information about the original circuit and is able to detect noise beyond a Clifford benchmarking regime. Moreover, we provide evidence that estimating average-computation expectation values requires running only a limited number of different circuit realizations.

Figures (2)

• Figure 1: Sensitivity to coherent noise. Expectation values are plotted versus the rotation angle in the imprecise T-gate $T=\text{diag}(1,e^{i \phi})$ after five layers of the circuit. Dashed line marks the correct value $\phi=\pi/4$. The three gates are given in Eq. \ref{['gateEX']}. This demonstrates that our benchmarking scheme can detect this type of coherent error, in contrast to Clifford benchmarking. We take the initial state as explained in the End Matter and operator $\sigma_X$ at position $T$.
• Figure 2: Main: Standard deviation $\sigma$ of a local observable's expectation value versus circuit depth ($T$), for operators at position $T-1$, where the average is zero, and at position $T$. The standard deviation is calculated over different circuit realizations, where gates are sampled according to a 4-way reflection ensemble $U_i^{(\pm \pm )}$. Inset: The full distribution of the expectation values $\langle O^{(T)} \rangle$ of different circuit realizations for depths $T=6,14$. The parameters of $U_i^{(\pm \pm )}$ were set to generic values not too far from dual-unitarity, $\theta_z=0.6, \delta_x=\delta_y=0.05$, and we used fixed randomly chosen single-site gates and a fixed operator. The particular choice of single-site gates does not significantly alter the distribution. Their specific values are reported in Sec. III of Appendix.