25
[12] M. J. Bremner, R. Jozsa, and D. J. Shepherd. Classical simu-
lation of commuting quantum computations implies collapse
of the polynomial hierarchy. In Proceedings of the Royal Soci-
ety of London A: Mathematical, Physical and Engineering Sci-
ences, page rspa20100301. The Royal Society, 2010. doi:
10.1098/rspa.2010.0301.
[13] M. J. Bremner, A. Montanaro, and D. J. Shepherd. Average-
case complexity versus approximate simulation of commut-
ing quantum computations. Physical Review Letters, 117(8):
080501, 2016. doi:10.1103/PhysRevLett.117.080501.
[14] S. Boixo, S. V. Isakov, V. N. Smelyanskiy, R. Babbush, N. Ding,
Z. Jiang, M. J. Bremner, J. M. Martinis, and H. Neven. Char-
acterizing quantum supremacy in near-term devices. Nature
Physics, 14(6):595, 2018. doi:10.1038/s41567-018-0124-x.
[15] S. Aaronson and L. Chen. Complexity-Theoretic Foundations
of Quantum Supremacy Experiments. In R. O’Donnell, edi-
tor, 32nd Computational Complexity Conference (CCC 2017),
volume 79 of Leibniz International Proceedings in Informat-
ics (LIPIcs), pages 22:1–22:67. Schloss Dagstuhl–Leibniz-
Zentrum fuer Informatik, 2017. ISBN 978-3-95977-040-8.
doi:10.4230/LIPIcs.CCC.2017.22.
[16] C. Neill, P. Roushan, K. Kechedzhi, S. Boixo, S. V. Isakov,
V. Smelyanskiy, A. Megrant, B. Chiaro, A. Dunsworth,
K. Arya, et al. A blueprint for demonstrating quan-
tum supremacy with superconducting qubits. Science, 360
(6385):195–199, 2018. doi:10.1126/science.aao4309.
[17] T. Douce, D. Markham, E. Kashefi, E. Diamanti, T. Coudreau,
P. Milman, P. van Loock, and G. Ferrini. Continuous-
variable instantaneous quantum computing is hard to
sample. Physical Review Letters, 118(7), 2017. doi:
10.1103/PhysRevLett.118.070503.
[18] A. Finnila, M. Gomez, C. Sebenik, C. Stenson, and J. Doll.
Quantum annealing: a new method for minimizing multi-
dimensional functions. Chemical Physics Letters, 219(5-6):
343–348, 1994. doi:10.1016/0009-2614(94)00117-0.
[19] M. W. Johnson, M. H. Amin, S. Gildert, T. Lanting, F. Hamze,
N. Dickson, R. Harris, A. J. Berkley, J. Johansson, P. Bunyk,
et al. Quantum annealing with manufactured spins. Nature,
473(7346):194–198, 2011. doi:10.1038/nature10012.
[20] M.-H. Yung, J. Casanova, A. Mezzacapo, J. McClean,
L. Lamata, A. Aspuru-Guzik, and E. Solano. From transistor
to trapped-ion computers for quantum chemistry. Scientific
Reports, 4:3589, 2014. doi:10.1038/srep03589.
[21] P. O’Malley, R. Babbush, I. Kivlichan, J. Romero, J. Mc-
Clean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding,
et al. Scalable quantum simulation of molecular en-
ergies. Physical Review X, 6(3):031007, 2016. doi:
10.1103/PhysRevX.6.031007.
[22] Y. Shen, X. Zhang, S. Zhang, J.-N. Zhang, M.-H. Yung,
and K. Kim. Quantum implementation of the unitary
coupled cluster for simulating molecular electronic struc-
ture. Physical Review A, 95(2):020501, 2017. doi:
10.1103/PhysRevA.95.020501.
[23] A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink,
J. M. Chow, and J. M. Gambetta. Hardware-efficient varia-
tional quantum eigensolver for small molecules and quan-
tum magnets. Nature, 549(7671):242–246, 2017. doi:
10.1038/nature23879.
[24] G. Rosenberg, P. Haghnegahdar, P. Goddard, P. Carr, K. Wu,
and M. L. de Prado. Solving the optimal trading trajectory
problem using a quantum annealer. IEEE Journal of Selected
Topics in Signal Processing, 10(6):1053–1060, 2016. doi:
10.1109/JSTSP.2016.2574703.
[25] A. Lucas. Ising formulations of many NP problems. Frontiers
in Physics, 2:5, 2014. doi:10.3389/fphy.2014.00005.
[26] F. Neukart, D. Von Dollen, G. Compostella, C. Seidel,
S. Yarkoni, and B. Parney. Traffic flow optimization using
a quantum annealer. Frontiers in ICT, 4:29, 2017. doi:
10.3389/fict.2017.00029.
[27] H. Neven, V. S. Denchev, G. Rose, and W. G. Macready. Train-
ing a large scale classifier with the quantum adiabatic algo-
rithm. arXiv preprint arXiv:0912.0779, 2009.
[28] K. L. Pudenz and D. A. Lidar. Quantum adiabatic machine
learning. Quantum Information Processing, 12(5):2027–
2070, 2013. doi:10.1007/s11128-012-0506-4.
[29] D. Crawford, A. Levit, N. Ghadermarzy, J. S. Oberoi, and
P. Ronagh. Reinforcement learning using quantum Boltz-
mann machines. Quantum Information & Computation, 18
(1-2):0051–0074, 2018. doi:10.26421/QIC18.1-2.
[30] M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and
R. Melko. Quantum boltzmann machine. Phys. Rev. X, 8:
021050, May 2018. doi:10.1103/PhysRevX.8.021050.
[31] D. Ristè, M. P. Da Silva, C. A. Ryan, A. W. Cross, A. D. Cór-
coles, J. A. Smolin, J. M. Gambetta, J. M. Chow, and B. R.
Johnson. Demonstration of quantum advantage in machine
learning. npj Quantum Information, 3(1):16, 2017. doi:
10.1038/s41534-017-0017-3.
[32] G. Verdon, M. Broughton, and J. Biamonte. A quantum al-
gorithm to train neural networks using low-depth circuits.
arXiv preprint arXiv:1712.05304, 2017.
[33] J. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, M. Block,
B. Bloom, S. Caldwell, N. Didier, E. S. Fried, S. Hong, et al.
Unsupervised machine learning on a hybrid quantum com-
puter. arXiv preprint arXiv:1712.05771, 2017.
[34] M. Schuld and N. Killoran. Quantum machine learning in
feature hilbert spaces. Physical Review Letters, 122:040504,
Feb 2019. doi:10.1103/PhysRevLett.122.040504.
[35] A. S. Green, P. L. Lumsdaine, N. J. Ross, P. Selinger, and B. Val-
iron. Quipper: a scalable quantum programming language.
In ACM SIGPLAN Notices, volume 48, pages 333–342. ACM,
2013. doi:10.1145/2491956.2462177.
[36] D. Wecker and K. M. Svore. Liqui|>: A software design ar-
chitecture and domain-specific language for quantum com-
puting. arXiv preprint arXiv:1402.4467, 2014.
[37] A. JavadiAbhari, S. Patil, D. Kudrow, J. Heckey, A. Lvov, F. T.
Chong, and M. Martonosi. ScaffCC: Scalable compilation
and analysis of quantum programs. Parallel Computing, 45:
2–17, 2015. doi:10.1016/j.parco.2014.12.001.
[38] M. Smelyanskiy, N. P. Sawaya, and A. Aspuru-Guzik. qHiP-
STER: the quantum high performance software testing envi-
ronment. arXiv preprint arXiv:1601.07195, 2016.
[39] S. Pakin. A quantum macro assembler. In High Performance
Extreme Computing Conference (HPEC), 2016 IEEE, pages 1–
8. IEEE, 2016. doi:10.1109/HPEC.2016.7761637.
[40] R. S. Smith, M. J. Curtis, and W. J. Zeng. A practi-
cal quantum instruction set architecture. arXiv preprint
arXiv:1608.03355, 2016.
[41] D. S. Steiger, T. Häner, and M. Troyer. ProjectQ: an open
source software framework for quantum computing. Quan-
tum, 2:49, 2018. doi:10.22331/q-2018-01-31-49.
[42] A. W. Cross, L. S. Bishop, J. A. Smolin, and J. M. Gam-
betta. Open quantum assembly language. arXiv preprint
arXiv:1707.03429, 2017.
[43] E. S. Fried, N. P. Sawaya, Y. Cao, I. D. Kivlichan, J. Romero,
and A. Aspuru-Guzik. qtorch: The quantum tensor con-
traction handler. PloS one, 13(12):e0208510, 2018. doi:
10.1371/journal.pone.0208510.
[44] A. J. McCaskey, E. F. Dumitrescu, D. Liakh, M. Chen, W.-c.