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Practical quantum computing will require error rates that are well below what is achievable with physical qubits.
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Gottesman, D · 1999
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Benchmarking quantum computers: the five-qubit error correcting code
Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C · 2001
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Topological quantum memory
Dennis, E., Kitaev, A., Landahl, A. & Preskill, J · 2002
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Fault-tolerant quantum computation by anyons
Kitaev, A. Y · 2003
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Quantum orders in an exact soluble model
Wen, X.-G · 2003
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Overhead and noise threshold of fault-tolerant quantum error correction
Steane, A. M · 2003
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Quantum-error correction on linear-nearest-neighbor qubit arrays
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Simulated quantum computation of molecular energies
Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M · 2005
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Scalable noise estimation with random unitary operators
Emerson, J., Alicki, R. & Życzkowski, K · 2005
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Fault-tolerant quantum computation for local leakage faults
Aliferis, P. & Terhal, B. M · 2005
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Shuffled iterative decoding
Zhang, J. & Fossorier, M · 2005
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Reduced-complexity decoding of LDPC codes
Chen, J., Dholakia, A., Eleftheriou, E., Fossorier, M. & Hu, X.-Y · 2005
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The snake optimizer for learning quantum processor control parameters
Klimov, P. V., Kelly, J., Martinis, J. M. & Neven, H · 2006
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Fault-tolerant quantum computation with high threshold in two dimensions
Raussendorf, R. & Harrington, J · 2007
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Charge-insensitive qubit design derived from the Cooper pair box
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Fidelity of quantum operations
Pedersen, L. H., Møller, N. M. & Mølmer, K · 2007
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Fault-tolerant quantum computation with constant error rate
Aharonov, D. & Ben-Or, M · 2008
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On the iterative decoding of sparse quantum codes
Poulin, D. & Chung, Y · 2008
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Threshold error rates for the toric and planar codes
Wang, D. S., Fowler, A. G., Stephens, A. M. & Hollenberg, L. C. L · 2010
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Surface code quantum computing with error rates over 1 % 1\%
Wang, D. S., Fowler, A. G. & Hollenberg, L. C. L · 2011
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Experimental repetitive quantum error correction
Schindler, P. et al · 2011
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Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor
Moussa, O., Baugh, J., Ryan, C. A. & Laflamme, R · 2011
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Experimental quantum error correction with high fidelity
Zhang, J., Gangloff, D., Moussa, O. & Laflamme, R · 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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Surface code quantum computing by lattice surgery
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Towards practical classical processing for the surface code
Fowler, A. G., Whiteside, A. C. & Hollenberg, L. C · 2012
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Fault-tolerant quantum computing with color codes (2011)
Landahl, A. J., Anderson, J. T. & Rice, P. R · 2012
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Realization of three-qubit quantum error correction with superconducting circuits
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Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code
Zhang, J., Laflamme, R. & Suter, D · 2012
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Optimal complexity correction of correlated errors in the surface code
Fowler, A. G · 2013
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Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
Geller, M. R. & Zhou, Z · 2013
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Quantum information theory (Cambridge University Press, 2013)
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Approximation of realistic errors by Clifford channels and Pauli measurements
Gutiérrez, M., Svec, L., Vargo, A. & Brown, K. R · 2013
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Coping with qubit leakage in topological codes
Fowler, A. G · 2013
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Efficient algorithms for maximum likelihood decoding in the surface code
Bravyi, S., Suchara, M. & Vargo, A · 2014
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Low-distance surface codes under realistic quantum noise
Tomita, Y. & Svore, K. M · 2014
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Experimental demonstration of a graph state quantum error-correction code
Bell, B. et al · 2014
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Quantum computations on a topologically encoded qubit
Nigg, D. et al · 2014
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Quantum error correction and universal gate set operation on a binomial bosonic logical qubit
Hu, L. et al · 2019
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Improved fault-tolerant quantum simulation of condensed-phase correlated electrons via trotterization
Kivlichan, I. D. et al · 2020
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Demonstration of quantum volume 64 on a superconducting quantum computing system
Jurcevic, P. et al · 2020
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Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms
Foxen, B. et al · 2020
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Quantum error correction of a qubit encoded in grid states of an oscillator
Campagne-Ibarcq, P. et al · 2020
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Quantum error correction in a solid-state hybrid spin register
Waldherr, G. et al · 2014
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Leakage suppression in the toric code
Suchara, M., Cross, A. W. & Gambetta, J. M · 2015
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State preservation by repetitive error detection in a superconducting quantum circuit
Kelly, J. et al · 2015
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Logical error rate in the Pauli twirling approximation
Katabarwa, A. & Geller, M. R · 2015
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Detecting bit-flip errors in a logical qubit using stabilizer measurements
Riste, D. et al · 2015
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Demonstration of a quantum error detection code using a square lattice of four superconducting qubits
Córcoles, A. D. et al · 2015
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Grimm, A. et al · 2020
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Refined belief propagation decoding of sparse-graph quantum codes
Kuo, K.-Y. & Lai, C.-Y · 2020
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Fault-tolerant weighted union-find decoding on the toric code
Huang, S., Newman, M. & Brown, K. R · 2020
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qsim (2020)
Quantum AI team & collaborators · 2020
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Benchmarking near-term devices with quantum error correction
Wootton, J. R · 2020
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Repeated quantum error detection in a surface code
Andersen, C. K. et al · 2020
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Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements
Bultink, C. et al · 2020
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How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
Gidney, C. & Ekera, M · 2021
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Strong quantum computational advantage using a superconducting quantum processor
Wu, Y. et al · 2021
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Realization of real-time fault-tolerant quantum error correction
Ryan-Anderson, C. et al · 2021
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Fault-tolerant control of an error-corrected qubit
Egan, L. et al · 2021
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Realizing topologically ordered states on a quantum processor
Satzinger, K. et al · 2021
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Exponential suppression of bit or phase errors with cyclic error correction
Chen, Z. et al · 2021
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The XZZX surface code
Bonilla Ataides, J. P., Tuckett, D. K., Bartlett, S. D., Flammia, S. T. & Brown, B. J · 2021
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Removing leakage-induced correlated errors in superconducting quantum error correction
McEwen, M. et al · 2021
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Statistical mechanical models for quantum codes with correlated noise
Chubb, C. T. & Flammia, S. T · 2021
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Improved quantum error correction using soft information
Pattison, C. A., Beverland, M. E., da Silva, M. P. & Delfosse, N · 2021
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Stim: a fast stabilizer circuit simulator
Gidney, C · 2021
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Degenerate Quantum LDPC Codes With Good Finite Length Performance
Panteleev, P. & Kalachev, G · 2021
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Almost-linear time decoding algorithm for topological codes
Delfosse, N. & Nickerson, N. H · 2021
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Simulations of quantum circuits with approximate noise using qsim and cirq
Isakov, S. V. et al · 2021
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Hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits
Battistel, F., Varbanov, B. M. & Terhal, B. M · 2021
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Realization of high-fidelity CZ and Z Z ZZ -free iSWAP gates with a tunable coupler
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Experimental exploration of five-qubit quantum error-correcting code with superconducting qubits
Gong, M. et al · 2021
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Quantum teleportation of physical qubits into logical code spaces
Luo, Y.-H. et al · 2021
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Realizing repeated quantum error correction in a distance-three surface code
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