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What Randomized Benchmarking Actually Measures

Physical Review Letters

Proctor, Timothy J.; Rudinger, Kenneth M.; Young, Kevin; Sarovar, Mohan S.; Blume-Kohout, Robin J.

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not a well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. These theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.

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TYPE Journal Article YEAR 2017
ScopusOSTIDOI

Experimental Demonstration of a Cheap and Accurate Phase Estimation

Physical Review Letters

Rudinger, Kenneth M.; Kimmel, Shelby; Lobser, Daniel L.; Maunz, Peter

We demonstrate an experimental implementation of robust phase estimation (RPE) to learn the phase of a single-qubit rotation on a trapped Yb+ ion qubit. We show this phase can be estimated with an uncertainty below 4×10-4 rad using as few as 176 total experimental samples, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We crossvalidate the results of RPE with the more resource-intensive protocol of gate set tomography.

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TYPE Journal Article YEAR 2017
ScopusOSTIDOI

Efficient Gate Set Tomography on a Multi-Qubit Superconducting Processor

Nielsen, Erik N.; Rudinger, Kenneth M.; Blume-Kohout, Robin J.; Bestwick, Andrew B.; Bloom, Benjamin B.; Block, Maxwell B.; Caldwell, Shane M.; Curtis, Michael J.; Hudson, Alex H.; Orgiazzi, Jean-Luc O.; Papageorge, Alexander P.; Polloreno, Anthony P.; Reagor, Matt R.; Rubin, Nicholas R.; Scheer, Michael S.; Selvanayagam, Michael S.; Sete, Eyob S.; Sinclair, Rodney S.; Smith, Robert S.; Vahidpour, Mehrnoosh V.; Villiers, Marius V.; Zeng, William J.; Rigetti, Chad R.

Abstract not provided.

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TYPE Conference Poster YEAR 2017
OSTI

Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography

Nature Communications

Blume-Kohout, Robin J.; Gamble, John K.; Nielsen, Erik N.; Rudinger, Kenneth M.; Mizrahi, Jonathan; Fortier, Kevin M.; Maunz, Peter

Quantum information processors promise fast algorithms for problems inaccessible to classical computers. But since qubits are noisy and error-prone, they will depend on fault-tolerant quantum error correction (FTQEC) to compute reliably. Quantum error correction can protect against general noise if - and only if - the error in each physical qubit operation is smaller than a certain threshold. The threshold for general errors is quantified by their diamond norm. Until now, qubits have been assessed primarily by randomized benchmarking, which reports a different error rate that is not sensitive to all errors, and cannot be compared directly to diamond norm thresholds. Here we use gate set tomography to completely characterize operations on a trapped-Yb+-ion qubit and demonstrate with greater than 95% confidence that they satisfy a rigorous threshold for FTQEC (diamond norm ≤6.7 × 10-4).

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TYPE Journal Article YEAR 2017
ScopusOSTIDOI
Results 51–75 of 102
Results 51–75 of 102