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Probing Many-Body Quantum Chaos with Quantum Simulators

Jun 29, 2021

26 pages

Published in:

Phys.Rev.X 12 (2022) 1, 011018

Published: Jan 1, 2022

e-Print:

2106.15530 [quant-ph]

DOI:

10.1103/PhysRevX.12.011018 (publication)

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Abstract: (APS)

The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified test bed to probe many-body quantum chaotic behavior, thermalization, and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin systems.

Note:

16+14 pages, 14 figures. The presentation throughout the paper is improved, without any change in the core content and results. New figure and appendix added. Matches with the published version

matrix model: random
spin: model
many-body problem
chaos
spectral
statistics
form factor
localization
Hamiltonian
energy eigenstate

References(135)

Figures(14)

[1]

Springer Series in Synergetics (, Berlin, )

F. Haake

[2]

Quantum statistical mechanics in a closed system

J.M. Deutsch

- Phys.Rev.A 43 (1991) 4, 2046
•
DOI:
- 10.1103/PhysRevA.43.2046

[3]

Chaos and Quantum Thermalization

Mark Srednicki
(
- UC, Santa Barbara
)

- Phys.Rev.E 50 888
•
e-Print:
- cond-mat/9403051
•
DOI:
- 10.1103/PhysRevE.50.888

[4]

Quantum simulations with trapped ions

R. Blatt
(
- Innsbruck U. and
- Vienna, OAW
)
,
C.F. Roos
(
- Innsbruck U. and
- Vienna, OAW
)

- Nature Phys. 8 (2012) 277-284
•
DOI:
- 10.1038/nphys2252

[5]

Dynamics of quantum information

R.J. Lewis-Swan
(
- JILA, Boulder and
- Colorado U.
)
,
A. Safavi-Naini
(
- JILA, Boulder and
- Colorado U.
)
,
A.M. Kaufman
(
- JILA, Boulder
)
,
A.M. Rey
(
- JILA, Boulder and
- Colorado U.
)

- Nature Rev.Phys. 1 (2019) 10, 627-634
•
e-Print:
- 1908.11747
•
DOI:
- 10.1038/s42254-019-0090-y

[6]

Programmable quantum simulations of spin systems with trapped ions

C. Monroe
(
- Joint Quantum Inst., College Park
)
,
W.C. Campbell
(
- UCLA
)
,
L.-M. Duan
(
- Peking U., Beijing, KIAA
)
,
Z.-X. Gong
(
- Colorado School of Mines
)
,
A.V. Gorshkov
(
- Joint Quantum Inst., College Park
)

et al.

- Rev.Mod.Phys. 93 (2021) 2, 025001
•
e-Print:
- 1912.07845
•
DOI:
- 10.1103/RevModPhys.93.025001

[7]

Many-body physics with individually controlled Rydberg atoms

- Nature Phys. 16 (2020) 2, 132-142
•
DOI:
- 10.1038/s41567-019-0733-z

[8]

Superconducting Qubits: Current State of Play

Morten Kjaergaard
(
- MIT
)
,
Mollie E. Schwartz
(
- MIT, Lincoln Lab
)
,
Jochen Braumüller
(
- MIT
)
,
Philip Krantz
(
- Chalmers U. Tech.
)
,
Joel I-Jan Wang
(
- MIT
)

et al.

- Physics 11 (2020) 369-395
•
e-Print:
- 1905.13641
•
DOI:
- 10.1146/annurev-conmatphys-031119-050605

[9]

Measuring entanglement entropy through the interference of quantum many-body twins

et al.

- Nature 528(7580):77-83 (2015)
•
e-Print:
- 1509.01160
•
DOI:
- 10.1038/nature15750

[10]

Quantum thermalization through entanglement in an isolated many-body system

et al.

- Science 353 (2016) 6301, aaf6725
•
DOI:
- 10.1126/science.aaf6725

[11]

Probing Rényi entanglement entropy via randomized measurements

Tiff Brydges
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Andreas Elben
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Petar Jurcevic
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Benoît Vermersch
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Christine Maier
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)

et al.

- Science 364 (2019) 6437, aau4963
•
DOI:
- 10.1126/science.aau4963

[12]

Confinement and entanglement dynamics on a digital quantum computer

- Sci.Rep. 11 (2021) 1, 11577
•
e-Print:
- 2001.03044
•
DOI:
- 10.1038/s41598-021-90849-5

[13]

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet

Martin Gärttner
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
Justin G. Bohnet
(
- NIST, Boulder
)
,
Arghavan Safavi-Naini
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
Michael L. Wall
(
- JILA, Boulder and
- U. Colorado, Boulder
)
,
John J. Bollinger
(
- NIST, Boulder
)

et al.

- Nature Phys. 13 (2017) 781
•
e-Print:
- 1608.08938
•
DOI:
- 10.1038/nphys4119

[14]

Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator

et al.

- Phys.Rev.X 7 (2017) 3, 031011
•
e-Print:
- 1609.01246
•
DOI:
- 10.1103/PhysRevX.7.031011

[15]

Exploring Localization in Nuclear Spin Chains

Ken Xuan Wei
(
- MIT, LNS
)
,
Chandrasekhar Ramanathan
(
- Dartmouth Coll.
)
,
Paola Cappellaro
(
- MIT
)

- Phys.Rev.Lett. 120 (2018) 7, 070501
•
DOI:
- 10.1103/PhysRevLett.120.070501

[16]

Verified Quantum Information Scrambling

K.A. Landsman
(
- Maryland U. and
- Joint Quantum Inst., College Park
)
,
C. Figgatt
(
- Maryland U. and
- Joint Quantum Inst., College Park
)
,
T. Schuster
(
- UC, Berkeley
)
,
N.M. Linke
(
- Maryland U. and
- Joint Quantum Inst., College Park
)
,
B. Yoshida
(
- Perimeter Inst. Theor. Phys.
)

et al.

- Nature 567 (2019) 7746, 61-65
•
e-Print:
- 1806.02807
•
DOI:
- 10.1038/s41586-019-0952-6

[17]

Detecting scrambling via statistical correlations between randomized measurements on an NMR quantum simulator

Xinfang Nie
(
- SUSTech, SKLQSE, Shenzhen and
- Hefei, CUST
)
,
Ze Zhang
(
- SUSTech, SKLQSE, Shenzhen
)
,
Xiuzhu Zhao
(
- SUSTech, SKLQSE, Shenzhen
)
,
Tao Xin
(
- SUSTech, SKLQSE, Shenzhen and
- PCL, Shenzhen
)
,
Dawei Lu
(
- SUSTech, SKLQSE, Shenzhen and
- PCL, Shenzhen
)

et al.

e-Print:
- 1903.12237

[18]

Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions

Manoj K. Joshi
(
- Innsbruck U.
)
,
Andreas Elben
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Benôıt Vermersch
(
)
,
Tiff Brydges
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)
,
Christine Maier
(
- Innsbruck U. and
- Innsbruck U., Quant. Opt. and Info.
)

et al.

- Phys.Rev.Lett. 124 (2020) 24, 240505
•
e-Print:
- 2001.02176
•
DOI:
- 10.1103/PhysRevLett.124.240505

[19]

Information scrambling in quantum circuits

Xiao Mi
(
- Google Inc.
)
,
Pedram Roushan
(
- Google Inc.
)
,
Chris Quintana
(
- Google Inc.
)
,
Salvatore Mandra
(
- NASA, Ames and
- Unlisted, US
)
,
Jeffrey Marshall
(
- NASA, Ames and
- Unlisted, US
)

et al.

- Science 374 (2021) 6574, abg5029
•
e-Print:
- 2101.08870
•
DOI:
- 10.1126/science.abg5029

[20]

Characteristic Vectors of Bordered Matrices with Infinite Dimensions

E. Wigner

- Ann. Math. 62 (1955) 548
•
DOI:
- 10.2307/1970079

[21]

Statistical theory of the energy levels of complex systems. I

F.J. Dyson

- J.Math.Phys. 3 (1962) 140-156
•
DOI:
- 10.1063/1.1703773

[22]

On the connection between quantization of nonintegrable systems and statistical theory of spectra

- Lett.Nuovo Cim. 28 (1980) 8, 279-282
•
DOI:
- 10.1007/BF02798790

[23]

Characterization of chaotic quantum spectra and universality of level fluctuation laws

- Phys.Rev.Lett. 52 (1984) 1-4
•
DOI:
- 10.1103/PhysRevLett.52.1

[24]

(, New York, )

M.L. Mehta

[25]

The approach to thermal equilibrium in quantized chaotic systems

Mark Srednicki

- J.Phys.A 32 (1999) 7, 1163
•
DOI:
- 10.1088/0305-4470/32/7/007

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