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Published April 29, 2024 | in press
Journal Article Open

Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays

Xu, Qian ORCID icon
Bonilla Ataides, J. Pablo ORCID icon
Pattison, Christopher A.
Raveendran, Nithin ORCID icon
Bluvstein, Dolev ORCID icon
Wurtz, Jonathan ORCID icon
Vasić, Bane ORCID icon
Lukin, Mikhail D. ORCID icon
Jiang, Liang ORCID icon
Zhou, Hengyun ORCID icon

Abstract

Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, potentially enabling low-overhead fault-tolerant quantum computing. However, implementing qLDPC codes involves nonlocal operations that require long-range connectivity between qubits. This makes their physical realization challenging in comparison to geometrically local codes, such as the surface code. Here we propose a hardware-efficient scheme for fault-tolerant quantum computation with high-rate qLDPC codes that is compatible with the recently demonstrated capabilities of reconfigurable atom arrays. Our approach utilizes the product structure inherent in many qLDPC codes to implement the nonlocal syndrome extraction circuit through atom rearrangement, resulting in an effectively constant overhead. We prove the fault tolerance of these protocols, and our simulations show that the qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits. We further find that quantum algorithms involving thousands of logical qubits can be performed using less than 105 physical qubits. Our work suggests that low-overhead quantum computing with qLDPC codes is within reach using current experimental technologies.

Copyright and License

© The Author(s), under exclusive licence to Springer Nature Limited 2024.

Acknowledgement

We acknowledge helpful discussions with D. Bandyopadhyay, N. Breuckmann, M. Cain, L. Cohen, C. Duckering, S. Ebadi, S. Evered, X. Gao, S. Geim, M. Kalinowski, S. Li, J. Liu, T. Manovitz, B. Matuz, N. Maskara, Q. Nguyen, H. P. Nautrup, D. Orsucci, N. Rengaswamy, M. Vasmer, P. Yu and H. Zheng, among others. We particularly thank A. Krishna for detailed feedback on our results and paper. We are grateful for the support from the University of Chicago Research Computing Center for assistance with numerical simulations. This work was supported by the Army Research Office (ARO; Grant No. W911NF-23-1-0077 to Q.X. and L.J.), ARO Multidisciplinary University Research Initiatives (MURI; Grant No. W911NF-21-1-0325 to Q.X. and L.J. and Grant No. W911NF-20-1-0082 to J.P.B.A., D.B., M.D.L. and H.Z.), Air Force Office of Scientific Research MURI (Grant Nos. FA9550-19-1-0399 and FA9550-21-1-0209 to Q.X. and L.J. and Grant No. FA9550-19-1-0360 to C.A.P.), the National Science Foundation (NSF; Grant Nos. OMA-1936118, ERC-1941583 and OMA-2137642 to Q.X. and L.J. and Grant Nos. CCF-2313084, CIF-1855879, CCF-2100013 and CIF-2106189 to N.R. and B.V.), NTT Research (L.J.), the Packard Foundation (Grant No. 2020-71479 to L.J.), the Quantum Systems Accelerator Center of the US Department of Energy (Grant Nos. 7568717 and DE-SC0021013 to J.P.B.A., D.B., M.D.L. and H.Z.), the Center for Ultracold Atoms (Grant No. NSF PHY-1734011 to J.P.B.A., D.B., M.D.L. and H.Z.), the NSF Institute for Quantum Information and Matter (C.A.P.), the Optimization with Noisy Intermediate-Scale Quantum Devices programme of the Defense Advanced Research Projects Agency (Grant No. W911NF2010021 to D.B., J.W., M.D.L. and H.Z.), the NSF Graduate Research Fellowship Program (Grant No. DGE1745303 to D.B.), the Fannie and John Hertz Foundation (D.B.), and the Ramsay Centre for Western Civilisation (J.P.B.A.).

Contributions

These authors contributed equally: Qian Xu, J. Pablo Bonilla Ataides.

M.D.L. and L.J. conceived the project. Q.X., J.P.B.A. and C.A.P. performed the numerical simulations. Q.X., J.P.B.A., C.A.P. and H.Z. proved the fault tolerance of the schemes. H.Z. identified the correspondence between product codes and product optical tools, H.Z. and Q.X. devised efficient implementations of various codes, and D.B. verified the experimental feasibility of the proposal. J.W. and H.Z. devised the 1D log-depth rearrangement algorithm. N.R. constructed the LP codes used in the simulations. All authors contributed to the design of the methodology and data analysis. All authors contributed to the writing of the paper. All work was supervised by B.V., M.D.L., L.J. and H.Z.

Data Availability

The data collected and analysed in this article are available at https://doi.org/10.5281/zenodo.8278063 (ref. 65). Source data are provided with this paper.

Extended Data Fig. 1 Product structure of HGP codes and LP codes.

Extended Data Fig. 2 Efficient non-intersecting rearrangement in log-depth.

Extended Data Fig. 3 Illustration of ordering of operations in pipelined syndrome extraction.

Extended Data Fig. 4 Achievable logical failure rates of the HGP codes with different idling error strengths.

Supplementary Discussion and Figs. 1–10.

Supplementary Video 1

Source Data for Fig. 1

Code Availability

All codes used to generate the figures are available upon request.

Conflict of Interest

M.D.L. is a co-founder and shareholder of QuEra Computing. J.W and H.Z. are employees of QuEra Computing. The other authors declare no competing interests.

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