Stim: a fast stabilizer circuit simulator

Craig Gidney

Google Inc., Santa Barbara, California 93117, USA

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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.

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► References

[1] Scott Aaronson and Daniel Gottesman. Improved simulation of stabilizer circuits. Physical Review A, 70 (5): 052328, 2004. 10.1103/​PhysRevA.70.052328.

[2] Thomas Alexander, Lev Bishop, Andrew Cross, Jay Gambetta, Ali Javadi-Abhari, Blake Johnson, and John Smolin. "a new openqasm for a new era of dynamic circuits". https:/​/​​qiskit/​a-new-openqasm-for-a-new-era-of-dynamic-circuits-87f031cac49, 2020. Accessed: 2021-01-26.

[3] Simon Anders and Hans J Briegel. Fast simulation of stabilizer circuits using a graph-state representation. Physical Review A, 73 (2): 022334, 2006. 10.1103/​PhysRevA.73.022334.

[4] Dave Bacon. Operator quantum error-correcting subsystems for self-correcting quantum memories. Physical Review A, 73 (1): 012340, 2006. 10.1103/​PhysRevA.73.012340.

[5] Sergey Bravyi and Dmitri Maslov. Hadamard-free circuits expose the structure of the clifford group. arXiv preprint arXiv:2003.09412, 2020. URL https:/​/​​abs/​2003.09412.

[6] Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard. Simulation of quantum circuits by low-rank stabilizer decompositions. Quantum, 3: 181, 2019. 10.22331/​q-2019-09-02-181.

[7] Kaifeng Bu and Dax Enshan Koh. Efficient classical simulation of clifford circuits with nonstabilizer input states. Physical review letters, 123 (17): 170502, 2019. 10.1103/​PhysRevLett.123.170502.

[8] Rui Chao, Michael E Beverland, Nicolas Delfosse, and Jeongwan Haah. Optimization of the surface code design for majorana-based qubits. Quantum, 4: 352, 2020. 10.22331/​q-2020-10-28-352.

[9] Qiskit Contributors. Qiskit: An open-source framework for quantum computing. 2019. 10.5281/​zenodo.2562110.

[10] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86: 032324, 2012. URL https:/​/​​10.1103/​PhysRevA.86.032324. arXiv:1208.0928.

[11] Craig Gidney and Austin G Fowler. Efficient magic state factories with a catalyzed $|ccz\rangle$ to $2|t\rangle $ transformation. Quantum, 3: 135, 2019. 10.22331/​q-2019-04-30-135.

[12] Craig Gidney, Austin Fowler, and Michael Newman. Informal private conversations about simulation bottlenecks, 2021.

[13] Daniel Gottesman. Stabilizer codes and quantum error correction. arXiv preprint quant-ph/​9705052, 1997. URL https:/​/​​abs/​quant-ph/​9705052.

[14] David Gross. Hudson’s theorem for finite-dimensional quantum systems. Journal of mathematical physics, 47 (12): 122107, 2006. 10.1063/​1.2393152.

[15] Clare Horsman, Austin G Fowler, Simon Devitt, and Rodney Van Meter. Surface code quantum computing by lattice surgery. New Journal of Physics, 14 (12): 123011, 2012. 10.1088/​1367-2630/​14/​12/​123011.

[16] Jakob Nielsen Hořeňovský. "response times: The 3 important limits". https:/​/​​articles/​response-times-3-important-limits/​, 1993. Accessed: 2021-01-26.

[17] Martin Hořeňovský. "generating random numbers using c++ standard library: the problems". https:/​/​​generating-random-numbers-using-c-standard-library-the-problems/​, 2020. Accessed: 2021-01-26.

[18] "Yack" (https:/​/​​users/​11887/​yack). Answer to "how many n-qubit stabilizer states are there?". Quantum Stack Exchange, 2020. URL https:/​/​​a/​11781/​119. URL:https:/​/​​a/​11781/​119 (version: 2021-01-27).

[19] Yifei Huang and Peter Love. Approximate stabilizer rank and improved weak simulation of clifford-dominated circuits for qudits. Physical Review A, 99 (5): 052307, 2019. 10.1103/​PhysRevA.99.052307.

[20] Yifei Huang and Peter Love. Feynman-path-type simulation using stabilizer projector decomposition of unitaries. Physical Review A, 103 (2), February 2021. 10.1103/​physreva.103.022428. URL https:/​/​​10.1103/​physreva.103.022428.

[21] Intel. Intel intrinsics guide (_mm256_and_si256). https:/​/​​sites/​landingpage/​IntrinsicsGuide/​#text=_mm256_and_si256&expand=301, 2021. Accessed: 2021-01-26.

[22] Angela Karanjai, Joel J Wallman, and Stephen D Bartlett. Contextuality bounds the efficiency of classical simulation of quantum processes. arXiv preprint arXiv:1802.07744, 2018. URL https:/​/​​abs/​1802.07744.

[23] Emanuel Knill. Quantum computing with realistically noisy devices. Nature, 434 (7029): 39–44, 2005. 10.1038/​nature03350.

[24] Shota Nagayama, Austin G Fowler, Dominic Horsman, Simon J Devitt, and Rodney Van Meter. Surface code error correction on a defective lattice. New Journal of Physics, 19 (2): 023050, 2017. 10.1088/​1367-2630/​aa5918.

[25] Jakob Nielsen. Usability engineering. Morgan Kaufmann, 1994.

[26] Peter Norvig. "approximate timing for various operations on a typical pc". http:/​/​​21-days.html#answers, 2014. Accessed: 2021-01-26.

[27] Patrick Rall, Daniel Liang, Jeremy Cook, and William Kretschmer. Simulation of qubit quantum circuits via pauli propagation. Physical Review A, 99 (6): 062337, 2019. 10.1103/​PhysRevA.99.062337.

[28] Quantum AI team and collaborators. Cirq, October 2020. URL https:/​/​​10.5281/​zenodo.4062499.

[29] Matthew Ware, Guilhem Ribeill, Diego Riste, Colm Ryan, Blake Johnson, and Marcus P da Silva. Experimental pauli-frame randomization on a superconducting qubit. In APS March Meeting Abstracts, volume 2017, pages L46–004, 2017. 10.1103/​PhysRevA.103.042604.

[30] Wikipedia. Advanced Vector Extensions — Wikipedia, the free encyclopedia. http:/​/​​w/​index.php?title=Advanced%20Vector%20Extensions&oldid=1021841294, 2021. [Online; accessed 11-May-2021].

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[1] Xhek Turkeshi, "Measurement-induced criticality as a data-structure transition", Physical Review B 106 14, 144313 (2022).

[2] Wang Fang and Mingsheng Ying, "Symbolic Execution for Quantum Error Correction Programs", Proceedings of the ACM on Programming Languages 8 PLDI, 1040 (2024).

[3] Piotr Sierant and Xhek Turkeshi, "Controlling Entanglement at Absorbing State Phase Transitions in Random Circuits", Physical Review Letters 130 12, 120402 (2023).

[4] Alex Townsend-Teague, Julio Magdalena de la Fuente, and Markus Kesselring, "Floquetifying the Colour Code", Electronic Proceedings in Theoretical Computer Science 384, 265 (2023).

[5] Leandro Stefanazzi, Kenneth Treptow, Neal Wilcer, Chris Stoughton, Collin Bradford, Sho Uemura, Silvia Zorzetti, Salvatore Montella, Gustavo Cancelo, Sara Sussman, Andrew Houck, Shefali Saxena, Horacio Arnaldi, Ankur Agrawal, Helin Zhang, Chunyang Ding, and David I. Schuster, "The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors", Review of Scientific Instruments 93 4, 044709 (2022).

[6] Thomas Grurl, Jürgen Fuß, and Robert Wille, 2023 IEEE 53rd International Symposium on Multiple-Valued Logic (ISMVL) 141 (2023) ISBN:978-1-6654-6416-1.

[7] Yangsen Ye, Tan He, He-Liang Huang, Zuolin Wei, Yiming Zhang, Youwei Zhao, Dachao Wu, Qingling Zhu, Huijie Guan, Sirui Cao, Fusheng Chen, Tung-Hsun Chung, Hui Deng, Daojin Fan, Ming Gong, Cheng Guo, Shaojun Guo, Lianchen Han, Na Li, Shaowei Li, Yuan Li, Futian Liang, Jin Lin, Haoran Qian, Hao Rong, Hong Su, Shiyu Wang, Yulin Wu, Yu Xu, Chong Ying, Jiale Yu, Chen Zha, Kaili Zhang, Yong-Heng Huo, Chao-Yang Lu, Cheng-Zhi Peng, Xiaobo Zhu, and Jian-Wei Pan, "Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor", Physical Review Letters 131 21, 210603 (2023).

[8] Piotr Sierant and Xhek Turkeshi, "Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions", Physical Review Letters 128 13, 130605 (2022).

[9] Suhas Vittal, Poulami Das, and Moinuddin Qureshi, 56th Annual IEEE/ACM International Symposium on Microarchitecture 509 (2023) ISBN:9798400703294.

[10] Junpyo Kim, Dongmoon Min, Jungmin Cho, Hyeonseong Jeong, Ilkwon Byun, Junhyuk Choi, Juwon Hong, and Jangwoo Kim, Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 1 (2024) ISBN:9798400703850.

[11] 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 626 7997, 58 (2024).

[12] Narges Alavisamani, Suhas Vittal, Ramin Ayanzadeh, Poulami Das, and Moinuddin Qureshi, Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3 818 (2024) ISBN:9798400703867.

[13] Ido Zuk, Daniel Cohen, Alexey V. Gorshkov, and Alex Retzker, "Robust gates with spin-locked superconducting qubits", Physical Review Research 6 1, 013217 (2024).

[14] Nathan Shammah, Anurag Saha Roy, Carmen G. Almudever, Sébastien Bourdeauducq, Anastasiia Butko, Gustavo Cancelo, Susan M. Clark, Johannes Heinsoo, Loïc Henriet, Gang Huang, Christophe Jurczak, Janne Kotilahti, Alessandro Landra, Ryan LaRose, Andrea Mari, Kasra Nowrouzi, Caspar Ockeloen-Korppi, Guen Prawiroatmodjo, Irfan Siddiqi, and William J. Zeng, "Open hardware solutions in quantum technology", APL Quantum 1 1, 011501 (2024).

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

[16] Craig Gidney, Michael Newman, and Matt McEwen, "Benchmarking the Planar Honeycomb Code", Quantum 6, 813 (2022).

[17] Adrien Suau, Gabriel Staffelbach, and Aida Todri-Sanial, "qprof: A gprof-Inspired Quantum Profiler", ACM Transactions on Quantum Computing 4 1, 1 (2023).

[18] Anbang Wu, Gushu Li, Hezi Zhang, Gian Giacomo Guerreschi, Yufei Ding, and Yuan Xie, Proceedings of the 49th Annual International Symposium on Computer Architecture 337 (2022) ISBN:9781450386104.

[19] Misty A. Wahl, Andrea Mari, Nathan Shammah, William J. Zeng, and Gokul Subramanian Ravi, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 888 (2023) ISBN:979-8-3503-4323-6.

[20] Sophia Fuhui Lin, Joshua Viszlai, Kaitlin N. Smith, Gokul Subramanian Ravi, Charles Yuan, Frederic T. Chong, and Benjamin J. Brown, Proceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2 216 (2024) ISBN:9798400703850.

[21] Jaime Alvarado-Valiente, Javier Romero-Álvarez, Enrique Moguel, José García-Alonso, and Juan M. Murillo, "Technological diversity of quantum computing providers: a comparative study and a proposal for API Gateway integration", Software Quality Journal (2023).

[22] Thien Nguyen, Dmitry Lyakh, Eugene Dumitrescu, David Clark, Jeff Larkin, and Alexander McCaskey, "Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale", ACM Transactions on Quantum Computing 4 1, 1 (2023).

[23] Theerapat Tansuwannont, Balint Pato, and Kenneth R. Brown, "Adaptive syndrome measurements for Shor-style error correction", Quantum 7, 1075 (2023).

[24] Kenton M. Barnes, Tomasz Bialas, Okan Buğdayci, Earl T. Campbell, Neil I. Gillespie, Kauser Johar, Ram Rajan, Adam W. Richardson, Luka Skoric, Canberk Topal, Mark L. Turner, and Abbas B. Ziad, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 375 (2023) ISBN:979-8-3503-4323-6.

[25] Michael A. Perlin, Vickram N. Premakumar, Jiakai Wang, Mark Saffman, and Robert Joynt, "Fault-tolerant measurement-free quantum error correction with multiqubit gates", Physical Review A 108 6, 062426 (2023).

[26] Daan Camps, Ermal Rrapaj, Katherine Klymko, Brian Austin, and Nicholas J. Wright, ISC High Performance 2024 Research Paper Proceedings (39th International Conference) 1 (2024) ISBN:978-3-9826336-0-2.

[27] Victor Wei, W. A. Coish, Pooya Ronagh, and Christine A. Muschik, "Neural-shadow quantum state tomography", Physical Review Research 6 2, 023250 (2024).

[28] P. Sierant and X. Turkeshi, "Entanglement and Absorbing State Transitions in (d+1)-Dimensional Stabilizer Circuits", Acta Physica Polonica A 144 6, 474 (2023).

[29] Qian Xu, J. Pablo Bonilla Ataides, Christopher A. Pattison, Nithin Raveendran, Dolev Bluvstein, Jonathan Wurtz, Bane Vasić, Mikhail D. Lukin, Liang Jiang, and Hengyun Zhou, "Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays", Nature Physics (2024).

[30] Niel de Beaudrap and Steven Herbert, "Fast Stabiliser Simulation with Quadratic Form Expansions", Quantum 6, 803 (2022).

[31] Samson Wang, Sam McArdle, and Mario Berta, "Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra", PRX Quantum 5 2, 020324 (2024).

[32] Younghun Kim, Jeongsoo Kang, and Younghun Kwon, "Design of quantum error correcting code for biased error on heavy-hexagon structure", Quantum Information Processing 22 6, 230 (2023).

[33] Daniel Tandeitnik and Thiago Guerreiro, "Evolving quantum circuits", Quantum Information Processing 23 3, 109 (2024).

[34] Alexander Tianlin Hu and Andrey Boris Khesin, "Improved graph formalism for quantum circuit simulation", Physical Review A 105 2, 022432 (2022).

[35] Dimitrios Thanos, Tim Coopmans, and Alfons Laarman, Lecture Notes in Computer Science 14216, 199 (2023) ISBN:978-3-031-45331-1.

[36] Kaavya Sahay, Junlan Jin, Jahan Claes, Jeff D. Thompson, and Shruti Puri, "High-Threshold Codes for Neutral-Atom Qubits with Biased Erasure Errors", Physical Review X 13 4, 041013 (2023).

[37] Jaime Alvarado-Valiente, Javier Romero-Álvarez, Danel Arias, Erik B. Terres, Jose Garcia-Alonso, Enrique Moguel, Pablo García Bringas, and Juan M. Murillo, Lecture Notes in Computer Science 14001, 180 (2023) ISBN:978-3-031-40724-6.

[38] Robin Harper and Steven T. Flammia, "Learning Correlated Noise in a 39-Qubit Quantum Processor", PRX Quantum 4 4, 040311 (2023).

[39] Avimita Chatterjee, Koustubh Phalak, and Swaroop Ghosh, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 70 (2023) ISBN:979-8-3503-4323-6.

[40] Leopoldo Sarra, Kevin Ellis, and Florian Marquardt, "Discovering quantum circuit components with program synthesis", Machine Learning: Science and Technology 5 2, 025029 (2024).

[41] Benjamin Bichsel, Anouk Paradis, Maximilian Baader, and Martin Vechev, "Abstraqt: Analysis of Quantum Circuits via Abstract Stabilizer Simulation", Quantum 7, 1185 (2023).

[42] Xhek Turkeshi, Marco Schirò, and Piotr Sierant, "Measuring nonstabilizerness via multifractal flatness", Physical Review A 108 4, 042408 (2023).

[43] Soronzonbold Otgonbaatar and Dieter Kranzlmüller, "Exploiting the Quantum Advantage for Satellite Image Processing: Review and Assessment", IEEE Transactions on Quantum Engineering 5, 1 (2024).

[44] Mingyu Kang, Wesley C. Campbell, and Kenneth R. Brown, "Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion", PRX Quantum 4 2, 020358 (2023).

[45] Satvik Maurya, Chaithanya Naik Mude, William D. Oliver, Benjamin Lienhard, and Swamit Tannu, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[46] Jianxin Chen, Dawei Ding, Cupjin Huang, and Linghang Kong, "Linear cross-entropy benchmarking with Clifford circuits", Physical Review A 108 5, 052613 (2023).

[47] Piotr Sierant, Marco Schirò, Maciej Lewenstein, and Xhek Turkeshi, "Entanglement Growth and Minimal Membranes in ( d+1 ) Random Unitary Circuits", Physical Review Letters 131 23, 230403 (2023).

[48] Eric Kubischta and Ian Teixeira, "Family of Quantum Codes with Exotic Transversal Gates", Physical Review Letters 131 24, 240601 (2023).

[49] Stefano Markidis, Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis 1478 (2023) ISBN:9798400707858.

[50] Oscar Higgott, "PyMatching: A Python Package for Decoding Quantum Codes with Minimum-Weight Perfect Matching", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[51] Áron Márton and János K. Asbóth, "Coherent errors and readout errors in the surface code", Quantum 7, 1116 (2023).

[52] Ilkwon Byun, Junpyo Kim, Dongmoon Min, Ikki Nagaoka, Kosuke Fukumitsu, Iori Ishikawa, Teruo Tanimoto, Masamitsu Tanaka, Koji Inoue, and Jangwoo Kim, Proceedings of the 49th Annual International Symposium on Computer Architecture 366 (2022) ISBN:9781450386104.

[53] Thomas Grurl, Christoph Pichler, Jürgen Fuß, and Robert Wille, 2023 36th International Conference on VLSI Design and 2023 22nd International Conference on Embedded Systems (VLSID) 301 (2023) ISBN:979-8-3503-4678-7.

[54] Jason Gavriel, Daniel Herr, Alexis Shaw, Michael J. Bremner, Alexandru Paler, and Simon J. Devitt, "Transversal injection for direct encoding of ancilla states for non-Clifford gates using stabilizer codes", Physical Review Research 5 3, 033019 (2023).

[55] Vivien Vandaele, Simon Martiel, Simon Perdrix, and Christophe Vuillot, " Optimal Hadamard gate count for Clifford + T synthesis of Pauli rotations sequences ", ACM Transactions on Quantum Computing 3639062 (2023).

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

[57] Madhav Krishnan Vijayan, Alexandru Paler, Jason Gavriel, Casey R Myers, Peter P Rohde, and Simon J Devitt, "Compilation of algorithm-specific graph states for quantum circuits", Quantum Science and Technology 9 2, 025005 (2024).

[58] Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown, "Anyon Condensation and the Color Code", PRX Quantum 5 1, 010342 (2024).

[59] Max McGinley, Sthitadhi Roy, and S. A. Parameswaran, "Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems", Physical Review Letters 129 9, 090404 (2022).

[60] Thomas R. Scruby, Michael Vasmer, and Dan E. Browne, "Non-Pauli errors in the three-dimensional surface code", Physical Review Research 4 4, 043052 (2022).

[61] 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).

[62] György P. Gehér, Campbell McLauchlan, Earl T. Campbell, Alexandra E. Moylett, and Ophelia Crawford, "Error-corrected Hadamard gate simulated at the circuit level", Quantum 8, 1394 (2024).

[63] Craig Gidney, "A Pair Measurement Surface Code on Pentagons", Quantum 7, 1156 (2023).

[64] Asim Sharma and Avah Banerjee, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 82 (2023) ISBN:979-8-3503-4323-6.

[65] Guglielmo Lami and Mario Collura, "Unveiling the Stabilizer Group of a Matrix Product State", Physical Review Letters 133 1, 010602 (2024).

[66] Lucas Berent, Lukas Burgholzer, and Robert Wille, Proceedings of the 28th Asia and South Pacific Design Automation Conference 709 (2023) ISBN:9781450397834.

[67] Suhas Vittal, Poulami Das, and Moinuddin Qureshi, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[68] Luka Skoric, Dan E. Browne, Kenton M. Barnes, Neil I. Gillespie, and Earl T. Campbell, "Parallel window decoding enables scalable fault tolerant quantum computation", Nature Communications 14 1, 7040 (2023).

[69] Yilun Zhao, Yu Chen, He Li, Ying Wang, Kaiyan Chang, Bingmeng Wang, Bing Li, and Yinhe Han, 2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD) 1 (2023) ISBN:979-8-3503-2225-5.

[70] Piotr Sierant, Marco Schirò, Maciej Lewenstein, and Xhek Turkeshi, "Measurement-induced phase transitions in (d+1) -dimensional stabilizer circuits", Physical Review B 106 21, 214316 (2022).

[71] Balint Pato, Theerapat Tansuwannont, Shilin Huang, and Kenneth R. Brown, "Optimization Tools for Distance-Preserving Flag Fault-Tolerant Error Correction", PRX Quantum 5 2, 020336 (2024).

[72] Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell, "Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes", Physical Review X 13 3, 031007 (2023).

[73] Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton, "A Fault-Tolerant Honeycomb Memory", Quantum 5, 605 (2021).

[74] Neereja Sundaresan, Theodore J. Yoder, Youngseok Kim, Muyuan Li, Edward H. Chen, Grace Harper, Ted Thorbeck, Andrew W. Cross, Antonio D. Córcoles, and Maika Takita, "Demonstrating multi-round subsystem quantum error correction using matching and maximum likelihood decoders", Nature Communications 14 1, 2852 (2023).

[75] Johannes Nokkala, Jyrki Piilo, and Ginestra Bianconi, "Complex quantum networks: a topical review", Journal of Physics A: Mathematical and Theoretical 57 23, 233001 (2024).

[76] Tanmay Singal, Che Chiang, Eugene Hsu, Eunsang Kim, Hsi-Sheng Goan, and Min-Hsiu Hsieh, "Counting stabiliser codes for arbitrary dimension", Quantum 7, 1048 (2023).

[77] Sascha Heußen, Don Winter, Manuel Rispler, and Markus Müller, "Dynamical subset sampling of quantum error-correcting protocols", Physical Review Research 6 1, 013177 (2024).

[78] Kaitlin N. Smith, Michael A. Perlin, Pranav Gokhale, Paige Frederick, David Owusu-Antwi, Richard Rines, Victory Omole, and Frederic Chong, Proceedings of the 50th Annual International Symposium on Computer Architecture 1 (2023) ISBN:9798400700958.

[79] Matt McEwen, Dave Bacon, and Craig Gidney, "Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics", Quantum 7, 1172 (2023).

[80] Manuel H. Muñoz-Arias, Stefanos Kourtis, and Alexandre Blais, "Low-depth Clifford circuits approximately solve MaxCut", Physical Review Research 6 2, 023294 (2024).

[81] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[82] Antonio deMarti iOlius, Patricio Fuentes, Román Orús, Pedro M. Crespo, and Josu Etxezarreta Martinez, "Decoding algorithms for surface codes", arXiv:2307.14989, (2023).

[83] Qian Xu, J. Pablo Bonilla Ataides, Christopher A. Pattison, Nithin Raveendran, Dolev Bluvstein, Jonathan Wurtz, Bane Vasic, Mikhail D. Lukin, Liang Jiang, and Hengyun Zhou, "Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays", arXiv:2308.08648, (2023).

[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.