Models of Quantum Complexity Growth

Brandão, Fernando G. S. L.; Chemissany, Wissam; Hunter-Jones, Nicholas; Kueng, Richard; Preskill, John

doi:10.1103/PRXQuantum.2.030316

Title: Models of Quantum Complexity Growth

Journal Article · Thu Jul 29 00:00:00 UTC 2021 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.2.030316 · OSTI ID:1811006

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0018407

OSTI ID:: 1811006

Journal Information:: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 3 Vol. 2; ISSN 2691-3399; ISSN PQRUAG

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (54)

Computational complexity and black hole horizons: Computational complexity and black hole horizons Susskind, Leonard Fortschritte der Physik, Vol. 64, Issue 1 https://doi.org/10.1002/prop.201500092	journal	January 2016
Entanglement is not enough: Entanglement is not enough Susskind, Leonard Fortschritte der Physik, Vol. 64, Issue 1 https://doi.org/10.1002/prop.201500095	journal	January 2016
Matrix Analysis Bhatia, Rajendra Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4612-0653-8	book	November 1996
Representation Theory Fulton, William; Harris, Joe Graduate Texts in Mathematics https://doi.org/10.1007/978-1-4612-0979-9	book	January 2004
Optimal quantum measurements Holevo, A. S. Theoretical and Mathematical Physics, Vol. 17, Issue 3 https://doi.org/10.1007/BF01037594	journal	December 1973
Complexity of formation in holography Chapman, Shira; Marrochio, Hugo; Myers, Robert C. Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)062	journal	January 2017
Subsystem complexity and holography Agón, Cesar A.; Headrick, Matthew; Swingle, Brian Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)145	journal	February 2019
Holographic complexity equals which action? Goto, Kanato; Marrochio, Hugo; Myers, Robert C. Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)160	journal	February 2019
Comments on holographic complexity Carmi, Dean; Myers, Robert C.; Rath, Pratik Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/JHEP03(2017)118	journal	March 2017
Towards the fast scrambling conjecture Lashkari, Nima; Stanford, Douglas; Hastings, Matthew Journal of High Energy Physics, Vol. 2013, Issue 4 https://doi.org/10.1007/JHEP04(2013)022	journal	April 2013
Chaos and complexity by design Roberts, Daniel A.; Yoshida, Beni Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)121	journal	April 2017
Entanglement, quantum randomness, and complexity beyond scrambling Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)041	journal	July 2018
Chaos, complexity, and random matrices Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)048	journal	November 2017
Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)097	journal	November 2017
On the time dependence of holographic complexity Carmi, Dean; Chapman, Shira; Marrochio, Hugo Journal of High Energy Physics, Vol. 2017, Issue 11 https://doi.org/10.1007/JHEP11(2017)188	journal	November 2017
Spectral decoupling in many-body quantum chaos Cotler, Jordan; Hunter-Jones, Nicholas Journal of High Energy Physics, Vol. 2020, Issue 12 https://doi.org/10.1007/JHEP12(2020)205	journal	December 2020
Integration with Respect to the Haar Measure on Unitary, Orthogonal and Symplectic Group Collins, Benoît; Śniady, Piotr Communications in Mathematical Physics, Vol. 264, Issue 3 https://doi.org/10.1007/s00220-006-1554-3	journal	March 2006
Weak Multiplicativity for Random Quantum Channels Montanaro, Ashley Communications in Mathematical Physics, Vol. 319, Issue 2 https://doi.org/10.1007/s00220-013-1680-7	journal	January 2013
Local Random Quantum Circuits are Approximate Polynomial-Designs Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał Communications in Mathematical Physics, Vol. 346, Issue 2 https://doi.org/10.1007/s00220-016-2706-8	journal	August 2016
Mixing Properties of Stochastic Quantum Hamiltonians Onorati, E.; Buerschaper, O.; Kliesch, M. Communications in Mathematical Physics, Vol. 355, Issue 3 https://doi.org/10.1007/s00220-017-2950-6	journal	July 2017
Low rank matrix recovery from rank one measurements Kueng, Richard; Rauhut, Holger; Terstiege, Ulrich Applied and Computational Harmonic Analysis, Vol. 42, Issue 1 https://doi.org/10.1016/j.acha.2015.07.007	journal	January 2017
The Theory of Quantum Information Watrous, John https://doi.org/10.1017/9781316848142	book	May 2018
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
Symmetric informationally complete quantum measurements Renes, Joseph M.; Blume-Kohout, Robin; Scott, A. J. Journal of Mathematical Physics, Vol. 45, Issue 6 https://doi.org/10.1063/1.1737053	journal	June 2004
Evenly distributed unitaries: On the structure of unitary designs Gross, D.; Audenaert, K.; Eisert, J. Journal of Mathematical Physics, Vol. 48, Issue 5 https://doi.org/10.1063/1.2716992	journal	May 2007
Asymptotic behavior of group integrals in the limit of infinite rank Weingarten, Don Journal of Mathematical Physics, Vol. 19, Issue 5 https://doi.org/10.1063/1.523807	journal	May 1978
Quantum computations: algorithms and error correction Kitaev, A. Yu Russian Mathematical Surveys, Vol. 52, Issue 6 https://doi.org/10.1070/RM1997v052n06ABEH002155	journal	December 1997
Tight informationally complete quantum measurements Scott, A. J. Journal of Physics A: Mathematical and General, Vol. 39, Issue 43 https://doi.org/10.1088/0305-4470/39/43/009	journal	October 2006
Black holes as mirrors: quantum information in random subsystems Hayden, Patrick; Preskill, John Journal of High Energy Physics, Vol. 2007, Issue 09 https://doi.org/10.1088/1126-6708/2007/09/120	journal	September 2007
Decoupling with unitary approximate two-designs Szehr, Oleg; Dupuis, Frédéric; Tomamichel, Marco New Journal of Physics, Vol. 15, Issue 5 https://doi.org/10.1088/1367-2630/15/5/053022	journal	May 2013
Scalable noise estimation with random unitary operators Emerson, Joseph; Alicki, Robert; Życzkowski, Karol Journal of Optics B: Quantum and Semiclassical Optics, Vol. 7, Issue 10 https://doi.org/10.1088/1464-4266/7/10/021	journal	September 2005
Hand-waving and interpretive dance: an introductory course on tensor networks Bridgeman, Jacob C.; Chubb, Christopher T. Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 22 https://doi.org/10.1088/1751-8121/aa6dc3	journal	May 2017
Exact and approximate unitary 2-designs and their application to fidelity estimation Dankert, Christoph; Cleve, Richard; Emerson, Joseph Physical Review A, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRevA.80.012304	journal	July 2009
Multiqubit Clifford groups are unitary 3-designs Zhu, Huangjun Physical Review A, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevA.96.062336	journal	December 2017
Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order Chen, Xie; Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 82, Issue 15 https://doi.org/10.1103/PhysRevB.82.155138	journal	October 2010
Emergent statistical mechanics of entanglement in random unitary circuits Zhou, Tianci; Nahum, Adam Physical Review B, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevB.99.174205	journal	May 2019
Complexity and shock wave geometries Stanford, Douglas; Susskind, Leonard Physical Review D, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevD.90.126007	journal	December 2014
Holographic complexity Alishahiha, Mohsen Physical Review D, Vol. 92, Issue 12 https://doi.org/10.1103/PhysRevD.92.126009	journal	December 2015
Complexity, action, and black holes Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard Physical Review D, Vol. 93, Issue 8 https://doi.org/10.1103/PhysRevD.93.086006	journal	April 2016
Second law of quantum complexity Brown, Adam R.; Susskind, Leonard Physical Review D, Vol. 97, Issue 8 https://doi.org/10.1103/PhysRevD.97.086015	journal	April 2018
Most Quantum States Are Too Entangled To Be Useful As Computational Resources Gross, D.; Flammia, S. T.; Eisert, J. Physical Review Letters, Vol. 102, Issue 19 https://doi.org/10.1103/PhysRevLett.102.190501	journal	May 2009
Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of Hilbert Space Poulin, David; Qarry, Angie; Somma, Rolando Physical Review Letters, Vol. 106, Issue 17 https://doi.org/10.1103/PhysRevLett.106.170501	journal	April 2011
Holographic Complexity Equals Bulk Action? Brown, Adam R.; Roberts, Daniel A.; Susskind, Leonard Physical Review Letters, Vol. 116, Issue 19 https://doi.org/10.1103/PhysRevLett.116.191301	journal	May 2016
Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics Nakata, Yoshifumi; Hirche, Christoph; Koashi, Masato Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/PhysRevX.7.021006	journal	April 2017
Operator Spreading in Random Unitary Circuits Nahum, Adam; Vijay, Sagar; Haah, Jeongwan Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021014	journal	April 2018
Improving Compressed Sensing With the Diamond Norm Kliesch, Martin; Kueng, Richard; Eisert, Jens IEEE Transactions on Information Theory, Vol. 62, Issue 12 https://doi.org/10.1109/TIT.2016.2606500	journal	December 2016
Comments on “Improving Compressed Sensing With the Diamond Norm”–Saturation of the Norm Inequalities Between Diamond and Nuclear Norm Michel, Ulrich; Kliesch, Martin; Kueng, Richard IEEE Transactions on Information Theory, Vol. 64, Issue 11 https://doi.org/10.1109/TIT.2018.2861887	journal	November 2018
Quantum Complexity Theory Bernstein, Ethan; Vazirani, Umesh SIAM Journal on Computing, Vol. 26, Issue 5 https://doi.org/10.1137/S0097539796300921	journal	October 1997
Moments and cumulants of polynomial random variables on unitarygroups, the Itzykson-Zuber integral, and free probability Collins, Benoît International Mathematics Research Notices, Vol. 2003, Issue 17, p. 953 https://doi.org/10.1155/S107379280320917X	journal	January 2003
Convex Analysis Rockafellar, Ralph Tyrell https://doi.org/10.1515/9781400873173	book	December 1970
Guaranteed recovery of quantum processes from few measurements Kliesch, Martin; Kueng, Richard; Eisert, Jens Quantum, Vol. 3 https://doi.org/10.22331/q-2019-08-12-171	journal	August 2019
Weingarten calculus via orthogonality relations: new applications Collins, Benoı̂t; Matsumoto, Sho Latin American Journal of Probability and Mathematical Statistics, Vol. 14, Issue 1 https://doi.org/10.30757/ALEA.v14-31	journal	January 2017
Watrous, John Theory of Computing, Vol. 5, Issue 1 https://doi.org/10.4086/toc.2009.v005a011	journal	January 2009
A Spectral Gap Theorem in SU$(d)$ Bourgain, Jean; Gamburd, Alex Journal of the European Mathematical Society, Vol. 14, Issue 5 https://doi.org/10.4171/JEMS/337	journal	January 2012

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