Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics

Matt McEwen1, Dave Bacon2, and Craig Gidney1

1Google Quantum AI, Santa Barbara, California 93117, USA
2Google Quantum AI, Seattle, Washington 98103, USA

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Abstract

The typical time-independent view of quantum error correction (QEC) codes hides significant freedom in the decomposition into circuits that are executable on hardware. Using the concept of detecting regions, we design time-dynamic QEC circuits directly instead of designing static QEC codes to decompose into circuits. In particular, we improve on the standard circuit constructions for the surface code, presenting new circuits that can embed on a hexagonal grid instead of a square grid, that can use ISWAP gates instead of CNOT or CZ gates, that can exchange qubit data and measure roles, and that move logical patches around the physical qubit grid while executing. All these constructions use no additional entangling gate layers and display essentially the same logical performance, having teraquop footprints within 25% of the standard surface code circuit. We expect these circuits to be of great interest to quantum hardware engineers, because they achieve essentially the same logical performance as standard surface code circuits while relaxing demands on hardware.

QEC is vital for future fault-tolerant quantum computing, and the surface code is one of the most common QEC codes targeted for experimental realization, and has acheivable but difficult circuit requirements: a square grid of qubits capable of performing CNOT/CZ gates at high fidelity. Using the new concept of detecting regions, we design new circuits for implementing the surface code, improving over previous constructions in several ways. In particular, we give circuits that embed on a hexagonal grid instead of a square grid, that can use ISWAP gates instead of CNOT or CZ gates, and that move logical patches around the physical qubit grid while executing. All these constructions use no additional entangling gate layers and display essentially the same logical performance. These new freedoms relax the requirements on hardware, helping enable future implimentations of the surface code.

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Cited by

[1] Earl Campbell, "A series of fast-paced advances in Quantum Error Correction", Nature Reviews Physics 6 3, 160 (2024).

[2] Mingzheng Zhu, Hao Fu, Jun Wu, Chi Zhang, Wei Xie, and Xiang-Yang Li, 2024 IEEE/ACM International Symposium on Code Generation and Optimization (CGO) 158 (2024) ISBN:979-8-3503-9509-9.

[3] V. Srinivasa, J. M. Taylor, and J. R. Petta, "Cavity-Mediated Entanglement of Parametrically Driven Spin Qubits via Sidebands", PRX Quantum 5 2, 020339 (2024).

[4] Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin, "Logical quantum processor based on reconfigurable atom arrays", Nature (2023).

[5] Bence Hetényi and James R. Wootton, "Tailoring quantum error correction to spin qubits", Physical Review A 109 3, 032433 (2024).

[6] Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J. Yoder, "High-threshold and low-overhead fault-tolerant quantum memory", Nature 627 8005, 778 (2024).

[7] Diego Ruiz, Jérémie Guillaud, Anthony Leverrier, Mazyar Mirrahimi, and Christophe Vuillot, "LDPC-cat codes for low-overhead quantum computing in 2D", arXiv:2401.09541, (2024).

[8] Oscar Higgott and Craig Gidney, "Sparse Blossom: correcting a million errors per core second with minimum-weight matching", arXiv:2303.15933, (2023).

[9] J. F. Marques, H. Ali, B. M. Varbanov, M. Finkel, H. M. Veen, S. L. M. van der Meer, S. Valles-Sanclemente, N. Muthusubramanian, M. Beekman, N. Haider, B. M. Terhal, and L. DiCarlo, "All-Microwave Leakage Reduction Units for Quantum Error Correction with Superconducting Transmon Qubits", Physical Review Letters 130 25, 250602 (2023).

[10] Grégoire de Gliniasty, Paul Hilaire, Pierre-Emmanuel Emeriau, Stephen C. Wein, Alexia Salavrakos, and Shane Mansfield, "A Spin-Optical Quantum Computing Architecture", arXiv:2311.05605, (2023).

[11] Hector Bombin, Chris Dawson, Terry Farrelly, Yehua Liu, Naomi Nickerson, Mihir Pant, Fernando Pastawski, and Sam Roberts, "Fault-tolerant complexes", arXiv:2308.07844, (2023).

[12] Craig Gidney, Michael Newman, Peter Brooks, and Cody Jones, "Yoked surface codes", arXiv:2312.04522, (2023).

[13] György P. Gehér, Ophelia Crawford, and Earl T. Campbell, "Tangling Schedules Eases Hardware Connectivity Requirements for Quantum Error Correction", PRX Quantum 5 1, 010348 (2024).

[14] Jiaxuan Zhang, Yu-Chun Wu, and Guo-Ping Guo, "Facilitating Practical Fault-tolerant Quantum Computing Based on Color Codes", arXiv:2309.05222, (2023).

[15] Hector Bombin, Daniel Litinski, Naomi Nickerson, Fernando Pastawski, and Sam Roberts, "Unifying flavors of fault tolerance with the ZX calculus", arXiv:2303.08829, (2023).

[16] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", arXiv:2307.11136, (2023).

[17] Stephanie Simmons, "Scalable Fault-Tolerant Quantum Technologies with Silicon Color Centers", PRX Quantum 5 1, 010102 (2024).

[18] Craig Gidney, "Inplace Access to the Surface Code Y Basis", Quantum 8, 1310 (2024).

[19] Nicolas Delfosse and Adam Paetznick, "Spacetime codes of Clifford circuits", arXiv:2304.05943, (2023).

[20] Adam Siegel, Armands Strikis, Thomas Flatters, and Simon Benjamin, "Adaptive surface code for quantum error correction in the presence of temporary or permanent defects", Quantum 7, 1065 (2023).

[21] V. Srinivasa, J. M. Taylor, and J. R. Petta, "Cavity-mediated entanglement of parametrically driven spin qubits via sidebands", arXiv:2307.06067, (2023).

[22] Craig Gidney and Dave Bacon, "Less Bacon More Threshold", arXiv:2305.12046, (2023).

[23] Craig Gidney and Cody Jones, "New circuits and an open source decoder for the color code", arXiv:2312.08813, (2023).

[24] Mingzheng Zhu, Hao Fu, Jun Wu, Chi Zhang, Wei Xie, and Xiang-Yang Li, "Ecmas: Efficient Circuit Mapping and Scheduling for Surface Code", arXiv:2312.15254, (2023).

[25] Suhas Vittal, Poulami Das, and Moinuddin Qureshi, "ERASER: Towards Adaptive Leakage Suppression for Fault-Tolerant Quantum Computing", arXiv:2309.13143, (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-24 18:38:59) and SAO/NASA ADS (last updated successfully 2024-05-24 18:39:00). The list may be incomplete as not all publishers provide suitable and complete citation data.