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Benchmarking quantum processors with a single qubit

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Abstract

The first generation of small noisy quantum processors have recently become available to non-specialists who are not required to understand specifics of the physical platforms and, in particular, the types and sources of noise. As such, it is useful to benchmark the performance of such computers against specific tasks that may be of interest to users, ideally keeping both the circuit depth and width as free parameters. Here, we benchmark the IBM quantum experience using the deterministic quantum computing with 1 qubit (DQC1) algorithm originally proposed by Knill and Laflamme in the context of liquid-state NMR. In the first set of experiments, we use DQC1 as a trace estimation algorithm to benchmark performance with respect to circuit depth. In the second set, we use this trace estimation algorithm to distinguish between knots, a classically difficult task which is known to be complete for DQC1. Our results indicate that the main limiting factor is the depth of the circuit and that both random and systematic errors become an issue when the gate count increases. Surprisingly, we find that at the same gate count wider circuits perform better, probably due to randomization of coherent errors.

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Notes

  1. The initialization procedure works for some fixed \(\alpha \ll 1\) that depends on the parameters of the experiment, and does not scale badly with N.

  2. Repeating experiments is generally not a scalable technique.

  3. However, this is not an apples-to-apples comparison since (without fault tolerance) a 4-qubit machine is expected to outperform a 14-qubit machine in a \(\le 4\)-qubit experiment.

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Acknowledgements

We acknowledge use of the IBM Q for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Q team. This work was partially supported by the CIFAR “Quantum Information Science” program and an NSERC grant “Experimental Quantum Information, Quantum Measurement, and Quantum Foundations With Entangled Photons and Ultracold Atoms” via Aephraim Steinberg’s research group. KBF acknowledges the NSERC PDF program for funding.

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Authors and Affiliations

  1. Department of Physics, Centre for Quantum Information and Quantum Control, University of Toronto, 60 St George St, Toronto, ON, M5S 1A7, Canada

    Oktay Göktaş, Weng Kian Tham, Kent Bonsma-Fisher & Aharon Brodutch

  2. Agnostiq Labs, 100 College St, Toronto, ON, M5G 1L5, Canada

    Oktay Göktaş

  3. National Research Council of Canada, 100 Sussex Dr., Ottawa, ON, K1A 0R6, Canada

    Kent Bonsma-Fisher

  4. The Edward S. Rogers Department of Electrical and Computer Engineering, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada

    Aharon Brodutch

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  1. Oktay Göktaş
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Göktaş, O., Tham, W.K., Bonsma-Fisher, K. et al. Benchmarking quantum processors with a single qubit. Quantum Inf Process 19, 146 (2020). https://doi.org/10.1007/s11128-020-02642-4

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