Stim: a fast stabilizer circuit simulator

Craig Gidney

Google Inc., Santa Barbara, California 93117, USA

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Abstract

This paper presents “Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the $inverse$ of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.

Quantum stabilizer circuits are simple enough to be efficiently simulated, but rich enough to represent important quantum effects like teleportation and error correction. Stim can analyze many stabilizer circuits tens of times faster than previous tools, and then collect samples tens of thousands of times faster than previous tools. This is useful because analyzing and simulating stabilizer circuits is a foundational part of quantum error correction research.

► BibTeX data

► References

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[84] Antonio deMarti iOlius and Josu Etxezarreta Martinez, "The closed-branch decoder for quantum LDPC codes", arXiv:2402.01532, (2024).

[85] Linnea Grans-Samuelsson, Ryan V. Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P. da Silva, and Parsa Bonderson, "Improved Pairwise Measurement-Based Surface Code", arXiv:2310.12981, (2023).

[86] Daniel Bochen Tan, Murphy Yuezhen Niu, and Craig Gidney, "A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing", arXiv:2404.18369, (2024).

[87] Sophia Fuhui Lin, Eric C. Peterson, Krishanu Sankar, and Prasahnt Sivarajah, "Spatially parallel decoding for multi-qubit lattice surgery", arXiv:2403.01353, (2024).

[88] Thomas R. Scruby, Timo Hillmann, and Joschka Roffe, "High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory", arXiv:2406.14445, (2024).

[89] Daniel Hothem, Ashe Miller, and Timothy Proctor, "What is my quantum computer good for? Quantum capability learning with physics-aware neural networks", arXiv:2406.05636, (2024).

[90] Evan T. Hockings, Andrew C. Doherty, and Robin Harper, "Scalable noise characterisation of syndrome extraction circuits with averaged circuit eigenvalue sampling", arXiv:2404.06545, (2024).

[91] Remmy Zen, Jan Olle, Luis Colmenarez, Matteo Puviani, Markus Müller, and Florian Marquardt, "Quantum Circuit Discovery for Fault-Tolerant Logical State Preparation with Reinforcement Learning", arXiv:2402.17761, (2024).

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

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

[94] Christophe Piveteau, Christopher T. Chubb, and Joseph M. Renes, "Tensor Network Decoding Beyond 2D", arXiv:2310.10722, (2023).

[95] Amit Jamadagni, Andreas M. Läuchli, and Cornelius Hempel, "Benchmarking Quantum Computer Simulation Software Packages: State Vector Simulators", arXiv:2401.09076, (2024).

[96] Timo Hillmann, Lucas Berent, Armanda O. Quintavalle, Jens Eisert, Robert Wille, and Joschka Roffe, "Localized statistics decoding: A parallel decoding algorithm for quantum low-density parity-check codes", arXiv:2406.18655, (2024).

[97] Misty A. Wahl, Andrea Mari, Nathan Shammah, William J. Zeng, and Gokul Subramanian Ravi, "Zero noise extrapolation on logical qubits by scaling the error correction code distance", arXiv:2304.14985, (2023).

[98] David Winderl, Qunsheng Huang, Arianne Meijer-van de Griend, and Richie Yeung, "Architecture-Aware Synthesis of Stabilizer Circuits from Clifford Tableaus", arXiv:2309.08972, (2023).

[99] Younghun Kim, Martin Sevior, and Muhammad Usman, "Transversal CNOT gate with multi-cycle error correction", arXiv:2406.12267, (2024).

[100] Hengyun Zhou, Chen Zhao, Madelyn Cain, Dolev Bluvstein, Casey Duckering, Hong-Ye Hu, Sheng-Tao Wang, Aleksander Kubica, and Mikhail D. Lukin, "Algorithmic Fault Tolerance for Fast Quantum Computing", arXiv:2406.17653, (2024).

[101] Naphan Benchasattabuse, Michal Hajdušek, and Rodney Van Meter, "Architecture and protocols for all-photonic quantum repeaters", arXiv:2306.03748, (2023).

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

[103] Dimitrios Thanos, Tim Coopmans, and Alfons Laarman, "Fast equivalence checking of quantum circuits of Clifford gates", arXiv:2308.01206, (2023).

[104] Kieran Young, Marcus Scese, and Ali Ebnenasir, "Simulating Quantum Computations on Classical Machines: A Survey", arXiv:2311.16505, (2023).

[105] Jason D. Chadwick, Christopher Kang, Joshua Viszlai, Sophia Fuhui Lin, and Frederic T. Chong, "Averting multi-qubit burst errors in surface code magic state factories", arXiv:2405.00146, (2024).

[106] Wang Fang and Mingsheng Ying, "SymPhase: Phase Symbolization for Fast Simulation of Stabilizer Circuits", arXiv:2311.03906, (2023).

[107] Wang Fang and Mingsheng Ying, "Symbolic Execution for Quantum Error Correction Programs", arXiv:2311.11313, (2023).

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

[109] Jannis Ruh and Simon Devitt, "Quantum Circuit Optimisation and MBQC Scheduling with a Pauli Tracking Library", arXiv:2405.03970, (2024).

[110] Brendan Reid, "A simple method for compiling quantum stabilizer circuits", arXiv:2404.19408, (2024).

[111] Jintae Kim, Jung Hoon Han, and Isaac H. Kim, "Fault-tolerant Quantum Error Correction Using a Linear Array of Emitters", arXiv:2403.01376, (2024).

[112] Srikar Chundury, Jiajia Li, In-Saeng Suh, and Frank Mueller, "DiaQ: Efficient State-Vector Quantum Simulation", arXiv:2405.01250, (2024).

[113] Allyson Silva, Xiangyi Zhang, Zak Webb, Mia Kramer, Chan Woo Yang, Xiao Liu, Jessica Lemieux, Ka-Wai Chen, Artur Scherer, and Pooya Ronagh, "Multi-qubit Lattice Surgery Scheduling", arXiv:2405.17688, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 10:38:27) and SAO/NASA ADS (last updated successfully 2024-07-15 10:38:28). The list may be incomplete as not all publishers provide suitable and complete citation data.