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Protecting expressive circuits with a quantum error detection code

Nature Physics volume 20, pages 219–224 (2024)Cite this article

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Abstract

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing quantum computers. In this context, we develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding k logical qubits into k + 2 physical qubits, this code presents fault-tolerant state-initialization and syndrome-measurement circuits that can detect any single-qubit error. It provides a universal set of local and global logical rotations that have physical support on only two qubits. A high-fidelity—although non fault-tolerant—compilation of this universal gate set is possible thanks to the two-qubit physical rotations present in trapped-ion computers with all-to-all connectivity. Given the particular structure of the logical operators, we nickname it the Iceberg code. We demonstrate the protection of circuits of eight logical qubits with up to 256 layers, saturate the logical quantum volume of 28 and show the positive effect of increasing the frequency of syndrome measurements in the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers.

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Fig. 1: Logical operators and fault-tolerant operations of the Iceberg code.
Fig. 2: Comparing the performance of a random mirror circuit encoded with the Iceberg code against the unencoded circuit.
Fig. 3: Numerical simulations of the performance of random mirror circuits for more logical qubits.
Fig. 4: Passing a QV test with eight logical qubits using the Iceberg code.

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Data availability

The data that support the findings of this study are available at Zenodo45. Source data are provided with this paper.

Code availability

Code to reproduce the findings of this study is available from the corresponding authors on reasonable request.

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Acknowledgements

We thank C. Ryan-Anderson, N. Burdick, B. Neyenhuis, C. Baldwin, Y. Kikuchi, M. Fiorentini, D. Hayes, K. Mayer and Y.H. Chen for fruitful discussions and feedback on the manuscript. The experiments were done using the Quantinuum system model H1-2, powered by Honeywell ion traps.

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  1. Quantinuum, Partnership House, London, UK

    Chris N. Self, Marcello Benedetti & David Amaro

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  1. Chris N. Self
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Contributions

All authors conceived and designed the study. D.A. performed analytic calculations and C.N.S. carried out numerical studies. All authors analysed the data, interpreted the results and wrote the manuscript.

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Correspondence to Chris N. Self, Marcello Benedetti or David Amaro.

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Nature Physics thanks Crystal Noel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Self, C.N., Benedetti, M. & Amaro, D. Protecting expressive circuits with a quantum error detection code. Nat. Phys. 20, 219–224 (2024). https://doi.org/10.1038/s41567-023-02282-2

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