Operational, gauge-free quantum tomography

Olivia Di Matteo1,2,3, John Gamble4, Chris Granade4, Kenneth Rudinger5, and Nathan Wiebe4,6,7

1TRIUMF, Vancouver, British Columbia, Canada V6T2A3
2Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, Canada
3Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada
4Microsoft Research, Quantum Architectures and Computation Group, Redmond, Washington 98052, USA
5Quantum Performance Laboratory, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
6Department of Physics, University of Washington, Seattle, WA 98195, USA
7Pacific Northwest National Laboratory, Richland, WA 99352, USA

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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 is $\textit{tomography}$, 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 (the $\textit{gauge problem}$). 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.

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