Abstract
As increasingly impressive quantum information processors are realized in laboratories around the world, robust and reliable characterization of these devices is now more urgent than ever. These diagnostics can take many forms, but one of the most popular categories istomography, where an underlying parameterized model is proposed for a device and inferred by experiments. Here, we introduce and implement efficient operational tomography, which uses experimental observables as these model parameters. This addresses a problem of ambiguity in representation that arises in current tomographic approaches (thegauge problem). Solving the gauge problem enables us to efficiently implement operational tomography in a Bayesian framework computationally, and hence gives us a natural way to include prior information and discuss uncertainty in fit parameters. We demonstrate this new tomography in a variety of different experimentally-relevant scenarios, including standard process tomography, Ramsey interferometry, randomized benchmarking, and gate set tomography.
Highlights
Background for randomized benchmarkingRB makes use of random elements of the Clifford group, which for one qubit is constructed using two generators, C = H, S, whereH = √1 1 1, and S = 1 0 . (25)Up to a phase, C contains 24 elements
We introduce operational quantum tomography (OQT), which is a general framework that allows us to reason about a host of different tomographic procedures in a manifestly gauge-independent manner
The left column of plots compares the likelihoods predicted for the test sequences from the OQT posterior distribution to the likelihoods of the ’perfect’ gate, the experimental counts, and the gate set reconstructed in [17] using the pyGSTi software package
Summary
RB makes use of random elements of the Clifford group, which for one qubit is constructed using two generators, C = H, S , where. We begin by preparing a known state ρψ, and apply a randomly chosen sequence of Clifford elements. This is followed by applying the element that is the inverse of the group element formed by the sequence (not just performing the sequence backwards). If there are no errors in the Clifford gates, the action of the sequence and its inverse would cancel, leaving the state exactly as we found it. We can compute what is termed the survival probability of the original state. As the sequences increase in length, the survival probability decays, as errors accumulate.
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