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Emergent quantum state designs from individual many-body wavefunctions

Cotler, Jordan S. and Mark, Daniel K. and Huang, Hsin-Yuan and Hernandez, Felipe and Choi, Joonhee and Shaw, Adam L. and Endres, Manuel and Choi, Soonwon (2021) Emergent quantum state designs from individual many-body wavefunctions. . (Unpublished)

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Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single non-random quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state k-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that k-designs arise naturally from generic states as well as individual states associated with strongly interacting, time-independent Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Mark, Daniel K.0000-0002-5017-5218
Huang, Hsin-Yuan0000-0001-5317-2613
Shaw, Adam L.0000-0002-8059-5950
Endres, Manuel0000-0002-4461-224X
Choi, Soonwon0000-0002-1247-062X
Additional Information:We thank Adam Bouland, Fernando Brandão, Aram Harrow, Wen Wei Ho, Nicholas Hunter-Jones, Anand Natarajan, and Hannes Pichler for valuable discussions. This work was partly supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907), the NSF CAREER award (1753386), the AFOSR YIP (FA9550-19-1-0044), the DARPA ONISQ program (W911NF2010021), the Army Research Office MURI program (W911NF2010136), and the NSF QLCI program (2016245). JSC is supported by a Junior Fellowship from the Harvard Society of Fellows, as well as in part by the Department of Energy under grant DE-SC0007870. HH is supported by the J. Yang & Family Foundation. FH is supported by the Fannie & John Hertz Foundation. JC acknowledges support from the IQIM postdoctoral fellowship. ALS acknowledges support from the Eddleman Quantum graduate fellowship. SC acknowledges support from the Miller Institute for Basic Research in Science.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-19-1-0044
Defense Advanced Research Projects Agency (DARPA)W911NF2010021
Army Research Office (ARO)W911NF2010136
Harvard Society of FellowsUNSPECIFIED
Department of Energy (DOE)DE-SC0007870
J. Yang Family and FoundationUNSPECIFIED
Fannie and John Hertz FoundationUNSPECIFIED
Eddleman Quantum graduate fellowshipUNSPECIFIED
Miller Institute for Basic Research in ScienceUNSPECIFIED
Record Number:CaltechAUTHORS:20210512-104037565
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109096
Deposited By: George Porter
Deposited On:12 May 2021 19:40
Last Modified:12 May 2021 19:40

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