A Silicon Surface Code Architecture Resilient Against Leakage Errors

Zhenyu Cai; Michael A. Fogarty; Simon Schaal; Sofia Patomäki; Simon C. Benjamin; John J. L. Morton

doi:10.22331/q-2019-12-09-212

A Silicon Surface Code Architecture Resilient Against Leakage Errors

Zhenyu Cai^1,2, Michael A. Fogarty^1,3, Simon Schaal³, Sofia Patomäki^1,3, Simon C. Benjamin^1,2, and John J. L. Morton^1,3,4

¹Quantum Motion Technologies Ltd, Nexus, Discovery Way, Leeds, West Yorkshire, LS2 3AA, United Kingdom
²Department of Materials, University of Oxford, Oxford, OX1 3PH, United Kingdom
³London Centre for Nanotechnology, UCL, 17-19 Gordon St, London, WC1H 0AH, United Kingdom
⁴Dept. of Electronic and Electrical Engineering, UCL, London, WC1E 7JE, United Kingdom

Published:	2019-12-09, volume 3, page 212
Eprint:	arXiv:1904.10378v3
Doi:	https://doi.org/10.22331/q-2019-12-09-212
Citation:	Quantum 3, 212 (2019).

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Abstract

Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98% fidelity and are improving rapidly. However, there are other types of error --- such as charge leakage and propagation --- that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. We propose a surface code architecture for silicon quantum dot spin qubits that is robust against leakage errors by incorporating multi-electron mediator dots. Charge leakage in the qubit dots is transferred to the mediator dots via charge relaxation processes and then removed using charge reservoirs attached to the mediators. A stabiliser-check cycle, optimised for our hardware, then removes the correlations between the residual physical errors. Through simulations we obtain the surface code threshold for the charge leakage errors and show that in our architecture the damage due to charge leakage errors is reduced to a similar level to that of the usual depolarising gate noise. Spin leakage errors in our architecture are constrained to only ancilla qubits and can be removed during quantum error correction via reinitialisations of ancillae, which ensure the robustness of our architecture against spin leakage as well. Our use of an elongated mediator dots creates spaces throughout the quantum dot array for charge reservoirs, measuring devices and control gates, providing the scalability in the design.

► BibTeX data

@article{Cai2019siliconsurfacecode,
  doi = {10.22331/q-2019-12-09-212},
  url = {https://doi.org/10.22331/q-2019-12-09-212},
  title = {A {S}ilicon {S}urface {C}ode {A}rchitecture {R}esilient {A}gainst {L}eakage {E}rrors},
  author = {Cai, Zhenyu and Fogarty, Michael A. and Schaal, Simon and Patom{\"{a}}ki, Sofia and Benjamin, Simon C. and Morton, John J. L.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {3},
  pages = {212},
  month = dec,
  year = {2019}
}

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[2] Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B. Hastings, and Marcus P. da Silva, "Performance of Planar Floquet Codes with Majorana-Based Qubits", PRX Quantum 4 1, 010310 (2023).

[3] C. C. Bultink, T. E. O’Brien, R. Vollmer, N. Muthusubramanian, M. W. Beekman, M. A. Rol, X. Fu, B. Tarasinski, V. Ostroukh, B. Varbanov, A. Bruno, and L. DiCarlo, "Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements", Science Advances 6 12, eaay3050 (2020).

[4] S. Schaal, I. Ahmed, J. A. Haigh, L. Hutin, B. Bertrand, S. Barraud, M. Vinet, C.-M. Lee, N. Stelmashenko, J. W. A. Robinson, J. Y. Qiu, S. Hacohen-Gourgy, I. Siddiqi, M. F. Gonzalez-Zalba, and J. J. L. Morton, "Fast Gate-Based Readout of Silicon Quantum Dots Using Josephson Parametric Amplification", Physical Review Letters 124 6, 067701 (2020).

[5] Xiaosi Xu, Simon C. Benjamin, and Xiao Yuan, "Variational Circuit Compiler for Quantum Error Correction", Physical Review Applied 15 3, 034068 (2021).

[6] Natalie C. Brown, Andrew Cross, and Kenneth R. Brown, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 286 (2020) ISBN:978-1-7281-8969-7.

[7] Zhenyu Cai, Adam Siegel, and Simon Benjamin, "Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device", PRX Quantum 4 2, 020345 (2023).

[8] Yu Shi and Edo Waks, "Error metric for non-trace-preserving quantum operations", Physical Review A 108 3, 032609 (2023).

[9] Jingyu Duan, Michael A. Fogarty, James Williams, Louis Hutin, Maud Vinet, and John J. L. Morton, "Remote Capacitive Sensing in Two-Dimensional Quantum-Dot Arrays", Nano Letters 20 10, 7123 (2020).

[10] Natalie C. Brown, Andrew W. Cross, and Kenneth R. Brown, "Critical faults of leakage errors on the surface code", arXiv:2003.05843, (2020).

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