Hu, L. et al. Quantum error correction and universal gate set operation on a binomial bosonic logical qubit. Nat. Phys. 15, 503–508 (2019).
Gertler, J. M. et al. Protecting a bosonic qubit with autonomous quantum error correction. Nature 590, 243–248 (2021).
Campagne-Ibarcq, P. et al. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368–372 (2020).
Krinner, S. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669–674 (2022).
Zhao, Y. et al. Realization of an error-correcting surface code with superconducting qubits. Phys. Rev. Lett. 129, 030501 (2022).
Sundaresan, N. et al. Matching and maximum likelihood decoding of a multi-round subsystem quantum error correction experiment. Preprint at https://arxiv.org/abs/2203.07205 (2022).
Google Quantum AI. Suppressing quantum errors by scaling a surface code logical qubit. Nature 614, 676–681 (2023).
Knill, E. & Laflamme, R. Theory of quantum error-correcting codes. Phys. Rev. A 55, 900–911 (1997).
Gottesman, D., Kitaev, A. & Preskill, J. Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001).
Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. N. J. Phys. 16, 045014 (2014).
Michael, M. H. et al. New class of quantum error-correcting codes for a bosonic mode. Phys. Rev. X 6, 031006 (2016).
Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).
Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996).
Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).
Noh, K. & Chamberland, C. Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code. Phys. Rev. A 101, 012316 (2020).
Terhal, B. M., Conrad, J. & Vuillot, C. Towards scalable bosonic quantum error correction. Quantum Sci. Technol. 5, 043001 (2020).
Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).
de Neeve, B., Nguyen, T.-L., Behrle, T. & Home, J. P. Error correction of a logical grid state qubit by dissipative pumping. Nat. Phys. 18, 296–300 (2022).
Ryan-Anderson, C. et al. Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11, 041058 (2021).
Egan, L. et al. Fault-tolerant control of an error-corrected qubit. Nature 598, 281–286 (2021).
Waldherr, G. et al. Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014).
Abobeih, M. et al. Fault-tolerant operation of a logical qubit in a diamond quantum processor. Nature 606, 884–889 (2022).
Xue, X. et al. Quantum logic with spin qubits crossing the surface code threshold. Nature 601, 343–347 (2022).
Place, A. P. et al. New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds. Nat. Commun. 12, 1779 (2021).
Reagor, M. et al. Quantum memory with millisecond coherence in circuit QED. Phys. Rev. B 94, 014506 (2016).
Royer, B., Singh, S. & Girvin, S. M. Stabilization of finite-energy Gottesman-Kitaev-Preskill states. Phys. Rev. Lett. 125, 260509 (2020).
Sutton, R. S. & Barto, A. G. Reinforcement Learning: an Introduction (MIT Press, 2018).
Schulman, J., Wolski, F., Dhariwal, P., Radford, A. & Klimov, O. Proximal policy optimization algorithms. Preprint at https://arxiv.org/abs/1707.06347 (2017).
Guadarrama, S. et al. TF-Agents: a library for reinforcement learning in TensorFlow. GitHub https://github.com/tensorflow/agents (2018).
Lescanne, R. et al. Exponential suppression of bit-flips in a qubit encoded in an oscillator. Nat. Phys. 16, 509–513 (2020).
Lloyd, S. & Viola, L. Engineering quantum dynamics. Phys. Rev. A 65, 010101 (2001).
Shen, C. et al. Quantum channel construction with circuit quantum electrodynamics. Phys. Rev. B 95, 134501 (2017).
Chen, Z. et al. Measuring and suppressing quantum state leakage in a superconducting qubit. Phys. Rev. Lett. 116, 020501 (2016).
Eickbusch, A. et al. Fast universal control of an oscillator with weak dispersive coupling to a qubit. Nat. Phys. 18, 1464–1469 (2022).
Kelly, J. et al. Optimal quantum control using randomized benchmarking. Phys. Rev. Lett. 112, 240504 (2014).
Werninghaus, M. et al. Leakage reduction in fast superconducting qubit gates via optimal control. npj Quantum Inf. 7, 14 (2021).
Sivak, V. V. et al. Model-free quantum control with reinforcement learning. Phys. Rev. X 12, 011059 (2022).
Terhal, B. M. & Weigand, D. Encoding a qubit into a cavity mode in circuit QED using phase estimation. Phys.l Rev. A 93, 012315 (2016).
Hastrup, J. & Andersen, U. L. Improved readout of qubit-coupled Gottesman-Kitaev-Preskill states. Quantum Sci. Technol. 6, 035016 (2021).
Klimov, P. V. et al. Fluctuations of energy-relaxation times in superconducting qubits. Phys. Rev. Lett. 121, 90502 (2018).
Nielsen, M. A. A simple formula for the average gate fidelity of a quantum dynamical operation. Phys. Lett. A 303, 249–252 (2002).
Bravyi, S. & Kitaev, A. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A 71, 022316 (2005).
Grimm, A. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020).
Chen, Z. et al. Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383–387 (2021).
Andersen, C. K. et al. Repeated quantum error detection in a surface code. Nat. Phys. 16, 875–880 (2020).
Ma, W.-L. et al. Path-independent quantum gates with noisy ancilla. Phys. Rev. Lett. 125, 110503 (2020).
Rosenblum, S. et al. Fault-tolerant detection of a quantum error. Science 361, 266–270 (2018).
Puri, S. et al. Stabilized cat in a driven nonlinear cavity: a fault-tolerant error syndrome detector. Phys. Rev. X 9, 041009 (2019).
Ni, Z. et al. Beating the break-even point with a discrete variable-encoded logical qubit. Nature https://doi.org/10.1038/s41586-023-05784-4 (2023).
Gross, J. A., Caves, C. M., Milburn, G. J. & Combes, J. Qubit models of weak continuous measurements: Markovian conditional and open-system dynamics. Quantum Sci. Technol. 3, 024005 (2018).
Pfaff, W. et al. Controlled release of multiphoton quantum states from a microwave cavity memory. Nat. Phys. 13, 882–887 (2017).
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