Non-equilibrium and equilibrium thermodynamic foundations of the 2D toric code within the SEAQT framework

Damian, Cesar; Saldana-Robles, Adriana; von Spakovsky, Michael

Non-equilibrium and equilibrium thermodynamic foundations of the 2D toric code within the SEAQT framework

Oct 31, 2024

31 pages

e-Print:

2410.24033 [quant-ph]

View in:

ADS Abstract Service

pdf

reference search0 citations

Citations per year

0 Citations

Abstract: (arXiv)

The 2D toric code is a prototypical example that exhibits non-trivial topological properties and a ground state possessing a non-trivial topological order. Until now, all the cases studied in the literature have been in the stable equilibrium regime, leaving the relaxation towards this state unexplored. In the present work, the dynamics of the toric code towards stable equilibrium is explored within the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework. Under these dynamics, information correlations such as the relative entropy, logarithmic negativity, magnetization, coherent information, and geometric entropy are described out of equilibrium, permitting a connection to be made between the out-of-equilibrium dynamics and these information measures.

Note:

31 pages, 15 figures

References(44)

Figures(29)

[1]

Topological entanglement entropy

Alexei Kitaev
(
- Caltech, IQI and
- Microsoft, Redmond
)
,
John Preskill
(
- Caltech, IQI
)

- Phys.Rev.Lett. 96 (2006) 110404
•
e-Print:
- hep-th/0510092
•
DOI:
- 10.1103/PhysRevLett.96.110404

[2]

Fault tolerant quantum computation by anyons

A.Yu. Kitaev
(
- Landau Inst.
)

- Annals Phys. 303 (2003) 2-30
•
e-Print:
- quant-ph/9707021
•
DOI:
- 10.1016/S0003-4916(02)00018-0

[3]

Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Lukas Homeier
(
- Munich U., ASC and
- MCQST, Munich
)
,
Christian Schweizer
(
- Munich U. and
- MCQST, Munich
)
,
Monika Aidelsburger
(
- Munich U. and
- MCQST, Munich
)
,
Arkady Fedorov
(
- Queensland U.
)
,
Fabian Grusdt
(
- Munich U., ASC and
- MCQST, Munich
)

- Phys.Rev.B 104 (2021) 8, 085138
•
e-Print:
- 2012.05235
•
DOI:
- 10.1103/PhysRevB.104.085138

[4]

Detecting Topological Order at Finite Temperature Using Entanglement Negativity

Tsung-Cheng Lu
(
- UC, San Diego
)
,
Timothy H. Hsieh
(
- Perimeter Inst. Theor. Phys.
)
,
Tarun Grover
(
- UC, San Diego
)

- Phys.Rev.Lett. 125 (2020) 11, 116801
•
e-Print:
- 1912.04293
•
DOI:
- 10.1103/PhysRevLett.125.116801

[5]

Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory

Ruihua Fan
(
- Harvard U.
)
,
Yimu Bao
(
- UC, Berkeley
)
,
Ehud Altman
(
- UC, Berkeley and
- LBL, Berkeley
)
,
Ashvin Vishwanath
(
- Harvard U.
)

- PRX Quantum 5 (2024) 2, 020343
•
e-Print:
- 2301.05689
•
DOI:
- 10.1103/PRXQuantum.5.020343

[6]

Quantum data processing and error correction

Benjamin Schumacher
(
- New Mexico U. and
- Los Alamos and
- Kenyon Coll.
)
,
M.A. Nielsen
(
- New Mexico U.
)

- Phys.Rev.A 54 (1996) 2629
•
e-Print:
- quant-ph/9604022
•
DOI:
- 10.1103/PhysRevA.54.2629

[7]

Approximate quantum error correction

B. Schumacher
,
M.D. Westmoreland

- Quant.Inf.Proc. 1 (2002) 5

[8]

Quantum State Merging and Negative Information

Michał Horodecki
(
- Gdansk U.
)
,
Jonathan Oppenheim
(
- Cambridge U., DAMTP
)
,
Andreas Winter
(
- Bristol U.
)

- Commun.Math.Phys. 269 (2006) 1, 107-136
•
e-Print:
- quant-ph/0512247
•
DOI:
- 10.1007/s00220-006-0118-x

[9]

Entanglement negativity and sudden death in the toric code at finite temperature

- Phys.Rev.B 97 (2018) 14, 144410
•
e-Print:
- 1710.11139
•
DOI:
- 10.1103/PhysRevB.97.144410

[10]

Characterizing long-range entanglement in a mixed state through an emergent order on the entangling surface

Tsung-Cheng Lu
(
- Perimeter Inst. Theor. Phys. and
- UC, San Diego
)
,
Sagar Vijay
(
- UC, Santa Barbara
)

- Phys.Rev.Res. 5 (2023) 3, 033031
•
e-Print:
- 2201.07792
•
DOI:
- 10.1103/PhysRevResearch.5.033031

[11]

Quantum topological phase transition at the microscopic level

C. Castelnovo
,
C. Chamon

- Phys.Rev.B 77 (2008) 054433
•
DOI:
- 10.1103/PhysRevB.77.054433

[12]

Nonlinear quantum evolution equations to model irreversible adiabatic relaxation with maximal entropy production and other nonunitary processes

G.P. Beretta

- Rept.Math.Phys. 64 (2009) 139
•
- https://doi.org/https://doi.org/10.1016/S0034-4877(09)90024-6

[13]

Maximum entropy production rate in quantum thermodynamics, in

G.P. Beretta

- J.Phys.Conf.Ser. 237 (2010) 012004

[14]

Steepest entropy ascent model for far-nonequilibrium thermodynamics: Unified implementation of the maximum entropy production principle

G.P. Beretta

- Phys.Rev.E 90 (2014) 042113
•
DOI:
- 10.1103/PhysRevE.90.042113

[15]

Generalized thermodynamic relations for a system experiencing heat and mass diffusion in the far-from-equilibrium realm based on steepest entropy ascent

G. Li
,
M.R. von Spakovsky

- Phys.Rev.E 94 (2016) 032117
•
DOI:
- 10.1103/PhysRevE.94.032117

[16]

Steepest-entropy-ascent model of mesoscopic quantum systems far from equilibrium along with generalized thermodynamic definitions of measurement and reservoir

G. Li
,
M.R. von Spakovsky

- Phys.Rev.E 98 (2018) 042113

[17]

Steepest-entropy-ascent quantum thermodynamic modeling of the relaxation process of isolated chemically reactive systems using density of states and the concept of hypoequilibrium state

G. Li
,
M.R. von Spakovsky

- Phys.Rev.E 93 (2016) 012137
•
DOI:
- 10.1103/PhysRevE.93.012137

[18]

The fourth law of thermodynamics: steepest entropy ascent

G.P. Beretta

- Phil.Trans.Roy.Soc.Lond.A 378 (2020) 20190168

[19]

Decoherence predictions in a superconducting quantum processor using the steepest-entropy-ascent quantum thermodynamics framework

J.A. Montanez-Barrera
(
- Guanajuato U.
)
,
Michael R. von Spakovsky
(
- Virginia Tech.
)
,
Cesar E. Damian Ascencio
(
- Guanajuato U.
)
,
Sergio Cano-Andrade
(
- Guanajuato U.
)

- Phys.Rev.A 106 (2022) 3, 032426
•
e-Print:
- 2203.08329
•
DOI:
- 10.1103/PhysRevA.106.032426

[20]

J. A. Montañez

Barrera
,
M.R. C. E. Damian-Ascencio

- Phys.Rev.A 101 (2020) 052336
•
DOI:
- 10.1103/PhysRevA.101.052336

[21]

Low-temperature atomistic spin relaxation and non-equilibrium intensive properties using steepest-entropy-ascent quantum-inspired thermodynamics modeling

R. Yamada
,
M.R. von Spakovsky
,
W.T. Reynolds

- J.Phys.Condens.Matter 31 (2019) 505901
•
DOI:
- 10.1088/1361-648X/ab4014

[22]

Relaxation dynamics of nonresonant excitation transfer processes assisted by coherent phonon environment

- Jap.J.Appl.Phys. 62 (2023) 10, 102005
•
DOI:
- 10.35848/1347-4065/acfcfa

[23]

A thermodynamic scaling law for electrically perturbed lipid membranes: Validation with steepest entropy ascent framework, Bioelectrochemistry 140 107800

I. Goswami
,
R. Bielitz
,
S.S. Verbridge
,
M.R. Von Spakovsky

[24]

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework, The Journal of Chemical Physics 158

J. McDonald
,
M.R. von Spakovsky
,
W.T. Reynolds

[25]

Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework, The Journal of Chemical Physics 158

J. McDonald
,
M.R. von Spakovsky
,
W.T. Reynolds

1-25 of 44
1
2
25 / page