Built on

R. F. Streater, A. S. Wightman, PCT, spin and statistics, and all that
1964
Earlier work this paper cites.
K. G. Wilson, J. Kogut, The renormalization group and the ϵ \epsilon expansion, Physics Reports 12, 75-199 (1974)
1974
Earlier work this paper cites.
James Glimm, Arthur Jaffe, Quantum physics: a functional integral point of view
1981
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R. P. Feynman, Simulating physics with computers, Int. J. Theor. Physics 21, 467-488 (1982)
1982
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Francisco Barahona, On the computational complexity of Ising spin glass models, Journal of Physics A: Mathematical and General 15, 3241 (1982)
1982
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Estia Eichten, John Preskill. Chiral gauge theories on the lattice, Nucl. Phys. 268, 179-208 (1985)
1985
Earlier work this paper cites.
David B. Kaplan, A Method for simulating chiral fermions on the lattice, Physics Letters B 288, 342-347 (1992)
1992
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Masuo Suzuki, General decomposition theory of ordered exponentials, Proceedings of the Japan Academy, Series B 69, 161-166 (1993)
1993
Earlier work this paper cites.
Juan Maldacena, The large-N limit of superconformal field theories and supergravity, International Journal of Theoretical Physics 38, 1113-1133 (1999), arXiv:hep-th/9711200
1999
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P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Rev. 41, 303-332 (1999)
1999
Earlier work this paper cites.
A. Y. Kitaev, A. Shen, M. N. Vyalyi, Classical and quantum computation
2002
Earlier work this paper cites.
Pasquale Calabrese, John Cardy, Evolution of entanglement entropy in one-dimensional systems, Journal of Statistical Mechanics: Theory and Experiment 2005.04, P04010 (2005), arXiv:cond-mat/0503393
2005
Earlier work this paper cites.
Tim Byrnes, Yoshihisa Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys.Rev. A73, 022328 (2006), arXiv:quant-ph/0510027
2006
Earlier work this paper cites.
Dorit Aharonov, Daniel Gottesman, Sandy Irani, Julia Kempe, The power of quantum systems on a line, Communications in Mathematical Physics 287, 41-65 (2009), arXiv:0705.4077
Original
2009
Earlier work this paper cites.
D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, Proceedings of Symposia in Applied Matthematics 68 (2010), arXiv:0904.2557
Original
2010
Earlier work this paper cites.
F. Verstraete, J. I. Cirac, Continuous Matrix Product States for Quantum Fields, Phys. Rev. Lett. 104, 190405 (2010), arXiv:1002.1824
Original
2010
Earlier work this paper cites.
Ulrich Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96-192 (2011), arXiv:1008.3477
Original
2011
Earlier work this paper cites.

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2018

Simulating quantum field theory with a quantum computer

Preskill, John

Understand

Forthcoming exascale digital computers will further advance our knowledge of quantum chromodynamics, but formidable challenges will remain.

In particular, Euclidean Monte Carlo methods are not well suited for studying real-time evolution in hadronic collisions, or the properties of hadronic matter at nonzero temperature and chemical potential.
Digital computers may never be able to achieve accurate simulations of such phenomena in QCD and other strongly-coupled field theories; quantum computers will do so eventually, though I'm not sure when.
Progress toward quantum simulation of quantum field theory will require the collaborative efforts of quantumists and field theorists, and though the physics payoff may still be far away, it's worthwhile to get started now.

Built on

R. F. Streater, A. S. Wightman, PCT, spin and statistics, and all that
1964
Earlier work this paper cites.
K. G. Wilson, J. Kogut, The renormalization group and the ϵ \epsilon expansion, Physics Reports 12, 75-199 (1974)
1974
Earlier work this paper cites.
James Glimm, Arthur Jaffe, Quantum physics: a functional integral point of view
1981
Earlier work this paper cites.
R. P. Feynman, Simulating physics with computers, Int. J. Theor. Physics 21, 467-488 (1982)
1982
Earlier work this paper cites.
Francisco Barahona, On the computational complexity of Ising spin glass models, Journal of Physics A: Mathematical and General 15, 3241 (1982)
1982
Earlier work this paper cites.
Estia Eichten, John Preskill. Chiral gauge theories on the lattice, Nucl. Phys. 268, 179-208 (1985)
1985
Earlier work this paper cites.
David B. Kaplan, A Method for simulating chiral fermions on the lattice, Physics Letters B 288, 342-347 (1992)
1992
Earlier work this paper cites.
Masuo Suzuki, General decomposition theory of ordered exponentials, Proceedings of the Japan Academy, Series B 69, 161-166 (1993)
1993
Earlier work this paper cites.
Juan Maldacena, The large-N limit of superconformal field theories and supergravity, International Journal of Theoretical Physics 38, 1113-1133 (1999), arXiv:hep-th/9711200
1999
Earlier work this paper cites.
P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Rev. 41, 303-332 (1999)
1999
Earlier work this paper cites.
A. Y. Kitaev, A. Shen, M. N. Vyalyi, Classical and quantum computation
2002
Earlier work this paper cites.
Pasquale Calabrese, John Cardy, Evolution of entanglement entropy in one-dimensional systems, Journal of Statistical Mechanics: Theory and Experiment 2005.04, P04010 (2005), arXiv:cond-mat/0503393
2005
Earlier work this paper cites.
Tim Byrnes, Yoshihisa Yamamoto, Simulating lattice gauge theories on a quantum computer, Phys.Rev. A73, 022328 (2006), arXiv:quant-ph/0510027
2006
Earlier work this paper cites.
Dorit Aharonov, Daniel Gottesman, Sandy Irani, Julia Kempe, The power of quantum systems on a line, Communications in Mathematical Physics 287, 41-65 (2009), arXiv:0705.4077
Original
2009
Earlier work this paper cites.
D. Gottesman, An introduction to quantum error correction and fault-tolerant quantum computation, Proceedings of Symposia in Applied Matthematics 68 (2010), arXiv:0904.2557
Original
2010
Earlier work this paper cites.
F. Verstraete, J. I. Cirac, Continuous Matrix Product States for Quantum Fields, Phys. Rev. Lett. 104, 190405 (2010), arXiv:1002.1824
Original
2010
Earlier work this paper cites.
Ulrich Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96-192 (2011), arXiv:1008.3477
Original
2011
Earlier work this paper cites.