Optimized Experiment Design and Analysis for Fully Randomized Benchmarking

Kwiatkowski, Alex

Graduate Thesis Or Dissertation

Optimized Experiment Design and Analysis for Fully Randomized Benchmarking Public Deposited

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Citations

Citeable URL: https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/79407z849

Abstract

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using a final measurement step to determine ‘success’ or ‘failure’ for each trial. The probabilities of success and failure over many trials can be used to determine an effective depolarizing error per step of the sequence, which is a metric of the gate quality. This thesis investigates the advantages of fully randomized benchmarking, where a new random sequence is drawn for each experimental trial. The advantages of full randomization include smaller confidence intervals on the inferred step error, the ability to use maximum likelihood analysis without heuristics, straightforward optimization of the sequence lengths, and the ability to model and measure behaviors that go beyond the typical assumption of time-independent error rates. We discuss concrete models of time-dependent or non-Markovian errors that generalize the basic RB model of a single exponential decay of the success probability. For any of these models, we implement an experiment-design protocol to minimize the uncertainty of the estimated parameters with a fixed constraint on the time for the complete experiment. Furthermore, we consider several previously published experiments and determine the potential for improvements with optimized full randomization. We observe such improvements in Clifford randomized benchmarking experiments run by our collaborators on a single trapped ion qubit at the National Institute of Standards and Technology (NIST). We also provide native-gate decompositions for future one and two qubit RB experiments in trapped ions, including an implementation of a convenient two-qubit two-design that has not been used previously for RB. Finally, we study non-Markovian errors in RB, where error processes involve an interaction with an arbitrary quantum environment. In the case of gate-independent non-Markovian errors, we put a concrete bound on the non-monotonicity of success probabilities.

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