Experimental quantum verification in the presence of temporally correlated noise

Abstract

Growth in the capabilities of quantum information hardware mandates access to techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). Our analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped 171 Yb + ion-qubit and inject engineered noise /σ z ð Þto probe protocol performance. Experiments on RB validate predictions that measured fidelities over sequences are described by a gamma distribution varying between approximately Gaussian, and a broad, highly skewed distribution for rapidly and slowly varying noise, respectively. Similarly we find a strong gate set dependence of default experimental GST procedures in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlatedσ z errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlatedσ x orσ y errors or depolarising noise processes, highlighting the impact of the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

On the freedom in representing quantum operations

“…Furthermore, the optimization can change the relative size of errors from different components of the device, leading to misunderstandings about their relative quality. This misidentification of error was recently observed experimentally in a trapped ion processor: in particular, figure 4(h) in [19] demonstrates that the gauge optimization procedure may effectively cancel some gate errors that were purposely added, resulting in a smaller 'diamond norm distance' than expected, which implies unrealistically good quantum gates. In that paper, and in other systems where, for example, a basis change in the classical software is used to achieve certain 'virtual' gates [20,21], experimentalists have a priori information about which operations are better.…”

Trapped-ion quantum computing: Progress and challenges

“…RB was first used to demonstrate average error probabilities of less than 0.5% in π/2 pulses in a 9 Be + qubit [185], and has since become a standard gate characterization tool for QC research. While RB is a good way of extracting stochastic errors that determine gate fidelity, it performs less well in the case of correlated errors-which may be either cancelled out or amplified depending upon the exact random gate series applied-so RB thus provides little information about the magnitude of such correlated errors [191,192]. Although it is a good method of decoupling SPaM errors from gate errors, randomized benchmarking does not fully characterize the gate errors that are present.…”

Dynamically corrected gates suppressing spatiotemporal error correlations as measured by randomized benchmarking

“…The key underlying concept is that in a randomized benchmarking sequence built up from many operations, the resultant net state transformation in the presence of noise,Ũ eff |ψ ( Fig. 1b), is determined by an interplay of both the sensitivity of each individual operation to the noise [35] and the impact of the sequence structure on error accumulation [32,46,48]. Specifically, nominally equivalent randomized benchmarking sequences (constructed to perform the same net operation) exhibit variations in correlated-noise susceptibility that are analytically calculable and verifiable in experiments.…”