Fetching the paper…
Reading the bibliography…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms.
S. Lloyd, Science 273
1996
Earlier work this paper cites.
A. Y. Kitaev, A. Shen, and M. N. Vyalyi, Classical and Quantum Computation (American Mathematical Society, 2002)
2002
Earlier work this paper cites.
A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science (New York, N.Y.) 309
2005
Earlier work this paper cites.
E. Knill, G. Ortiz, and R. D. Somma, Physical Review A 75
2007
Earlier work this paper cites.
D. W. Berry, G. Ahokas, R. Cleve, and B. C. Sanders, Communications in Mathematical Physics 270
2007
Earlier work this paper cites.
M. Dobšíček, G. Johansson, V. Shumeiko, and G. Wendin, Physical Review A 76
2007
Earlier work this paper cites.
M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information (Cambridge University Press, 2010)
2010
Earlier work this paper cites.
C. Ferrie, C. E. Granade, and D. G. Cory, Quantum Information Processing 12
2013
Earlier work this paper cites.
A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O’Brien, Nature Communications 5
2014
Cited alongside, same era.
B. M. Hoffman, D. Lukoyanov, Z.-Y. Yang, D. R. Dean, and L. C. Seefeldt, Chemical Reviews 114
2014
Cited alongside, same era.
N. Wiebe, C. Granade, C. Ferrie, and D. G. Cory, Physical Review Letters 112
2014
Cited alongside, same era.
D. Wecker, M. B. Hastings, and M. Troyer, Physical Review A 92
2015
Cited alongside, same era.
N. Wiebe, C. Granade, A. Kapoor, and K. M. Svore, “Approximate Bayesian Inference via Rejection Filtering,” (2015)
2015
Cited alongside, same era.
J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, New Journal of Physics 18
N. Wiebe and C. Granade, Physical Review Letters 117
2016
Later among the works it cites.
D. Maslov, Phys. Rev. A 93
2016
Later among the works it cites.
M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Proceedings of the National Academy of Sciences of the United States of America 114
2017
Later among the works it cites.
S. Paesani, A. A. Gentile, R. Santagati, J. Wang, N. Wiebe, D. P. Tew, J. L. O’Brien, and M. G. Thompson, Physical Review Letters 118
2017
Later among the works it cites.
R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, Phys. Rev. X 8
2018
Closest in time.
T. E. O’Brien, B. Tarasinski, and B. M. Terhal, ArXiv e-prints (2018), arXiv:1809.09697 [quant-ph]
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2016
Cited alongside, same era.
P. J. J. O’Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, et al. , Physical Review X 6
2016
Cited alongside, same era.
One could alternatively bound the circuit area or total number of quantum gates. We use circuit depth for simplicity
Cited in the paper.
See Supplemental Material below for Appendices A. Derivation of Proposition 1, B. RFPE-with-restarts, and C. δ \delta -bound and state collapse. In A, we build on Refs. [ 17 , 25 ] . In C, we follow the analysis of Ref. [ 26 ]
Cited in the paper.
An actual standard deviation of ϵ \epsilon on an unbiased posterior mean implies “precision ϵ \epsilon ” in Kitaev’s sense by Markov’s inequality. The converse is not true. In the Supplementary Material [ 18 ] , we numerically verify that our new definition of ϵ \epsilon well approximates the true error
Cited in the paper.
In our pre-fault-tolerant setting, the CNOT gate count is the most relevant resource count
Cited in the paper.
Locally optimal ( M , θ ) (M,\theta) at each iteration may not be globally optimal over a number of iterations. In fact, A ≈ 1.154 A\approx 1.154 differs from the globally optimal heuristic of 1.25 1.25 , but this distinction between local and global is besides the main point here and shall not be further discussed
Cited in the paper.
2018
Closest in time.
J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Quantum Science and Technology 4
2019
Closest in time.