Does SGD Seek Flatness or Sharpness? An Exactly Solvable Model.

Isaac L. Chuang Massachusetts Institute of Technology, Co-Design Center for Quantum Advantage, Cambridge, MA, USA http://feynman.mit.edu/ike https://orcid.org/0000-0001-7296-523X https://scholar.google.com/citations?user=QKyb_9oAAAAJ https://zbmath.org/authors/?q=ai:chuang.isaac-l https://mathscinet.ams.org/mathscinet/MRAuthorID/601042 https://mathgenealogy.org/id.php?id=250913 https://en.wikipedia.org/wiki/Isaac_Chuang https://www.wikidata.org/entity/Q15421399 https://id.loc.gov/authorities/names/n00003023 https://d-nb.info/gnd/141904585

Yizhou Xu Pierfrancesco Beneventano Isaac L. Chuang Liu Ziyin 0001 Does SGD Seek Flatness or Sharpness? An Exactly Solvable Model. 2026 February abs/2602.05065 CoRR https://doi.org/10.48550/arXiv.2602.05065 db/journals/corr/corr2602.html#abs-2602-05065 streams/journals/corr

Zane M. Rossi Jack L. Ceroni Isaac L. Chuang Modular quantum signal processing in many variables. 1776 2025 9 Quantum https://doi.org/10.22331/q-2025-06-18-1776 db/journals/quantum/quantum9.html#RossiCC25 streams/journals/quantum

John M. Martyn Zane M. Rossi Kevin Z. Cheng Yuan Liu 0023 Isaac L. Chuang Parallel Quantum Signal Processing Via Polynomial Factorization. 1834 2025 9 Quantum https://doi.org/10.22331/q-2025-08-27-1834 db/journals/quantum/quantum9.html#MartynRCLC25 streams/journals/quantum

Yuan Liu 0023 John M. Martyn Jasmine Sinanan-Singh Kevin Smith Steven M. Girvin Isaac L. Chuang Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform. 3641-3655 2025 73 IEEE Trans. Signal Process. https://doi.org/10.1109/TSP.2025.3599462 db/journals/tsp/tsp73.html#LiuMSSGC25 streams/journals/tsp

Liu Ziyin 0001 Isaac L. Chuang Tomer Galanti Tomaso A. Poggio Formation of Representations in Neural Networks. 2025 ICLR https://openreview.net/forum?id=Njx1NjHIx4 conf/iclr/2025 db/conf/iclr/iclr2025.html#0001CGP25 Liu Ziyin 0001 Yizhou Xu Isaac L. Chuang Remove Symmetries to Control Model Expressivity and Improve Optimization. 2025 ICLR https://openreview.net/forum?id=Gv0TOAigIY conf/iclr/2025 db/conf/iclr/iclr2025.html#0001XC25

Liu Ziyin 0001 Yizhou Xu Tomaso A. Poggio Isaac L. Chuang Parameter Symmetry Breaking and Restoration Determines the Hierarchical Learning in AI Systems. 2025 February abs/2502.05300 CoRR https://doi.org/10.48550/arXiv.2502.05300 db/journals/corr/corr2502.html#abs-2502-05300 streams/journals/corr

Liu Ziyin 0001 Isaac L. Chuang Tomaso A. Poggio Heterosynaptic Circuits Are Universal Gradient Machines. 2025 May abs/2505.02248 CoRR https://doi.org/10.48550/arXiv.2505.02248 db/journals/corr/corr2505.html#abs-2505-02248 streams/journals/corr

Liu Ziyin 0001 Yizhou Xu Isaac L. Chuang Neural Thermodynamics I: Entropic Forces in Deep and Universal Representation Learning. 2025 May abs/2505.12387 CoRR https://doi.org/10.48550/arXiv.2505.12387 db/journals/corr/corr2505.html#abs-2505-12387 streams/journals/corr

Ziyin Liu 0001 Isaac L. Chuang Proof of a perfect platonic representation hypothesis. 2025 July abs/2507.01098 CoRR https://doi.org/10.48550/arXiv.2507.01098 db/journals/corr/corr2507.html#abs-2507-01098 streams/journals/corr

Hong-Yi Wang Di Luo Tomaso A. Poggio Isaac L. Chuang Liu Ziyin 0001 A universal compression theory: Lottery ticket hypothesis and superpolynomial scaling laws. 2025 October abs/2510.00504 CoRR https://doi.org/10.48550/arXiv.2510.00504 db/journals/corr/corr2510.html#abs-2510-00504 streams/journals/corr

Yongyi Yang Tomaso A. Poggio Isaac L. Chuang Liu Ziyin 0001 Topological Invariance and Breakdown in Learning. 2025 October abs/2510.02670 CoRR https://doi.org/10.48550/arXiv.2510.02670 db/journals/corr/corr2510.html#abs-2510-02670 streams/journals/corr

Jasmine Sinanan-Singh Gabriel L. Mintzer Isaac L. Chuang Yuan Liu 0023 Single-shot Quantum Signal Processing Interferometry. 1427 2024 8 Quantum https://doi.org/10.22331/q-2024-07-30-1427 db/journals/quantum/quantum8.html#Sinanan-SinghMC24

Andrew K. Tan Matthew H. Ho Isaac L. Chuang Reliable Computation by Large-Alphabet Formulas in the Presence of Noise. 9152-9164 2024 December 70 IEEE Trans. Inf. Theory 12 https://doi.org/10.1109/TIT.2024.3486278 db/journals/tit/tit70.html#TanHC24 streams/journals/tit

James Ang 0001 Gabriella Carini Yanzhu Chen Isaac L. Chuang Michael DeMarco Sophia E. Economou Alec Eickbusch Andrei Faraon Kai-Mei Fu Steven M. Girvin Michael Hatridge Andrew A. Houck Paul Hilaire Kevin Krsulich Ang Li 0006 Chenxu Liu Yuan Liu 0023 Margaret Martonosi David C. McKay Jim Misewich Mark B. Ritter Robert J. Schoelkopf Samuel A. Stein Sara Sussman Hong Tang Wei Tang Teague Tomesh Norm M. Tubman Chen Wang Nathan Wiebe Yongxin Yao Dillon Yost Yiyu Zhou ARQUIN: Architectures for Multinode Superconducting Quantum Computers. 19:1-19:59 2024 September 5 ACM Trans. Quantum Comput. 3 https://doi.org/10.1145/3674151 db/journals/tqc/tqc5.html#AngCCCDEEFFGHHHKLLLMMMR24 streams/journals/tqc

Liu Ziyin 0001 Yizhou Xu Isaac L. Chuang Remove Symmetries to Control Model Expressivity. 2024 abs/2408.15495 CoRR https://doi.org/10.48550/arXiv.2408.15495 db/journals/corr/corr2408.html#abs-2408-15495 streams/journals/corr

Liu Ziyin 0001 Isaac L. Chuang Tomer Galanti Tomaso A. Poggio Formation of Representations in Neural Networks. 2024 abs/2410.03006 CoRR https://doi.org/10.48550/arXiv.2410.03006 db/journals/corr/corr2410.html#abs-2410-03006 streams/journals/corr

Tatsuhiko N. Ikeda Asir Abrar Isaac L. Chuang Sho Sugiura Minimum Trotterization Formulas for a Time-Dependent Hamiltonian. 1168 2023 November 7 Quantum https://doi.org/10.22331/q-2023-11-06-1168 db/journals/quantum/quantum7.html#IkedaACS23

Samuel A. Stein Sara Sussman Teague Tomesh Charles Guinn Esin Tureci Sophia Fuhui Lin Wei Tang James Ang 0001 Srivatsan Chakram Ang Li 0006 Margaret Martonosi Fred Chong Andrew A. Houck Isaac L. Chuang Michael Austin DeMarco HetArch: Heterogeneous Microarchitectures for Superconducting Quantum Systems. 539-554 2023 MICRO https://doi.org/10.1145/3613424.3614300 https://ieeexplore.ieee.org/document/10411374 https://www.wikidata.org/entity/Q130907747 conf/micro/2023 db/conf/micro/micro2023.html#SteinSTGTLTACLM23

Samuel A. Stein Sara Sussman Teague Tomesh Charles Guinn Esin Tureci Sophia Fuhui Lin Wei Tang James Ang 0001 Srivatsan Chakram Ang Li 0006 Margaret Martonosi Frederic T. Chong Andrew A. Houck Isaac L. Chuang Michael Austin DeMarco Microarchitectures for Heterogeneous Superconducting Quantum Computers. 2023 abs/2305.03243 CoRR https://doi.org/10.48550/arXiv.2305.03243 db/journals/corr/corr2305.html#abs-2305-03243

Andrew K. Tan Matthew Ho Isaac L. Chuang On reliable computation over larger alphabets. 2023 abs/2306.13262 CoRR https://doi.org/10.48550/arXiv.2306.13262 db/journals/corr/corr2306.html#abs-2306-13262

Andrew K. Tan Isaac L. Chuang Resource savings from fault-tolerant circuit design. 2023 abs/2311.02132 CoRR https://doi.org/10.48550/arXiv.2311.02132 db/journals/corr/corr2311.html#abs-2311-02132

Andrew K. Tan Max Tegmark Isaac L. Chuang Pareto-Optimal Clustering with the Primal Deterministic Information Bottleneck. 771 2022 24 Entropy 6 https://doi.org/10.3390/e24060771 db/journals/entropy/entropy24.html#TanTC22

Zane M. Rossi Isaac L. Chuang Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle. 811 2022 September 6 Quantum https://doi.org/10.22331/q-2022-09-20-811 db/journals/quantum/quantum6.html#RossiC22

Alexander Zlokapa Andrew K. Tan John M. Martyn Max Tegmark Isaac L. Chuang Biological error correction codes generate fault-tolerant neural networks. 2022 abs/2202.12887 CoRR https://arxiv.org/abs/2202.12887 db/journals/corr/corr2202.html#abs-2202-12887

Andrew K. Tan Max Tegmark Isaac L. Chuang Pareto-optimal clustering with the primal deterministic information bottleneck. 2022 abs/2204.02489 CoRR https://doi.org/10.48550/arXiv.2204.02489 db/journals/corr/corr2204.html#abs-2204-02489

Curtis G. Northcutt Lu Jiang 0004 Isaac L. Chuang Confident Learning: Estimating Uncertainty in Dataset Labels. 1373-1411 2021 70 J. Artif. Intell. Res. https://doi.org/10.1613/jair.1.12125 db/journals/jair/jair70.html#NorthcuttJC21

Arkopal Dutt Edwin Pednault Chai Wah Wu Sarah Sheldon John A. Smolin Lev Bishop Isaac L. Chuang Active Learning of Quantum System Hamiltonians yields Query Advantage. 2021 abs/2112.14553 CoRR https://arxiv.org/abs/2112.14553 db/journals/corr/corr2112.html#abs-2112-14553

Daniela Ganelin Isaac L. Chuang IP Geolocation Underestimates Regressive Economic Patterns in MOOC Usage. 2020 abs/2006.03977 CoRR https://arxiv.org/abs/2006.03977 db/journals/corr/corr2006.html#abs-2006-03977

Tailin Wu Ian S. Fischer Isaac L. Chuang Max Tegmark Learnability for the Information Bottleneck. 924 2019 21 Entropy 10 https://doi.org/10.3390/e21100924 db/journals/entropy/entropy21.html#WuFCT19

Guang Hao Low Isaac L. Chuang Hamiltonian Simulation by Qubitization. 163 2019 3 Quantum https://doi.org/10.22331/q-2019-07-12-163 db/journals/quantum/quantum3.html#LowC19

Ilia Rushkin Isaac L. Chuang Dustin Tingley Modelling and Using Response Times in Online Courses. 2019 December 6 J. Learn. Anal. 3 https://doi.org/10.18608/jla.2019.63.10 db/journals/solarjla/solarjla6.html#RushkinCT19

Catherine Medlock Alan V. Oppenheim Isaac L. Chuang Qi Ding Operating Characteristics for Binary Hypothesis Testing in Quantum Systems. 1136-1145 2019 Allerton https://doi.org/10.1109/ALLERTON.2019.8919700 conf/allerton/2019 db/conf/allerton/allerton2019.html#MedlockOCD19 Daniela Ganelin Isaac L. Chuang IP Geolocation Underestimates Regressive Economic Patterns in MOOC Usage. 268-272 2019 ICETC https://doi.org/10.1145/3369255.3369301 conf/icetc/2019 db/conf/icetc/icetc2019.html#GanelinC19 Tailin Wu Ian S. Fischer Isaac L. Chuang Max Tegmark Learnability for the Information Bottleneck. 1050-1060 2019 UAI http://proceedings.mlr.press/v115/wu20b.html http://auai.org/uai2019/proceedings/papers/380.pdf conf/uai/2019 db/conf/uai/uai2019.html#WuFCT19

Murphy Yuezhen Niu Lior Horesh Isaac L. Chuang Recurrent Neural Networks in the Eye of Differential Equations. 2019 abs/1904.12933 CoRR http://arxiv.org/abs/1904.12933 db/journals/corr/corr1904.html#abs-1904-12933

Tailin Wu Ian S. Fischer Isaac L. Chuang Max Tegmark Learnability for the Information Bottleneck. 2019 abs/1907.07331 CoRR http://arxiv.org/abs/1907.07331 db/journals/corr/corr1907.html#abs-1907-07331

Curtis G. Northcutt Lu Jiang 0004 Isaac L. Chuang Confident Learning: Estimating Uncertainty in Dataset Labels. 2019 abs/1911.00068 CoRR http://arxiv.org/abs/1911.00068 db/journals/corr/corr1911.html#abs-1911-00068

Rich Rines Isaac L. Chuang High Performance Quantum Modular Multipliers. 2018 abs/1801.01081 CoRR http://arxiv.org/abs/1801.01081 db/journals/corr/corr1801.html#abs-1801-01081

Ilia Rushkin Isaac L. Chuang Dustin Tingley Modelling and Using Response Times in Online Courses. 2018 abs/1801.07618 CoRR http://arxiv.org/abs/1801.07618 db/journals/corr/corr1801.html#abs-1801-07618

Tailin Wu John Peurifoy Isaac L. Chuang Max Tegmark Meta-learning autoencoders for few-shot prediction. 2018 abs/1807.09912 CoRR http://arxiv.org/abs/1807.09912 db/journals/corr/corr1807.html#abs-1807-09912

Glenn Lopez Daniel T. Seaton Andrew M. Ang Dustin Tingley Isaac L. Chuang Google BigQuery for Education: Framework for Parsing and Analyzing edX MOOC Data. 181-184 2017 L@S https://doi.org/10.1145/3051457.3053980 conf/lats/2017 db/conf/lats/lats2017.html#LopezSATC17 Curtis G. Northcutt Tailin Wu Isaac L. Chuang Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels. 2017 UAI http://auai.org/uai2017/proceedings/papers/35.pdf conf/uai/2017 db/conf/uai/uai2017.html#NorthcuttWC17

Curtis G. Northcutt Tailin Wu Isaac L. Chuang Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels. 2017 abs/1705.01936 CoRR http://arxiv.org/abs/1705.01936 db/journals/corr/corr1705.html#NorthcuttWC17

Michael A. Nielsen Isaac L. Chuang Quantum Computation and Quantum Information (10th Anniversary edition). I-XXXI, 1-676 Cambridge University Press 2016 978-1-10-700217-3 https://www.cambridge.org/de/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-computation-and-quantum-information-10th-anniversary-edition?format=HB

Curtis G. Northcutt Andrew D. Ho Isaac L. Chuang Detecting and preventing "multiple-account" cheating in massive open online courses. 71-80 2016 100 Comput. Educ. https://doi.org/10.1016/j.compedu.2016.04.008 db/journals/ce/ce100.html#NorthcuttHC16

Amira M. Eltony Dorian Gangloff Molu Shi Alexei Bylinskii Vladan Vuletic Isaac L. Chuang Technologies for trapped-ion quantum information systems. 5351-5383 2016 15 Quantum Inf. Process. 12 https://doi.org/10.1007/s11128-016-1298-8 https://www.wikidata.org/entity/Q60316453 db/journals/qip/qip15.html#EltonyGSBVC16

Cody A. Coleman Daniel T. Seaton Isaac L. Chuang Probabilistic Use Cases: Discovering Behavioral Patterns for Predicting Certification. 141-148 2015 L@S https://doi.org/10.1145/2724660.2724662 conf/lats/2015 db/conf/lats/lats2015.html#ColemanSC15

Curtis G. Northcutt Andrew D. Ho Isaac L. Chuang Detecting and Preventing "Multiple-Account" Cheating in Massive Open Online Courses. 2015 abs/1508.05699 CoRR http://arxiv.org/abs/1508.05699 db/journals/corr/corr1508.html#NorthcuttHC15

Daniel T. Seaton Yoav Bergner Isaac L. Chuang Piotr Mitros David E. Pritchard Who does what in a massive open online course? 58-65 2014 57 Commun. ACM 4 https://doi.org/10.1145/2500876 db/journals/cacm/cacm57.html#SeatonBCMP14

Jon P. Daries Justin Reich Jim Waldo Elise M. Young Jonathan Whittinghill Andrew D. Ho Daniel T. Seaton Isaac L. Chuang Privacy, anonymity, and big data in the social sciences. 56-63 2014 57 Commun. ACM 9 https://doi.org/10.1145/2643132 https://www.wikidata.org/entity/Q125931602 db/journals/cacm/cacm57.html#DariesRWYWHSC14

Sergiy O. Nesterko Daniel T. Seaton Justin Reich Joseph McIntyre Qiuyi Han Isaac L. Chuang Andrew D. Ho Due dates in MOOCs: does stricter mean better? 193-194 2014 L@S https://doi.org/10.1145/2556325.2567877 conf/lats/2014 db/conf/lats/lats2014.html#NesterkoSRMHCH14

Guang Hao Low Theodore J. Yoder Isaac L. Chuang Quantum Inference on Bayesian Networks. 2014 abs/1402.7359 CoRR http://arxiv.org/abs/1402.7359 db/journals/corr/corr1402.html#LowYC14

Daniel T. Seaton Albert J. Rodenius Cody A. Coleman David E. Pritchard Isaac L. Chuang Analysis of Video Use in edX Courses. 2013 AIED Workshops https://ceur-ws.org/Vol-1009/0111.pdf conf/aied/2013w db/conf/aied/aied2013w.html#SeatonRCPC13 Daniel T. Seaton Yoav Bergner Isaac L. Chuang Piotr Mitros David E. Pritchard Towards Real-Time Analytics in MOOCs. 2013 IWTA@LAK https://ceur-ws.org/Vol-985/paper3.pdf conf/lak/2013iwta db/conf/lak/iwta2013.html#SeatonBCMP13

Bei Zeng Andrew W. Cross Isaac L. Chuang Transversality Versus Universality for Additive Quantum Codes. 6272-6284 2011 57 IEEE Trans. Inf. Theory 9 https://doi.org/10.1109/TIT.2011.2161917 db/journals/tit/tit57.html#ZengCC11

David R. Leibrandt Jaroslaw Labaziewicz Robert J. Clark Isaac L. Chuang Ryan J. Epstein Christian Ospelkaus Janus H. Wesenberg John J. Bollinger Dietrich Leibfried David J. Wineland Daniel Stick Jonathan D. Sterk Christopher R. Monroe Chien-Shing Pai Yee Low Robert E. Frahm Richart E. Slusher Demonstration of a scalable, multiplexed ion trap for quantum information processing. 901-919 2009 9 Quantum Inf. Comput. 11&12 https://doi.org/10.26421/QIC9.11-12-1 db/journals/qic/qic9.html#LeibrandtLCCEOWBLWSSMPLFS11

Tzvetan S. Metodi Darshan D. Thaker Andrew W. Cross Isaac L. Chuang Frederic T. Chong High-level interconnect model for the quantum logic array architecture. 2008 4 ACM J. Emerg. Technol. Comput. Syst. 1 https://doi.org/10.1145/1330521.1330522 https://www.wikidata.org/entity/Q130924865 db/journals/jetc/jetc4.html#MetodiTCCC08 1:1-1:28

Tzvetan S. Metodi Andrew W. Cross Darshan D. Thaker Isaac L. Chuang Frederic T. Chong Design-space exploration of fault-tolerant building blocks for large-scale quantum computing. 7-14 2007 NANOARCH https://doi.org/10.1109/NANOARCH.2007.4400851 https://doi.ieeecomputersociety.org/10.1109/NANOARCH.2007.4400851 http://dl.acm.org/citation.cfm?id=1548928 https://www.wikidata.org/entity/Q130927619 conf/nanoarch/2007 db/conf/nanoarch/nanoarch2007.html#MetodiCTCC07 Dave Bacon Isaac L. Chuang Aram W. Harrow The quantum Schur and Clebsch-Gordan transforms: I. efficient qudit circuits. 1235-1244 2007 conf/soda/2007 SODA http://dl.acm.org/citation.cfm?id=1283383.1283516 db/conf/soda/soda2007.html#BaconCH07

Krysta M. Svore Alfred V. Aho Andrew W. Cross Isaac L. Chuang Igor L. Markov A Layered Software Architecture for Quantum Computing Design Tools. 74-83 2006 39 Computer 1 https://doi.org/10.1109/MC.2006.4 http://doi.ieeecomputersociety.org/10.1109/MC.2006.4 db/journals/computer/computer39.html#SvoreACCM06

Krysta M. Svore Andrew W. Cross Isaac L. Chuang Alfred V. Aho A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing. 193-212 2006 6 Quantum Inf. Comput. 3 https://doi.org/10.26421/QIC6.3-1 http://portal.acm.org/citation.cfm?id=2011687 db/journals/qic/qic6.html#SvoreCCA06

Darshan D. Thaker Tzvetan S. Metodi Andrew W. Cross Isaac L. Chuang Frederic T. Chong Quantum Memory Hierarchies: Efficient Designs to Match Available Parallelism in Quantum Computing. 378-390 2006 conf/isca/2006 ISCA https://doi.org/10.1109/ISCA.2006.32 https://doi.ieeecomputersociety.org/10.1109/ISCA.2006.32 http://dl.acm.org/citation.cfm?id=1136518 https://www.wikidata.org/entity/Q130930166 db/conf/isca/isca2006.html#ThakerMCCC06

Darshan D. Thaker François Impens Isaac L. Chuang Rajeevan Amirtharajah Frederic T. Chong Recursive TMR: Scaling Fault Tolerance in the Nanoscale Era. 298-305 2005 22 IEEE Des. Test Comput. 4 https://doi.org/10.1109/MDT.2005.93 http://doi.ieeecomputersociety.org/10.1109/MDT.2005.93 db/journals/dt/dt22.html#ThakerICAC05

Chandrasekhar Ramanathan Nicolas Boulant Zhiying Chen David G. Cory Isaac L. Chuang Matthias Steffen NMR Quantum Information Processing. 15-44 2004 3 Quantum Inf. Process. 1-5 https://doi.org/10.1007/s11128-004-3668-x db/journals/qip/qip3.html#RamanathanBCCCS04

Nemanja Isailovic Mark Whitney Yatish Patel John Kubiatowicz Dean Copsey Frederic T. Chong Isaac L. Chuang Mark Oskin Datapath and control for quantum wires. 34-61 2004 1 ACM Trans. Archit. Code Optim. 1 https://doi.org/10.1145/980152.980155 https://www.wikidata.org/entity/Q130927155 db/journals/taco/taco1.html#IsailovicWPKCCCO04

Mark Oskin Frederic T. Chong Isaac L. Chuang John Kubiatowicz Building Quantum Wires: The Long and the Short of It. 374-385 2003 conf/isca/2003 ISCA https://doi.org/10.1109/ISCA.2003.1207015 https://doi.ieeecomputersociety.org/10.1109/ISCA.2003.1207015 https://doi.org/10.1145/859618.859661 https://www.wikidata.org/entity/Q130927151 db/conf/isca/isca2003.html#OskinCCK03 Dean Copsey Mark Oskin Tzvetan S. Metodi Frederic T. Chong Isaac L. Chuang John Kubiatowicz The effect of communication costs in solid-state quantum computing architectures. 65-74 2003 conf/spaa/2003 SPAA https://doi.org/10.1145/777412.777424 https://www.wikidata.org/entity/Q130927648 db/conf/spaa/spaa2003.html#CopseyOMCCK03

Mark Oskin Frederic T. Chong Isaac L. Chuang A Practical Architecture for Reliable Quantum Computers. 79-87 2002 35 Computer 1 https://doi.org/10.1109/2.976922 http://doi.ieeecomputersociety.org/10.1109/2.976922 db/journals/computer/computer35.html#OskinCC02

Matthias Steffen Lieven M. K. Vandersypen Isaac L. Chuang Toward Quantum Computation: A Five-Qubit Quantum Processor. 24-34 2001 21 IEEE Micro 2 https://doi.org/10.1109/40.918000 http://doi.ieeecomputersociety.org/10.1109/40.918000 db/journals/micro/micro21.html#SteffenVC01

Lieven M. K. Vandersypen Isaac L. Chuang NMR quantum computing: lessons for the future. 134-142 2001 1 Quantum Inf. Comput. 4 https://doi.org/10.26421/QIC1.s-15 http://portal.acm.org/citation.cfm?id=2017009 db/journals/qic/qic1.html#VandersypenC01

Isaac L. Chuang Dharmendra S. Modha Reversible arithmetic coding for quantum data compression. 1104-1116 2000 46 IEEE Trans. Inf. Theory 3 db/journals/tit/tit46.html#ChuangM00 https://doi.org/10.1109/18.841192

Asir Abrar Alfred V. Aho Rajeevan Amirtharajah Andrew M. Ang James Ang 0001 Dave Bacon Pierfrancesco Beneventano Yoav Bergner Lev Bishop John J. Bollinger Nicolas Boulant Alexei Bylinskii Gabriella Carini Jack L. Ceroni Srivatsan Chakram Yanzhu Chen Zhiying Chen Kevin Z. Cheng Fred ChongFrederic T. Chong Robert J. Clark Cody A. Coleman Dean Copsey David G. Cory Andrew W. Cross Jon P. Daries Michael DeMarcoMichael Austin DeMarco Qi Ding Arkopal Dutt Sophia E. Economou Alec Eickbusch Amira M. Eltony Ryan J. Epstein Andrei Faraon Ian S. Fischer Robert E. Frahm Kai-Mei Fu Tomer Galanti Daniela Ganelin Dorian Gangloff Steven M. Girvin Charlie GuinnCharles Guinn Qiuyi Han Aram W. Harrow Michael Hatridge Paul Hilaire Andrew D. Ho Matthew Ho Matthew H. Ho Lior Horesh Andrew A. Houck Tatsuhiko N. Ikeda François Impens Nemanja Isailovic Lu Jiang 0004 Kevin Krsulich John Kubiatowicz Jaroslaw Labaziewicz Dietrich Leibfried David R. Leibrandt Ang Li 0006 Sophia Fuhui Lin Chenxu Liu Yuan Liu 0023 Glenn Lopez Guang Hao Low Yee Low Di Luo Igor L. Markov Margaret Martonosi John M. Martyn Joseph McIntyre David C. McKay Catherine Medlock Tzvetan S. Metodi Gabriel L. Mintzer Jim Misewich Piotr Mitros Dharmendra S. Modha Christopher R. Monroe Sergiy O. Nesterko Michael A. Nielsen Murphy Yuezhen Niu Curtis G. Northcutt Alan V. Oppenheim Mark Oskin Christian Ospelkaus Chien-Shing Pai Yatish Patel Edwin Pednault John Peurifoy Tomaso A. Poggio David E. Pritchard Chandrasekhar Ramanathan Justin Reich Rich Rines Mark B. Ritter Albert J. Rodenius Zane M. Rossi Ilia Rushkin Robert J. Schoelkopf Daniel T. Seaton Sarah Sheldon Molu Shi Jasmine Sinanan-Singh Richart E. Slusher Kevin Smith John A. Smolin Matthias Steffen Samuel A. Stein Jonathan D. Sterk Daniel Stick Sho Sugiura Sara Sussman Krysta M. Svore Andrew K. Tan Hong Tang Wei Tang Max Tegmark Darshan D. Thaker Dustin Tingley Teague Tomesh Norm M. Tubman Esin Tureci Lieven M. K. Vandersypen Vladan Vuletic Jim Waldo Chen Wang Hongyi WangHong-Yi Wang Janus H. Wesenberg Mark Whitney Jonathan Whittinghill Nathan Wiebe David J. Wineland Chai Wah Wu Tailin Wu Yizhou Xu Yongyi Yang Yongxin Yao Theodore J. Yoder Dillon Yost Elise M. Young Bei Zeng Yiyu Zhou Liu Ziyin 0001Ziyin Liu 0001 Alexander Zlokapa