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1973
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A. Berthiaume and G. Brassard, “ The quantum challenge to structural complexity theory
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2002
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H. Kleinert and V. Schulte-Frohlinde, “ Critical Properties of ϕ 4 \phi^{4} Theories
2004
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M. A. Nielsen, M. R. Dowling, M. Gu, and A. M. Doherty, Quantum Computation as Geometry
2006
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S. Ghosh and B. Sanders, “ Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps
2007
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Cambridge University Press, 2009
S. Arora and B. Barak, Computational Complexity: A Modern Approach · 2009
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J. Watrous, Quantum computational complexity · 2009
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Oxford University Press, 2011
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S. Sachdev, “ Quantum phase transitions
2011
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L. Y. Hung, R. C. Myers and M. Smolkin, “Some Calculable Contributions to Holographic Entanglement Entropy
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Original
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Original
2012
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J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “ Entanglement Renormalization for Quantum Fields in Real Space
Original
2013
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S. P. Jordan, K. S. M. Lee and J. Preskill, “ Quantum Computation of Scattering in Scalar Quantum Field Theories
Original
2014
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2018

Circuit complexity in interacting QFTs and RG flows

Bhattacharyya, Arpan, Shekar, Arvind, Sinha, Aninda

Understand

We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the $\phi^4$ theory.

We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of the theory.
Our approach uses Nielsen's geometric method, which translates into working out the geodesic equation arising from a certain cost functional.
We present a general method, making use of integral transforms, to do the required lattice sums analytically and give explicit expressions for the $d=2,3$ cases.

Built on

C. Bennett, “ Logical reversibility of computation
1973
Earlier work this paper cites.
A. Berthiaume and G. Brassard, “ The quantum challenge to structural complexity theory
1992
Earlier work this paper cites.
E. Bernstein and U. Vazirani, “ Quantum complexity theory
1993
Earlier work this paper cites.
S. Lloyd, “ Ultimate physical Limits to computation”
2000
Earlier work this paper cites.
J. Smit, “ Introduction to Quantum Fields on a Lattice
2002
Earlier work this paper cites.
H. Kleinert and V. Schulte-Frohlinde, “ Critical Properties of ϕ 4 \phi^{4} Theories
2004
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu, and A. M. Doherty, Quantum Computation as Geometry
2006
Earlier work this paper cites.
S. Ghosh and B. Sanders, “ Non-Gaussian ancilla states for continuous variable quantum computation via Gaussian maps
2007
Earlier work this paper cites.
Cambridge University Press, 2009
S. Arora and B. Barak, Computational Complexity: A Modern Approach · 2009
Earlier work this paper cites.
Springer, 2009
J. Watrous, Quantum computational complexity · 2009
Earlier work this paper cites.
Oxford University Press, 2011
C. Moore and S. Mertens, The Nature of Computation · 2011
Earlier work this paper cites.
S. Sachdev, “ Quantum phase transitions
2011
Earlier work this paper cites.
L. Y. Hung, R. C. Myers and M. Smolkin, “Some Calculable Contributions to Holographic Entanglement Entropy
Original
2011
Earlier work this paper cites.
T. J. Osborne, Hamiltonian complexity
2012
Earlier work this paper cites.
S. P. Jordan, K. S. M. Lee and J. Preskill, “ Quantum Algorithms for Quantum Field Theories
Original
2012
Earlier work this paper cites.
B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
M. Nozaki, S. Ryu and T. Takayanagi, “ Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
Original
2012
Earlier work this paper cites.
R. C. Myers and A. Sinha, “ Holographic c-theorems in arbitrary dimensions
Original
2012
Earlier work this paper cites.
J. Haegeman, T. J. Osborne, H. Verschelde and F. Verstraete, “ Entanglement Renormalization for Quantum Fields in Real Space
Original
2013
Earlier work this paper cites.
S. P. Jordan, K. S. M. Lee and J. Preskill, “ Quantum Computation of Scattering in Scalar Quantum Field Theories
Original
2014
Earlier work this paper cites.