Built on

E. Wigner, On the quantum correction for thermodynamic equilibrium , Phys. Rev. 40
1932
Earlier work this paper cites.
Springer Netherlands, Dordrecht, 1985
G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories · 1985
Earlier work this paper cites.
World Scientific, Singapore River Edge, N.J, 1999
Chern, Lectures on differential geometry · 1999
Earlier work this paper cites.
Springer New York, New York, 2000, 10.1007/978-1-4612-1268-3
D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry · 2000
Earlier work this paper cites.
Wspc, 2001
Z. Shen, Lectures on finsler geometry (Series on Multivariate Analysis) · 2001
Earlier work this paper cites.
World Scientific Pub Co Inc, 2005
C. Zachos, D. Fairlie and T. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific) · 2005
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu and A. C. Doherty, Quantum computation as geometry , Science 311
2006
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds , Quantum Info. Comput. 6
2006
Earlier work this paper cites.
World Scientific, Singapore Hackensack, NJ, 2006
M. Xiaohuan, An introduction to Finsler geometry · 2006
Earlier work this paper cites.
M. R. Dowling and M. A. Nielsen, The geometry of quantum computation , Quantum Info. Comput. 8
2008
Earlier work this paper cites.
S. Deng and Z. Hou, Positive definite minkowski lie algebras and bi-invariant finsler metrics on lie groups , Geometriae Dedicata 136
2008
Earlier work this paper cites.
D. Latifi and A. Razavi, Bi-invariant finsler metrics on lie groups , Journal of Basic and Applied Sciences 5
2011
Earlier work this paper cites.
Cambridge University Press, Cambridge New York, 2012
T. Frankel, The geometry of physics : an introduction · 2012
Earlier work this paper cites.
T. L. Curtright and C. K. Zachos, Quantum Mechanics in Phase Space , Asia Pac. Phys. Newslett. 1
Original
2012
Earlier work this paper cites.
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls , JHEP 06
Original
2013
Earlier work this paper cites.
D. Latifi and M. Toomanian, On the existence of bi-invariant finsler metrics on lie groups , Mathematical Sciences 7
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.

Similar

D. A. Roberts, D. Stanford and L. Susskind, Localized shocks , JHEP 03
Original
2015
Cited alongside, same era.
M. Alishahiha, Holographic Complexity , Phys. Rev. D92
Original
2015
Cited alongside, same era.
Springer International Publishing, Cham, 2015
M. M. Alexandrino and R. G. Bettiol, Lie Groups with Bi-invariant Metrics , pp. 27–47 · 2015
Cited alongside, same era.
1607.05256
Original
S. Aaronson, The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes , 2016 · 2016
Cited alongside, same era.
L. Susskind, Computational Complexity and Black Hole Horizons , Fortsch. Phys. 64
Original
2016
Cited alongside, same era.

Then

A. R. Brown, L. Susskind and Y. Zhao, Quantum Complexity and Negative Curvature , Phys. Rev. D95
Original
2017
Later among the works it cites.
R. A. Jefferson and R. C. Myers, Circuit complexity in quantum field theory , JHEP 10
Original
2017
Later among the works it cites.
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories , Phys. Rev. Lett. 119
Original
2017
Later among the works it cites.
P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT , JHEP 11
Original
2017
Later among the works it cites.
K. Hashimoto, N. Iizuka and S. Sugishita, Time evolution of complexity in Abelian gauge theories , Phys. Rev. D96

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2018

More on complexity of operators in quantum field theory

Yang, Run-Qiu, An, Yu-Sen, Niu, Chao et al.

Understand

Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory.

It is based on three axioms and one assumption regarding the complexity in continuous systems.
By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type.
We also clarify the relation between our complexity and other works.

Built on

E. Wigner, On the quantum correction for thermodynamic equilibrium , Phys. Rev. 40
1932
Earlier work this paper cites.
Springer Netherlands, Dordrecht, 1985
G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories · 1985
Earlier work this paper cites.
World Scientific, Singapore River Edge, N.J, 1999
Chern, Lectures on differential geometry · 1999
Earlier work this paper cites.
Springer New York, New York, 2000, 10.1007/978-1-4612-1268-3
D. Bao, S.-S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry · 2000
Earlier work this paper cites.
Wspc, 2001
Z. Shen, Lectures on finsler geometry (Series on Multivariate Analysis) · 2001
Earlier work this paper cites.
World Scientific Pub Co Inc, 2005
C. Zachos, D. Fairlie and T. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific) · 2005
Earlier work this paper cites.
M. A. Nielsen, M. R. Dowling, M. Gu and A. C. Doherty, Quantum computation as geometry , Science 311
2006
Earlier work this paper cites.
M. A. Nielsen, A geometric approach to quantum circuit lower bounds , Quantum Info. Comput. 6
2006
Earlier work this paper cites.
World Scientific, Singapore Hackensack, NJ, 2006
M. Xiaohuan, An introduction to Finsler geometry · 2006
Earlier work this paper cites.
M. R. Dowling and M. A. Nielsen, The geometry of quantum computation , Quantum Info. Comput. 8
2008
Earlier work this paper cites.
S. Deng and Z. Hou, Positive definite minkowski lie algebras and bi-invariant finsler metrics on lie groups , Geometriae Dedicata 136
2008
Earlier work this paper cites.
D. Latifi and A. Razavi, Bi-invariant finsler metrics on lie groups , Journal of Basic and Applied Sciences 5
2011
Earlier work this paper cites.
Cambridge University Press, Cambridge New York, 2012
T. Frankel, The geometry of physics : an introduction · 2012
Earlier work this paper cites.
T. L. Curtright and C. K. Zachos, Quantum Mechanics in Phase Space , Asia Pac. Phys. Newslett. 1
Original
2012
Earlier work this paper cites.
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls , JHEP 06
Original
2013
Earlier work this paper cites.
D. Latifi and M. Toomanian, On the existence of bi-invariant finsler metrics on lie groups , Mathematical Sciences 7
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries , Phys. Rev. D90
Original
2014
Earlier work this paper cites.

Similar

D. A. Roberts, D. Stanford and L. Susskind, Localized shocks , JHEP 03
Original
2015
Cited alongside, same era.
M. Alishahiha, Holographic Complexity , Phys. Rev. D92
Original
2015
Cited alongside, same era.
Springer International Publishing, Cham, 2015
M. M. Alexandrino and R. G. Bettiol, Lie Groups with Bi-invariant Metrics , pp. 27–47 · 2015
Cited alongside, same era.
1607.05256
Original
S. Aaronson, The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes , 2016 · 2016
Cited alongside, same era.
L. Susskind, Computational Complexity and Black Hole Horizons , Fortsch. Phys. 64
Original
2016
Cited alongside, same era.