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 171Yb+ ion-qubit and inject engineered noise $$\left( { \propto \hat \sigma _z} \right)$$∝σ^z to 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 correlated $$\hat \sigma _z$$σ^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 correlated $$\hat \sigma _x$$σ^x or $$\hat \sigma _y$$σ^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.Quantum verification: the complications of temporally correlated noiseExperiments reveal that the presence of correlated noise may compromise the interpretation of techniques for the validation of quantum hardware. A team led by Michael Biercuk at Australia’s University of Sydney and National Measurement Institute, carried out experiments on a single trapped 171Yb+ ion to test the reliability of widespread techniques for characterisation, validation and verification of quantum hardware. Although error processes are often assumed to be statistically independent, in practice slowly varying external fields may introduce temporal correlations in noise. The experiments revealed that the outcome of randomised benchmarking and gate-set tomography differ substantially in presence of correlated noise, and reveal an unexpected sequence-dependent behaviour. These results demonstrate that the reliability of standard performance benchmarking techniques is strongly influenced by the statistical properties of the noise affecting the hardware, complicating direct comparisons between experiments.