Quantum supremacy using a programmable superconducting processor

Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

Devoret, M. H., Martinis, J. M. & Clarke, J. Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased Josephson junction. Phys. Rev. Lett. 55, 1908 (1985).

Nakamura, Y., Chen, C. D. & Tsai, J. S. Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by Josephson coupling. Phys. Rev. Lett. 79, 2328 (1997).

Mooij, J. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).

Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

You, J. Q. & Nori, F. Atomic physics and quantum optics using superconducting circuits. Nature 474, 589–597 (2011).

Preskill, J. Quantum computing and the entanglement frontier. Rapporteur Talk at the 25th Solvay Conference on Physics, Brussels https://doi.org/10.1142/8674 (World Scientific, 2012).

Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. In Proc. 43rd Ann. Symp. on Theory of Computing https://doi.org/10.1145/1993636.1993682 (ACM, 2011).

Bremner, M. J., Montanaro, A. & Shepherd, D. J. Average-case complexity versus approximate simulation of commuting quantum computations. Phys. Rev. Lett. 117, 080501 (2016).

Boixo, S. et al. Characterizing quantum supremacy in near-term devices. Nat. Phys. 14, 595 (2018).

Bouland, A., Fefferman, B., Nirkhe, C. & Vazirani, U. On the complexity and verification of quantum random circuit sampling. Nat. Phys. 15, 159 (2019).

Aaronson, S. & Chen, L. Complexity-theoretic foundations of quantum supremacy experiments. In 32nd Computational Complexity Conf. https://doi.org/10.4230/LIPIcs.CCC.2017.22 (Schloss Dagstuhl–Leibniz Zentrum für Informatik, 2017).

Neill, C. et al. A blueprint for demonstrating quantum supremacy with superconducting qubits. Science 360, 195–199 (2018).

Preskill, J. Quantum computing in the NISQ era and beyond. Quantum 2, 79 (2018).

Kechedzhi, K. et al. Efficient population transfer via non-ergodic extended states in quantum spin glass. In 13th Conf. on the Theory of Quantum Computation, Communication and Cryptography http://drops.dagstuhl.de/opus/volltexte/2018/9256/pdf/LIPIcs-TQC-2018-9.pdf (Schloss Dagstuhl–Leibniz Zentrum für Informatik, 2018).

Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum simulations of classical annealing processes. Phys. Rev. Lett. 101, 130504 (2008).

Farhi, E. & Neven, H. Classification with quantum neural networks on near term processors. Preprint at https://arxiv.org/abs/1802.06002 (2018).

McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. Nat. Commun. 9, 4812 (2018).

Cong, I., Choi, S. & Lukin, M. D. Quantum convolutional neural networks. Nat. Phys. https://doi.org/10.1038/s41567-019-0648-8 (2019).

Bravyi, S., Gosset, D. & König, R. Quantum advantage with shallow circuits. Science 362, 308–311 (2018).

Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005).

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014).

Hempel, C. et al. Quantum chemistry calculations on a trapped-ion quantum simulator. Phys. Rev. X 8, 031022 (2018).

Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring proceedings. In Proc. 35th Ann. Symp. on Foundations of Computer Science https://doi.org/10.1109/SFCS.1994.365700 (IEEE, 1994).

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).

Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014).

Córcoles, A. D. et al. Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nat. Commun. 6, 6979 (2015).

Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441 (2016).

Vool, U. & Devoret, M. Introduction to quantum electromagnetic circuits. Int. J. Circuit Theory Appl. 45, 897–934 (2017).

Chen, Y. et al. Qubit architecture with high coherence and fast tunable coupling circuits. Phys. Rev. Lett. 113, 220502 (2014).

Yan, F. et al. A tunable coupling scheme for implementing high-fidelity two-qubit gates. Phys. Rev. Appl. 10, 054062 (2018).

Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515 (2007).

Jeffrey, E. et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014).

Chen, Z. et al. Measuring and suppressing quantum state leakage in a superconducting qubit. Phys. Rev. Lett. 116, 020501 (2016).

Klimov, P. V. et al. Fluctuations of energy-relaxation times in superconducting qubits. Phys. Rev. Lett. 121, 090502 (2018).

Yan, F. et al. The flux qubit revisited to enhance coherence and reproducibility. Nat. Commun. 7, 12964 (2016).

Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).

Magesan, E., Gambetta, J. M. & Emerson, J. Scalable and robust randomized benchmarking of quantum processes. Phys. Rev. Lett. 106, 180504 (2011).

Cross, A. W., Magesan, E., Bishop, L. S., Smolin, J. A. & Gambetta, J. M. Scalable randomised benchmarking of non-Clifford gates. npj Quant. Inform. 2, 16012 (2016).

Wallraff, A. et al. Approaching unit visibility for control of a superconducting qubit with dispersive readout. Phys. Rev. Lett. 95, 060501 (2005).

De Raedt, H. et al. Massively parallel quantum computer simulator, eleven years later. Comput. Phys. Commun. 237, 47–61 (2019).

Markov, I. L., Fatima, A., Isakov, S. V. & Boixo, S. Quantum supremacy is both closer and farther than it appears. Preprint at https://arxiv.org/abs/1807.10749 (2018).

Villalonga, B. et al. A flexible high-performance simulator for the verification and benchmarking of quantum circuits implemented on real hardware. npj Quant. Inform. (in the press); preprint at https://arxiv.org/abs/1811.09599 (2018).

Boixo, S., Isakov, S. V., Smelyanskiy, V. N. & Neven, H. Simulation of low-depth quantum circuits as complex undirected graphical models. Preprint at https://arxiv.org/abs/1712.05384 (2017).

Chen, J., Zhang, F., Huang, C., Newman, M. & Shi, Y. Classical simulation of intermediate-size quantum circuits. Preprint at https://arxiv.org/abs/1805.01450 (2018).

Villalonga, B. et al. Establishing the quantum supremacy frontier with a 281 pflop/s simulation. Preprint at https://arxiv.org/abs/1905.00444 (2019).

Pednault, E. et al. Breaking the 49-qubit barrier in the simulation of quantum circuits. Preprint at https://arxiv.org/abs/1710.05867 (2017).

Chen, Z. Y. et al. 64-qubit quantum circuit simulation. Sci. Bull. 63, 964–971 (2018).

Chen, M.-C. et al. Quantum-teleportation-inspired algorithm for sampling large random quantum circuits. Preprint at https://arxiv.org/abs/1901.05003 (2019).

Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).

Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

Mohseni, M. et al. Commercialize quantum technologies in five years. Nature 543, 171 (2017).

Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997).

Bernstein, E. & Vazirani, U. Quantum complexity theory. In Proc. 25th Ann. Symp. on Theory of Computing https://doi.org/10.1145/167088.167097 (ACM, 1993).