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Quantum computers have the potential to perform computational tasks beyond the reach of classical machines.
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Elliptic curve cryptosystems
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Rapid solution of problems by quantum computation
Deutsch, D. & Jozsa, R · 1992
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Quantum measurements and the Abelian Stabilizer Problem
Kitaev, A. Y · 1995
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Scheme for reducing decoherence in quantum computer memory
Shor, P. W · 1995
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Good quantum error-correcting codes exist
Calderbank, A. R. & Shor, P. W · 1996
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Fault-tolerant quantum computation
Shor, P. W · 1996
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Error correcting codes in quantum theory
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Simple quantum error-correcting codes
Steane, A. M · 1996
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Quantum networks for elementary arithmetic operations
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On the power of quantum computation
Simon, D. R · 1997
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Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W · 1997
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Theory of fault-tolerant quantum computation
Gottesman, D · 1998
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Fault-tolerant quantum computation by anyons
Kitaev, A. Y · 2003
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Shor’s discrete logarithm quantum algorithm for elliptic curves
Proos, J. & Zalka, C · 2003
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arXiv:quant-ph/0410184 [quant-ph]
Cuccaro, S. A., Draper, T. G., Kutin, S. A. & Moulton, D. P. (2004) · 2004
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A logarithmic-depth quantum carry-lookahead adder
Draper, T. G., Kutin, S. A., Rains, E. M. & Svore, K. M · 2004
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Universal quantum computation with ideal Clifford gates and noisy ancillas
Bravyi, S. & Kitaev, A · 2005
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Two-dimensional transport and transfer of a single atomic qubit in optical tweezers
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Quantum information with Rydberg atoms
Saffman, M., Walker, T. G. & Mølmer, K · 2010
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Demonstration of a Neutral Atom Controlled-NOT Quantum Gate
Isenhower, L. et al · 2010
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Tradeoffs for Reliable Quantum Information Storage in 2D Systems
Bravyi, S., Poulin, D. & Terhal, B · 2010
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Scalable architecture for quantum information processing with atoms in optical micro-structures
Schlosser, M., Tichelmann, S., Kruse, J. & Birkl, G · 2011
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Surface codes: Towards practical large-scale quantum computation
Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N · 2012
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Layered architecture for quantum computing
Jones, N. C. et al · 2012
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Surface code quantum computing by lattice surgery
Horsman, C., Fowler, A. G., Devitt, S. & Meter, R. V · 2012
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A bridge to lower overhead quantum computation
Fowler, A. G. & Devitt, S. J · 2012
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Time-optimal quantum computation
Fowler, A. G · 2012
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Quasi-cyclic LDPC codes: Influence of proto-and Tanner-graph structure on minimum Hamming distance upper bounds
Smarandache, R. & Vontobel, P. O · 2012
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Low-overhead constructions for the fault-tolerant toffoli gate
Jones, C · 2013
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A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits
Amy, M., Maslov, D., Mosca, M. & Roetteler, M · 2013
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Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
Bombín, H · 2013
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An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays
Barredo, D., De Léséleuc, S., Lienhard, V., Lahaye, T. & Browaeys, A · 2016
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Atom-by-atom assembly of defect-free one-dimensional cold atom arrays
Endres, M. et al · 2016
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Trading classical and quantum computational resources
Bravyi, S., Smith, G. & Smolin, J. A · 2016
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Fault-tolerant error correction with the gauge color code
Brown, B. J., Nickerson, N. H. & Browne, D. E · 2016
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Quantum computation with realistic magic-state factories
O’Gorman, J. & Campbell, E. T · 2017
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Quantum resource estimates for computing elliptic curve discrete logarithms
Roetteler, M., Naehrig, M., Svore, K. M. & Lauter, K · 2017
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Fault-tolerant interface between quantum memories and quantum processors
Poulsen Nautrup, H., Friis, N. & Briegel, H. J · 2017
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Halving the cost of quantum addition
Gidney, C · 2018
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Encoding electronic spectra in quantum circuits with linear t complexity
Babbush, R. et al · 2018
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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Gidney, C. & Ekerå, M · 2019
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Degenerate Quantum LDPC Codes With Good Finite Length Performance
Panteleev, P. & Kalachev, G · 2019
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Magic State Distillation: Not as Costly as You Think
Litinski, D · 2019
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A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
Litinski, D · 2019
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Improved quantum circuits for elliptic curve discrete logarithms
Häner, T., Jaques, S., Naehrig, M., Roetteler, M. & Soeken, M · 2020
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Decoding across the quantum low-density parity-check code landscape
Roffe, J., White, D. R., Burton, S. & Campbell, E · 2020
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Quantum Low-Density Parity-Check Codes
Breuckmann, N. P. & Eberhardt, J. N · 2021
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Quantum LDPC codes with almost linear minimum distance
Panteleev, P. & Kalachev, G · 2021
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Quantum low-density parity-check codes
Breuckmann, N. P. & Eberhardt, J. N · 2021
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Stim: a fast stabilizer circuit simulator
Gidney, C · 2021
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Demonstration of fault-tolerant universal quantum gate operations
Postler, L. et al · 2022
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A quantum processor based on coherent transport of entangled atom arrays
Bluvstein, D. et al · 2022
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Multi-qubit entanglement and algorithms on a neutral-atom quantum computer
Graham, T. M. et al · 2022
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Asymptotically good quantum and locally testable classical ldpc codes
Panteleev, P. & Kalachev, G · 2022
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Leverrier, A. & Zémor, G · 2022
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Good Quantum LDPC Codes with Linear Time Decoders
Dinur, I., Hsieh, M.-H. H., Lin, T.-C. C. & Vidick, T · 2022
Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays
Zhou, H. et al · 2025
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Tour de gross: A modular quantum computer based on bivariate bicycle codes
Yoder, T. J. et al · 2025
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Fast and parallelizable logical computation with homological product codes
Xu, Q. et al · 2025
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High-rate surgery: towards constant-overhead logical operations
Zheng, G., Jiang, L. & Xu, Q · 2025
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Reducing the number of qubits in quantum factoring
Chevignard, C., Fouque, P.-A. & Schrottenloher, A · 2025
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Low-overhead fault-tolerant quantum computing using long-range connectivity
Cohen, L. Z., Kim, I. H., Bartlett, S. D. & Brown, B. J · 2022
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Universal gate operations on nuclear spin qubits in an optical tweezer array of Yb 171 {}^{171}\mathrm{Yb} atoms
Ma, S. et al · 2022
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Ytterbium nuclear-spin qubits in an optical tweezer array
Jenkins, A., Lis, J. W., Senoo, A., McGrew, W. F. & Kaufman, A. M · 2022
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Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
Wu, Y., Kolkowitz, S., Puri, S. & Thompson, J. D · 2022
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Litinski, D. & Nickerson, N · 2022
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Homomorphic Logical Measurements
Huang, S., Jochym-O’Connor, T. & Yoder, T. J · 2022
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Manetsch, H. J. et al · 2025
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Continuous operation of a coherent 3,000-qubit system
Chiu, N.-C. et al · 2025
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Benchmarking and Fidelity Response Theory of High-Fidelity Rydberg Entangling Gates
Tsai, R. B.-S., Sun, X., Shaw, A. L., Finkelstein, R. & Endres, M · 2025
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Leveraging erasure errors in logical qubits with metastable 171
Zhang, B. et al · 2025
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Fast and fault-tolerant logical measurements: Auxiliary hypergraphs and transversal surgery (2025)
Cowtan, A., He, Z., Williamson, D. J. & Yoder, T. J · 2025
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Transversal dimension jump for product qldpc codes (2025)
Li, C., Preskill, J. & Xu, Q · 2025
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Microsecond-scale high-survival and number-resolved detection of ytterbium atom arrays
Muzi Falconi, A. et al · 2025
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How to factor 2048 bit rsa integers with less than a million noisy qubits
Gidney, C · 2025
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Improved belief propagation is sufficient for real-time decoding of quantum memory
Müller, T. et al · 2025
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Extractors: Qldpc architectures for efficient pauli-based computation
He, Z., Cowtan, A., Williamson, D. J. & Yoder, T. J · 2025
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Computing efficiently in qldpc codes
Malcolm, A. J. et al · 2025
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Magic tricycles: Efficient magic state generation with finite block-length quantum ldpc codes (2025)
Menon, V. et al · 2025
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Batched high-rate logical operations for quantum ldpc codes
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Processing and decoding Rydberg decay error with MBQC (2025)
Yu, C.-C. et al · 2025
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Quantum error correction resilient against atom loss (2025)
Perrin, H., Jandura, S. & Pupillo, G · 2025
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Leveraging atom loss errors in fault tolerant quantum algorithms (2025)
Baranes, G. et al · 2025
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Fault-tolerant quantum architectures based on erasure qubits
Gu, S., Retzker, A. & Kubica, A · 2025
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Neural decoders for universal quantum algorithms (2025)
Ataides, J. P. B., Gu, A., Yelin, S. F. & Lukin, M. D · 2025
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Generalized toric codes on twisted tori for quantum error correction
Liang, Z., Liu, K., Song, H. & Chen, Y.-A · 2025
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Fold-transversal surface code cultivation (2025)
Sahay, K. et al · 2025
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Time-efficient logical operations on quantum low-density parity check codes
Zhang, G. & Li, Y · 2025
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Parallel logical measurements via quantum code surgery
Cowtan, A., He, Z., Williamson, D. J. & Yoder, T. J · 2025
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Fast surgery for quantum ldpc codes
Baspin, N., Berent, L. & Cohen, L. Z · 2025
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Single-shot universality in quantum ldpc codes via code-switching (2025)
Tan, S. J. S., Hong, Y., Lin, T.-C., Gullans, M. J. & Hsieh, M.-H · 2025
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Constant-overhead addressable gates via single-shot code switching
Golowich, L., Chang, K. & Zhu, G · 2025
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Sequences of bivariate bicycle codes from covering graphs
Symons, B. C., Rajput, A. & Browne, D. E · 2025
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On the minimum distances of finite-length lifted product quantum ldpc codes
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Explicit construction of low-overhead gadgets for gates on quantum ldpc codes
Webster, P., Smith, S. C. & Cohen, L. Z · 2025
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Fault-tolerant logical clifford gates from code automorphisms
Sayginel, H., Koutsioumpas, S., Webster, M., Rajput, A. & Browne, D. E · 2025
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Constant-overhead magic state injection into qldpc codes with error independence guarantees
Zhang, G., Zhu, Y., Yuan, X. & Li, Y · 2025
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Transversal star architecture for megaquop-scale quantum simulation with neutral atoms
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Unified architecture for quantum lookup tables
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