Machine-learning-assisted correction of correlated qubit errors in a topological code
1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands
2QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands
Published: | 2018-01-29, volume 2, page 48 |
Eprint: | arXiv:1705.07855v3 |
Doi: | https://doi.org/10.22331/q-2018-01-29-48 |
Citation: | Quantum 2, 48 (2018). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
A fault-tolerant quantum computation requires an efficient means to detect and correct errors that accumulate in encoded quantum information. In the context of machine learning, neural networks are a promising new approach to quantum error correction. Here we show that a recurrent neural network can be trained, using only experimentally accessible data, to detect errors in a widely used topological code, the surface code, with a performance above that of the established minimum-weight perfect matching (or blossom) decoder. The performance gain is achieved because the neural network decoder can detect correlations between bit-flip (X) and phase-flip (Z) errors. The machine learning algorithm adapts to the physical system, hence no noise model is needed. The long short-term memory layers of the recurrent neural network maintain their performance over a large number of quantum error correction cycles, making it a practical decoder for forthcoming experimental realizations of the surface code.
![](https://quantum-journal.org/wp-content/uploads/2018/01/1705.07855v3.png)
Popular summary
► BibTeX data
► References
[1] D. A. Lidar, T. A. Brun, editors, Quantum error correction (Cambridge University Press, 2013).
[2] B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
https://doi.org/10.1103/RevModPhys.87.307
[3] A. G. Fowler, A. C. Whiteside, and L. C. L. Hollenberg, Towards practical classical processing for the surface code, Phys. Rev. Lett. 108, 180501 (2012).
https://doi.org/10.1103/PhysRevLett.108.180501
[4] S. B. Bravyi and A. Yu. Kitaev, Quantum codes on a lattice with boundary, arXiv:quant-ph/9811052.
arXiv:quant-ph/9811052
[5] D. S. Wang, A. G. Fowler, and L. C. L. Hollenberg, Surface code quantum computing with error rates over 1$\%$, Phys. Rev. A 83, 020302 (2011).
https://doi.org/10.1103/PhysRevA.83.020302
[6] 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).
https://doi.org/10.1103/PhysRevA.86.032324
[7] Yu Tomita and K. M. Svore. Low-distance surface codes under realistic quantum noise, Phys. Rev. A 90, 062320 (2014).
https://doi.org/10.1103/PhysRevA.90.062320
[8] J. R. Wootton, A. Peter, J. R. Winkler, and D. Loss, Proposal for a minimal surface code experiment, Phys. Rev. A 96, 032338 (2017).
https://doi.org/10.1103/PhysRevA.96.032338
[9] N. H. Nickerson, Error correcting power of small topological codes, arXiv:1609.01753.
arXiv:1609.01753
[10] G. Torlai and R. G. Melko, Neural decoder for topological codes, Phys. Rev. Lett. 119, 030501 (2017).
https://doi.org/10.1103/PhysRevLett.119.030501
[11] R. Rojas, Neural Networks, (Springer, Berlin, Heidelberg, 1996).
https://doi.org/10.1007/978-3-642-61068-4
[12] Y. Bengio, Learning deep architectures for AI, Foundations and Trends in Machine Learning 2, 1 (2009).
https://doi.org/10.1561/2200000006
[13] S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: From theory to algorithms (Cambridge University Press, 2014).
[14] A. Yu. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Physics 303, 2 (2003).
https://doi.org/10.1016/S0003-4916(02)00018-0
[15] J. Edmonds, Paths, trees, and flowers, Canad. J. Math. 17, 449 (1965).
https://doi.org/10.4153/CJM-1965-045-4
[16] E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, Topological quantum memory, J. Math. Phys. 43, 4452 (2002).
https://doi.org/10.1063/1.1499754
[17] A. G. Fowler, Minimum weight perfect matching of fault-tolerant topological quantum error correction in average $O(1)$ parallel time, Quantum Inf. Comput. 15, 0145 (2015).
[18] S. Varsamopoulos, B. Criger, and K. Bertels, Decoding small surface codes with feedforward neural networks, Quantum Sci. Technol. 3, 015004 (2018).
https://doi.org/10.1088/2058-9565/aa955a
[19] S. Krastanov and L. Jiang, Deep neural network probabilistic decoder for stabilizer codes, Sci. Rep. 7, 11003 (2017).
https://doi.org/10.1038/s41598-017-11266-1
[20] J. Kelly, R. Barends, A. G. Fowler, A. Megrant, E. Jeffrey, T. C. White, D. Sank, J. Y. Mutus, B. Campbell, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, I.-C. Hoi, C. Neill, P. J. J. O'Malley, C. Quintana, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, State preservation by repetitive error detection in a superconducting quantum circuit, Nature 519, 66 (2015).
https://doi.org/10.1038/nature14270
[21] M. Takita, A. D. Córcoles, E. Magesan, B. Abdo, M. Brink, A. Cross, J. M. Chow, and J. M. Gambetta, Demonstration of weight-four parity measurements in the surface code architecture, Phys. Rev. Lett. 117, 210505 (2016).
https://doi.org/10.1103/PhysRevLett.117.210505
[22] R. Versluis, S. Poletto, N. Khammassi, B. Tarasinski, N. Haider, D. J. Michalak, A. Bruno, K. Bertels, and L. DiCarlo, Scalable quantum circuit and control for a superconducting surface code, Phys. Rev. Applied 8, 034021 (2017).
https://doi.org/10.1103/PhysRevApplied.8.034021
[23] P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
https://doi.org/10.1103/PhysRevA.52.R2493
[24] A. Steane, Multiple-particle interference and quantum error correction, Proc. Royal Soc. A 452, 2551 (1996).
https://doi.org/10.1098/rspa.1996.0136
[25] D. Gottesman, Stabilizer codes and quantum error correction (Doctoral dissertation, California Institute of Technology, 1997).
[26] M.-H. Hsieh and F. Le Gall, NP-hardness of decoding quantum error-correction codes, Phys. Rev. A 83, 052331 (2011).
https://doi.org/10.1103/PhysRevA.83.052331
[27] S. Bravyi, M. Suchara, and A. Vargo, Efficient algorithms for maximum likelihood decoding in the surface code, Phys. Rev. A 90, 032326 (2014).
https://doi.org/10.1103/PhysRevA.90.032326
[28] T. E. O'Brien, B. Tarasinski, and L. DiCarlo, Density-matrix simulation of small surface codes under current and projected experimental noise, npj Quantum Information 3, 39 (2017). The source code of the quantum simulator can be found at https://github.com/brianzi/quantumsim. The source code of the Surface-17 simulation can be found at https://github.com/obriente/surf17_circuit.
https://doi.org/10.1038/s41534-017-0039-x
[29] The source code of the blossom decoder can be found at https://github.com/obriente/qgarden.
https://github.com/obriente/qgarden
[30] B. Heim, K. M. Svore, and M. B. Hastings, Optimal circuit-level decoding for surface codes, arXiv:1609.06373.
arXiv:1609.06373
[31] H. Bombin, and M. A. Martin-Delgado, Optimal resources for topological two-dimensional stabilizer codes: Comparative study, Phys. Rev. A 76, 012305 (2007).
https://doi.org/10.1103/PhysRevA.76.012305
[32] A. G. Fowler, Optimal complexity correction of correlated errors in the surface code, arXiv:1310.0863.
arXiv:1310.0863
[33] S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural Computation 9, 1735 (1997).
https://doi.org/10.1162/neco.1997.9.8.1735
[34] W. Zaremba, I. Sutskever, and O. Vinyals, Recurrent neural network regularization, arXiv:1409.2329.
arXiv:1409.2329
[35] N. Delfosse and J.-P. Tillich, A decoding algorithm for CSS codes using the X/Z correlations, 2014 IEEE International Symposium on Information Theory, 1071 (2014).
https://doi.org/10.1109/ISIT.2014.6874997
[36] B. Criger and I. Ashraf, Multi-path summation for decoding 2D topological codes, arXiv:1709.02154.
arXiv:1709.02154
[37] G. Duclos-Cianci and D. Poulin, Fast decoders for topological quantum codes, Phys. Rev. Lett. 104, 050504 (2010).
https://doi.org/10.1103/PhysRevLett.104.050504
[38] A. Hutter, J. R. Wootton, and D. Loss, Efficient Markov chain Monte Carlo algorithm for the surface code, Phys. Rev. A 89, 022326 (2014).
https://doi.org/10.1103/PhysRevA.89.022326
[39] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefowicz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, R. Monga, S. Moore, D. Murray, C. Olah, M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng, TensorFlow: Large-scale machine learning on heterogeneous distributed systems, arXiv:1603.04467.
arXiv:1603.04467
[40] The source code of the neural network decoder can be found at https://github.com/baireuther/ neural_network_decoder.
https://github.com/baireuther/neural_network_decoder
[41] The source code of the error model can be found at https://github.com/baireuther/circuit_model.
https://github.com/baireuther/circuit_model
[42] C. Horsman, A. G. Fowler, S. Devitt, and R. van Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
https://doi.org/10.1088/1367-2630/14/12/123011
[43] D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
arXiv:1412.6980
[44] G. E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov, Improving neural networks by preventing co-adaptation of feature detectors, arXiv:1207.0580.
arXiv:1207.0580
Cited by
[1] Ramon W. J. Overwater, Masoud Babaie, and Fabio Sebastiano, "Neural-Network Decoders for Quantum Error Correction Using Surface Codes: A Space Exploration of the Hardware Cost-Performance Tradeoffs", IEEE Transactions on Quantum Engineering 3, 1 (2022).
[2] Laia Domingo Colomer, Michalis Skotiniotis, and Ramon Muñoz-Tapia, "Reinforcement learning for optimal error correction of toric codes", Physics Letters A 384 17, 126353 (2020).
[3] Ying-Jie 英杰 Qu 曲, Zhao 钊 Chen 陈, Wei-Jie 伟杰 Wang 王, and Hong-Yang 鸿洋 Ma 马, "Approximate error correction scheme for three-dimensional surface codes based reinforcement learning", Chinese Physics B 32 10, 100307 (2023).
[4] Ettore Canonici, Stefano Martina, Riccardo Mengoni, Daniele Ottaviani, and Filippo Caruso, "Machine Learning based Noise Characterization and Correction on Neutral Atoms NISQ Devices", Advanced Quantum Technologies 7 1, 2300192 (2024).
[5] Brhyeton Hall, Spiro Gicev, and Muhammad Usman, "Artificial neural network syndrome decoding on IBM quantum processors", Physical Review Research 6 3, L032004 (2024).
[6] Alireza Seif, Kevin A Landsman, Norbert M Linke, Caroline Figgatt, C Monroe, and Mohammad Hafezi, "Machine learning assisted readout of trapped-ion qubits", Journal of Physics B: Atomic, Molecular and Optical Physics 51 17, 174006 (2018).
[7] Kenneth Rudinger, Timothy Proctor, Dylan Langharst, Mohan Sarovar, Kevin Young, and Robin Blume-Kohout, "Probing Context-Dependent Errors in Quantum Processors", Physical Review X 9 2, 021045 (2019).
[8] Javier Valls, Francisco Garcia-Herrero, Nithin Raveendran, and Bane Vasic, "Syndrome-Based Min-Sum vs OSD-0 Decoders: FPGA Implementation and Analysis for Quantum LDPC Codes", IEEE Access 9, 138734 (2021).
[9] Lingling Lao and Carmen G. Almudever, "Fault-tolerant quantum error correction on near-term quantum processors using flag and bridge qubits", Physical Review A 101 3, 032333 (2020).
[10] Stefanie Czischek, Springer Theses 53 (2020) ISBN:978-3-030-52714-3.
[11] Andrew S. Darmawan and David Poulin, "Linear-time general decoding algorithm for the surface code", Physical Review E 97 5, 051302 (2018).
[12] Chenfeng Cao, Chao Zhang, Zipeng Wu, Markus Grassl, and Bei Zeng, "Quantum variational learning for quantum error-correcting codes", Quantum 6, 828 (2022).
[13] Milap Sheth, Sara Zafar Jafarzadeh, and Vlad Gheorghiu, "Neural ensemble decoding for topological quantum error-correcting codes", Physical Review A 101 3, 032338 (2020).
[14] Ye-Hua Liu and David Poulin, "Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes", Physical Review Letters 122 20, 200501 (2019).
[15] Haowen Wang, Zhaoyang Song, Yinuo Wang, Yanbing Tian, and Hongyang Ma, "Target-generating quantum error correction coding scheme based on generative confrontation network", Quantum Information Processing 21 8, 280 (2022).
[16] Fan 帆 Li 李, Ao-Qing 熬庆 Li 李, Qi-Di 启迪 Gan 甘, and Hong-Yang 鸿洋 Ma 马, "Recurrent neural network decoding of rotated surface codes based on distributed strategy", Chinese Physics B 33 4, 040307 (2024).
[17] E. Flurin, L. S. Martin, S. Hacohen-Gourgy, and I. Siddiqi, "Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations", Physical Review X 10 1, 011006 (2020).
[18] V. Saggio, B. E. Asenbeck, A. Hamann, T. Strömberg, P. Schiansky, V. Dunjko, N. Friis, N. C. Harris, M. Hochberg, D. Englund, S. Wölk, H. J. Briegel, and P. Walther, "Experimental quantum speed-up in reinforcement learning agents", Nature 591 7849, 229 (2021).
[19] Andrey Zhukov and Walter Pogosov, "Quantum error reduction with deep neural network applied at the post-processing stage", Quantum Information Processing 21 3, 93 (2022).
[20] Thomas Fösel, Petru Tighineanu, Talitha Weiss, and Florian Marquardt, "Reinforcement Learning with Neural Networks for Quantum Feedback", Physical Review X 8 3, 031084 (2018).
[21] S. Varona and M. A. Martin-Delgado, "Determination of the semion code threshold using neural decoders", Physical Review A 102 3, 032411 (2020).
[22] Jing Hao Chai and Hui Khoon Ng, "On the Fault‐Tolerance Threshold for Surface Codes with General Noise", Advanced Quantum Technologies 5 10, 2200008 (2022).
[23] Savvas Varsamopoulos, Koen Bertels, and Carmen Garcia Almudever, "Comparing Neural Network Based Decoders for the Surface Code", IEEE Transactions on Computers 69 2, 300 (2020).
[24] 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).
[25] Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie Vogt-Maranto, and Lenka Zdeborová, "Machine learning and the physical sciences", Reviews of Modern Physics 91 4, 045002 (2019).
[26] Patricio Fuentes, Josu Etxezarreta Martinez, Pedro M. Crespo, and Javier Garcia-Frias, "Approach for the construction of non-Calderbank-Steane-Shor low-density-generator-matrix–based quantum codes", Physical Review A 102 1, 012423 (2020).
[27] Juan Carrasquilla and Giacomo Torlai, "How To Use Neural Networks To Investigate Quantum Many-Body Physics", PRX Quantum 2 4, 040201 (2021).
[28] I. A. Simakov, I. S. Besedin, and A. V. Ustinov, "Simulation of the five-qubit quantum error correction code on superconducting qubits", Physical Review A 105 3, 032409 (2022).
[29] Dong Suk Kang and Shimeng Yu, "Time-Based Compute-in-Memory for Cryogenic Neural Network With Successive Approximation Register Time-to-Digital Converter", IEEE Journal on Exploratory Solid-State Computational Devices and Circuits 8 2, 128 (2022).
[30] Leonid P. Pryadko, "On maximum-likelihood decoding with circuit-level errors", Quantum 4, 304 (2020).
[31] David Fitzek, Mattias Eliasson, Anton Frisk Kockum, and Mats Granath, "Deep Q-learning decoder for depolarizing noise on the toric code", Physical Review Research 2 2, 023230 (2020).
[32] Nikolas P. Breuckmann and Xiaotong Ni, "Scalable Neural Network Decoders for Higher Dimensional Quantum Codes", Quantum 2, 68 (2018).
[33] Bobak Toussi Kiani, Giacomo De Palma, Milad Marvian, Zi-Wen Liu, and Seth Lloyd, "Learning quantum data with the quantum earth mover’s distance", Quantum Science and Technology 7 4, 045002 (2022).
[34] Hao-Wen Wang , Qian Cao , Yun-Jia Xue , Li Ding , Han-Yang Liu , Yu-Min Dong , and Hong-Yang Ma , "Determining quantum topological semion code decoder performance and error correction effectiveness with reinforcement learning", Frontiers in Physics 10, 981225 (2022).
[35] Eric Sabo, Arun B. Aloshious, and Kenneth R. Brown, "Trellis Decoding for Qudit Stabilizer Codes and Its Application to Qubit Topological Codes", IEEE Transactions on Quantum Engineering 5, 1 (2024).
[36] Xiaotong Ni, "Neural Network Decoders for Large-Distance 2D Toric Codes", Quantum 4, 310 (2020).
[37] Konstantin Tiurev, Peter-Jan H. S. Derks, Joschka Roffe, Jens Eisert, and Jan-Michael Reiner, "Correcting non-independent and non-identically distributed errors with surface codes", Quantum 7, 1123 (2023).
[38] Rouven Koch and Jose L. Lado, "Designing quantum many-body matter with conditional generative adversarial networks", Physical Review Research 4 3, 033223 (2022).
[39] Christopher Chamberland, Luis Goncalves, Prasahnt Sivarajah, Eric Peterson, and Sebastian Grimberg, "Techniques for combining fast local decoders with global decoders under circuit-level noise", Quantum Science and Technology 8 4, 045011 (2023).
[40] Christopher Chamberland and Pooya Ronagh, "Deep neural decoders for near term fault-tolerant experiments", Quantum Science and Technology 3 4, 044002 (2018).
[41] Dominik Koutný, Libor Motka, Zdeněk Hradil, Jaroslav Řeháček, and Luis L. Sánchez-Soto, "Neural-network quantum state tomography", Physical Review A 106 1, 012409 (2022).
[42] Oleksandr Balabanov and Mats Granath, "Unsupervised interpretable learning of topological indices invariant under permutations of atomic bands", Machine Learning: Science and Technology 2 2, 025008 (2021).
[43] Simone Bordoni and Stefano Giagu, "Convolutional neural network based decoders for surface codes", Quantum Information Processing 22 3, 151 (2023).
[44] Andrey Zhukov and Walter Pogosov, "Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics", Quantum Information Processing 23 3, 80 (2024).
[45] Simone Cantori, Andrea Mari, David Vitali, and Sebastiano Pilati, "Synergy between noisy quantum computers and scalable classical deep learning for quantum error mitigation", EPJ Quantum Technology 11 1, 45 (2024).
[46] Ryan Sweke, Markus S Kesselring, Evert P L van Nieuwenburg, and Jens Eisert, "Reinforcement learning decoders for fault-tolerant quantum computation", Machine Learning: Science and Technology 2 2, 025005 (2021).
[47] Stefan Krastanov and Liang Jiang, "Deep Neural Network Probabilistic Decoder for Stabilizer Codes", Scientific Reports 7 1, 11003 (2017).
[48] Naomi H. Nickerson and Benjamin J. Brown, "Analysing correlated noise on the surface code using adaptive decoding algorithms", Quantum 3, 131 (2019).
[49] Vedran Dunjko and Hans J Briegel, "Machine learning & artificial intelligence in the quantum domain: a review of recent progress", Reports on Progress in Physics 81 7, 074001 (2018).
[50] Hugo Théveniaut and Everard van Nieuwenburg, "A NEAT quantum error decoder", SciPost Physics 11 1, 005 (2021).
[51] Sangkha Borah, Bijita Sarma, Michael Kewming, Gerard J. Milburn, and Jason Twamley, "Measurement-Based Feedback Quantum Control with Deep Reinforcement Learning for a Double-Well Nonlinear Potential", Physical Review Letters 127 19, 190403 (2021).
[52] Valentin Gebhart and Martin Bohmann, "Neural-network approach for identifying nonclassicality from click-counting data", Physical Review Research 2 2, 023150 (2020).
[53] Roger G. Melko and Juan Carrasquilla, "Language models for quantum simulation", Nature Computational Science 4 1, 11 (2024).
[54] Akram Youssry, Robert J Chapman, Alberto Peruzzo, Christopher Ferrie, and Marco Tomamichel, "Modeling and control of a reconfigurable photonic circuit using deep learning", Quantum Science and Technology 5 2, 025001 (2020).
[55] Karl Hammar, Alexei Orekhov, Patrik Wallin Hybelius, Anna Katariina Wisakanto, Basudha Srivastava, Anton Frisk Kockum, and Mats Granath, "Error-rate-agnostic decoding of topological stabilizer codes", Physical Review A 105 4, 042616 (2022).
[56] Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori, and Anton Frisk Kockum, "Classification and reconstruction of optical quantum states with deep neural networks", Physical Review Research 3 3, 033278 (2021).
[57] Debasmita Bhoumik, Ritajit Majumdar, Dhiraj Madan, Dhinakaran Vinayagamurthy, Shesha Raghunathan, and Susmita Sur-Kolay, "Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning", ACM Transactions on Quantum Computing 3636516 (2023).
[58] P Baireuther, M D Caio, B Criger, C W J Beenakker, and T E O’Brien, "Neural network decoder for topological color codes with circuit level noise", New Journal of Physics 21 1, 013003 (2019).
[59] Amarsanaa Davaasuren, Yasunari Suzuki, Keisuke Fujii, and Masato Koashi, "General framework for constructing fast and near-optimal machine-learning-based decoder of the topological stabilizer codes", Physical Review Research 2 3, 033399 (2020).
[60] Gang Wang, Bang-Hai Wang, and Shao-Ming Fei, "An RNN–policy gradient approach for quantum architecture search", Quantum Information Processing 23 5, 184 (2024).
[61] Oleksandr Balabanov and Mats Granath, "Unsupervised learning using topological data augmentation", Physical Review Research 2 1, 013354 (2020).
[62] Akram Youssry, Gerardo A. Paz-Silva, and Christopher Ferrie, "Characterization and control of open quantum systems beyond quantum noise spectroscopy", npj Quantum Information 6 1, 95 (2020).
[63] Mario Krenn, Jonas Landgraf, Thomas Foesel, and Florian Marquardt, "Artificial intelligence and machine learning for quantum technologies", Physical Review A 107 1, 010101 (2023).
[64] Poulami Das, Christopher A. Pattison, Srilatha Manne, Douglas M. Carmean, Krysta M. Svore, Moinuddin Qureshi, and Nicolas Delfosse, 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA) 259 (2022) ISBN:978-1-6654-2027-3.
[65] Naihua Ji, Zhao Chen, Yingjie Qu, Rongyi Bao, Xin Yang, and Shumei Wang, "Fault-tolerant quaternary belief propagation decoding based on a neural network", Frontiers in Physics 11, 1164567 (2023).
[66] Philip Andreasson, Joel Johansson, Simon Liljestrand, and Mats Granath, "Quantum error correction for the toric code using deep reinforcement learning", Quantum 3, 183 (2019).
[67] Yuya Ichikawa, Akira Goda, Chihiro Matsui, and Ken Takeuchi, 2022 IEEE International Memory Workshop (IMW) 1 (2022) ISBN:978-1-6654-9947-7.
[68] Savvas Varsamopoulos, Koen Bertels, and Carmen G. Almudever, "Decoding surface code with a distributed neural network–based decoder", Quantum Machine Intelligence 2 1, 3 (2020).
[69] Chen Lin, YiChen Wang, JinZhao Wu, and GuoWu Yang, "Efficient Decoding Scheme of Non-Uniform Concatenation Quantum Code with Deep Neural Network", International Journal of Theoretical Physics 60 3, 848 (2021).
[70] Hendrik Poulsen Nautrup, Nicolas Delfosse, Vedran Dunjko, Hans J. Briegel, and Nicolai Friis, "Optimizing Quantum Error Correction Codes with Reinforcement Learning", Quantum 3, 215 (2019).
[71] Chaitanya Chinni, Abhishek Kulkami, Dheeraj MPai, Kaushik Mitra, and Pradeep K Sarvepalli, 2019 IEEE Information Theory Workshop (ITW) 1 (2019) ISBN:978-1-5386-6900-6.
[72] L. M. K. Vandersypen, H. Bluhm, J. S. Clarke, A. S. Dzurak, R. Ishihara, A. Morello, D. J. Reilly, L. R. Schreiber, and M. Veldhorst, "Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent", npj Quantum Information 3 1, 34 (2017).
[73] Akram Youssry, Yang Yang, Robert J. Chapman, Ben Haylock, Francesco Lenzini, Mirko Lobino, and Alberto Peruzzo, "Experimental graybox quantum system identification and control", npj Quantum Information 10 1, 9 (2024).
[74] Florian Marquardt, "Machine learning and quantum devices", SciPost Physics Lecture Notes 29 (2021).
[75] S. Krinner, S. Lazar, A. Remm, C.K. Andersen, N. Lacroix, G.J. Norris, C. Hellings, M. Gabureac, C. Eichler, and A. Wallraff, "Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits", Physical Review Applied 14 2, 024042 (2020).
[76] Hossein Dehghani, Ali Lavasani, Mohammad Hafezi, and Michael J. Gullans, "Neural-network decoders for measurement induced phase transitions", Nature Communications 14 1, 2918 (2023).
[77] Spiro Gicev, Lloyd C. L. Hollenberg, and Muhammad Usman, "A scalable and fast artificial neural network syndrome decoder for surface codes", Quantum 7, 1058 (2023).
[78] Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O'Connor, "Advantages of versatile neural-network decoding for topological codes", Physical Review A 99 5, 052351 (2019).
[79] Panni Wang, Xiaochen Peng, Wriddhi Chakraborty, Asif Islam Khan, Suman Datta, and Shimeng Yu, 2020 IEEE International Electron Devices Meeting (IEDM) 38.5.1 (2020) ISBN:978-1-7281-8888-1.
[80] Pankaj Mehta, Marin Bukov, Ching-Hao Wang, Alexandre G. R. Day, Clint Richardson, Charles K. Fisher, and David J. Schwab, "A high-bias, low-variance introduction to Machine Learning for physicists", Physics Reports 810, 1 (2019).
[81] David K. Tuckett, Stephen D. Bartlett, and Steven T. Flammia, "Ultrahigh Error Threshold for Surface Codes with Biased Noise", Physical Review Letters 120 5, 050505 (2018).
[82] Christopher T. Chubb and Steven T. Flammia, "Statistical mechanical models for quantum codes with correlated noise", Annales de l'Institut Henri Poincare D 8 2, 269 (2021).
[83] Christopher T. Chubb, "General tensor network decoding of 2D Pauli codes", arXiv:2101.04125, (2021).
[84] Hendrik Poulsen Nautrup, Nicolas Delfosse, Vedran Dunjko, Hans J. Briegel, and Nicolai Friis, "Optimizing Quantum Error Correction Codes with Reinforcement Learning", arXiv:1812.08451, (2018).
[85] Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O'Connor, "Advantages of versatile neural-network decoding for topological codes", arXiv:1802.08680, (2018).
[86] Nikolas P. Breuckmann, "PhD thesis: Homological Quantum Codes Beyond the Toric Code", arXiv:1802.01520, (2018).
[87] Simone Cantori and Sebastiano Pilati, "Challenges and opportunities in the supervised learning of quantum circuit outputs", arXiv:2402.04992, (2024).
[88] S. T. Spitz, B. Tarasinski, C. W. J. Beenakker, and T. E. O'Brien, "Adaptive weight estimator for quantum error correction", arXiv:1712.02360, (2017).
[89] Ramon Overwater, Masoud Babaie, and Fabio Sebastiano, "Neural-Network Decoders for Quantum Error Correction using Surface Codes:A Space Exploration of the Hardware Cost-Performance Trade-Offs", arXiv:2202.05741, (2022).
The above citations are from Crossref's cited-by service (last updated successfully 2024-08-22 05:40:02) and SAO/NASA ADS (last updated successfully 2024-08-22 05:40:03). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.