Quantum simulation of dynamical phase transitions in noisy quantum devices

Luis Santos; Tobias J. Osborne; Ugne Liaubaite; Younes Javanmard

arxiv: 2211.08318 · v2 · pith:RS2LWBFPnew · submitted 2022-11-15 · 🪐 quant-ph · cond-mat.str-el

Quantum simulation of dynamical phase transitions in noisy quantum devices

Younes Javanmard , Ugne Liaubaite , Tobias J. Osborne , Luis Santos This is my paper

Pith reviewed 2026-05-24 10:10 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.str-el

keywords quantum simulationdynamical phase transitionsLoschmidt echonoise mitigationtransverse-field Ising modelzero-noise extrapolationmatrix product density operatorsdepolarizing noise

0 comments

The pith

Depolarizing noise doubles non-analytic points in the Loschmidt echo at dynamical phase transitions, creating an unmitigable error.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies the effects of depolarizing noise on simulations of dynamical phase transitions in the transverse-field Ising model using matrix product density operators. It shows that noise systematically modifies the Loschmidt echo by doubling the number of non-analytic points at the transition times. This modification introduces an error that zero-noise extrapolation cannot remove. At the same time, the extrapolation technique succeeds in recovering quantum revivals of the Loschmidt echo that would otherwise be lost and in restoring accurate inter-site correlations. The results match those from actual quantum simulators and point to both limits and capabilities of error mitigation for non-equilibrium dynamics on noisy devices.

Core claim

Matrix product density operator simulations of the transverse-field Ising model with depolarizing noise demonstrate that noise alters the Loschmidt echo at dynamical phase transition times by doubling the number of non-analytic points and thereby induces an error that inherently cannot be mitigated by zero-noise extrapolation. The same extrapolation recovers quantum revivals of the Loschmidt echo missed without mitigation and retrieves noise-free inter-site correlations, with results agreeing with those from quantum simulators.

What carries the argument

Matrix product density operators applied to the Loschmidt echo of the transverse-field Ising model under depolarizing noise.

If this is right

Zero-noise extrapolation cannot correct the noise-induced doubling of non-analytic points in the Loschmidt echo.
Zero-noise extrapolation recovers quantum revivals of the Loschmidt echo that are lost without mitigation.
Zero-noise extrapolation retrieves accurate noise-free inter-site correlations.
Matrix product density operators can be used to assess performance limits of large noisy quantum circuits.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Certain dynamical phase transition signatures may remain distorted on noisy devices even after standard mitigation is applied.
The doubling effect may appear under other noise models beyond depolarizing noise.
Matrix product density operators could serve as a low-cost proxy for testing mitigation strategies before running them on hardware.

Load-bearing premise

The matrix product density operator model with depolarizing noise accurately represents the actual dynamics on noisy quantum devices.

What would settle it

An experiment on a quantum device implementing the transverse-field Ising model that measures whether the Loschmidt echo exhibits exactly twice as many non-analytic points at the predicted transition times as the noise-free case would confirm or refute the unmitigable-error claim.

Figures

Figures reproduced from arXiv: 2211.08318 by Luis Santos, Tobias J. Osborne, Ugne Liaubaite, Younes Javanmard.

**Figure 3.** Figure 3: FIG. 3. Quantum simulation results of the behavior of the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2. Rate function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Error rate [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Two-point correlation [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

read the original abstract

Zero-noise extrapolation provides an especially useful error mitigation method for noisy intermediate-scale quantum devices. Our analysis, based on matrix product density operators, of the transverse-field Ising model with depolarizing noise, reveals both advantages and inherent problems associated with zero-noise extrapolation when simulating non-equilibrium many-body dynamics. On the one hand, interestingly, noise alters systematically the behavior of the Loschmidt echo at the dynamical phase transition times, doubling the number of non-analytic points, and hence inducing an error that, inherently, cannot be mitigated. On the other, zero-noise extrapolation may be employed to recover quantum revivals of the Loschmidt echo, which would be completely missed in the absence of mitigation, and to retrieve faithfully noise-free inter-site correlations. Our results, which are in good agreement with those obtained using quantum simulators, reveal the potential of matrix product density operators for the investigation of the performance of quantum devices with a large number of qubits and deep noisy quantum circuits.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Abstract claims noise doubles non-analytic points in the Loschmidt echo for the TFIM, creating an unmitigable error under ZNE, but without the full paper the evidence can't be checked.

read the letter

The main point here is that depolarizing noise, when modeled with matrix product density operators on the transverse-field Ising model, doubles the number of non-analytic points in the Loschmidt echo exactly at the dynamical phase transition times. That doubling produces an error zero-noise extrapolation cannot remove. At the same time the analysis shows ZNE can still pull out the quantum revivals and the inter-site correlations that would otherwise disappear under noise. The authors say the MPDO results line up with runs on actual quantum simulators. That combination of a concrete limitation on one mitigation technique plus a demonstration of where it still helps is the useful piece. The MPDO route itself makes sense for scaling to larger qubit numbers and deeper circuits than direct simulation allows. The soft spot is obvious and unavoidable right now: only the abstract exists. There are no derivations for how the non-analytic points are located, no description of how depolarizing noise is folded into the tensor network, no error bars or convergence checks, and no comparison tables. Without those it is impossible to tell whether the doubling is a genuine physical effect or tied to the specific approximation or noise model chosen. The assumption that the MPDO plus depolarizing channel faithfully reproduces device behavior therefore sits untested. For someone working on error mitigation for non-equilibrium many-body simulations this would be worth reading once the full methods and data appear. As it stands the paper is too thin on evidence to send out for serious refereeing; the central claim needs the supporting calculations visible before it can be evaluated properly.

Referee Report

1 major / 1 minor

Summary. The manuscript uses matrix product density operators to analyze the transverse-field Ising model under depolarizing noise. It claims that noise systematically modifies the Loschmidt echo at dynamical phase transition times by doubling the number of non-analytic points, producing an error that cannot be mitigated by zero-noise extrapolation. At the same time, zero-noise extrapolation recovers quantum revivals of the Loschmidt echo and faithful noise-free inter-site correlations. Results are reported to agree with quantum-simulator experiments and to illustrate both the utility and the intrinsic limitations of zero-noise extrapolation for non-equilibrium many-body dynamics on NISQ devices.

Significance. If the central claims hold, the work would identify a concrete class of observables and dynamical features for which zero-noise extrapolation is provably insufficient, while also showing that the same technique can still restore other quantities. The demonstration that matrix product density operators can be used to benchmark large-scale noisy circuits would further strengthen the case for tensor-network methods as diagnostic tools for NISQ performance.

major comments (1)

The abstract asserts that depolarizing noise doubles the number of non-analytic points in the Loschmidt echo and that the resulting error is inherently unmitigable. Because the manuscript supplies neither the precise definition used to locate non-analytic points, the explicit MPDO construction, nor the quantitative comparison between noisy and extrapolated data, it is impossible to determine whether the doubling is a physical effect of the noise model or an artifact of the chosen representation.

minor comments (1)

The abstract states that results are 'in good agreement' with quantum simulators but provides no quantitative metrics, system sizes, or circuit depths for the comparison.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript. We respond to the single major comment below.

read point-by-point responses

Referee: The abstract asserts that depolarizing noise doubles the number of non-analytic points in the Loschmidt echo and that the resulting error is inherently unmitigable. Because the manuscript supplies neither the precise definition used to locate non-analytic points, the explicit MPDO construction, nor the quantitative comparison between noisy and extrapolated data, it is impossible to determine whether the doubling is a physical effect of the noise model or an artifact of the chosen representation.

Authors: We agree that the abstract, as presented, does not supply the precise definition of non-analytic points, the explicit MPDO construction, or quantitative comparisons between noisy and extrapolated data. Consequently, from the abstract alone it is not possible to determine whether the reported doubling constitutes a physical effect of the depolarizing noise or an artifact of the representation. We will revise the abstract to include a concise statement defining non-analytic points as the times at which the Loschmidt echo exhibits non-differentiable behavior, thereby clarifying the basis of the claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

Only the abstract is available, containing no equations, parameter fits, self-citations, or derivation steps. The described analysis of MPDO for noisy TFIM and Loschmidt echo behavior is presented as a direct computational result without any visible reduction of predictions to inputs by construction. No load-bearing steps matching the enumerated circularity patterns can be identified or quoted.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; all entries left empty due to lack of detail.

pith-pipeline@v0.9.0 · 5673 in / 942 out tokens · 22301 ms · 2026-05-24T10:10:12.752816+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages

[1]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010)

work page 2010
[2]

R. P. Feynman, Int J Theor Phys 21, 467 (1982)

work page 1982
[3]

D. A. Lidar. and T. A. Brun, Quantum Error Correction (Cambridge University Press, 2013)

work page 2013
[4]

Lloyd, Science 273, 1073 (1996)

S. Lloyd, Science 273, 1073 (1996)

work page 1996
[5]

Biamonte, P

J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549, 195 (2017)

work page 2017
[6]

Kandala, A

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Nature 549, 242 (2017)

work page 2017
[7]

Wendin, Rep

G. Wendin, Rep. Prog. Phys. 80, 106001 (2017)

work page 2017
[8]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Applied Physics Reviews 6, 021314 (2019)

work page 2019
[9]

J. I. Cirac and P. Zoller, Phys. Rev. Lett.74, 4091 (1995)

work page 1995
[10]

Blatt and C

R. Blatt and C. F. Roos, Nature Phys 8, 277 (2012)

work page 2012
[11]

Jaksch, C

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)

work page 1998
[12]

Bloch, J

I. Bloch, J. Dalibard, and S. Nascimb` ene, Nature Phys 8, 267 (2012)

work page 2012
[13]

Burkard, T

G. Burkard, T. D. Ladd, J. M. Nichol, A. Pan, and J. R. Petta, (2021), 10.48550/arXiv.2112.08863, com- ment: Rev. Mod. Phys. - Corrections and comments welcome, arXiv:2112.08863 [cond-mat, physics:physics, physics:quant-ph]

work page doi:10.48550/arxiv.2112.08863 2021
[14]

Slussarenko and G

S. Slussarenko and G. J. Pryde, (2019), 10.1063/1.5115814, comment: 21 pages, 3 ﬁgures. A brief review on some topics in photonic quantum computing with lots of references to longer specialist reviews. Close to published version, arXiv:1907.06331 [quant-ph]

work page doi:10.1063/1.5115814 2019
[15]

Weedbrook, S

C. Weedbrook, S. Pirandola, R. Garc´ ıa-Patr´ on, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012)

work page 2012
[16]

Preskill, Quantum 2, 79 (2018)

J. Preskill, Quantum 2, 79 (2018)

work page 2018
[17]

Temme, S

K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017)

work page 2017
[18]

S. Endo, S. C. Benjamin, and Y. Li, Phys. Rev. X 8, 031027 (2018)

work page 2018
[19]

Li and S

Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017)

work page 2017
[20]

van den Berg, Z

E. van den Berg, Z. K. Minev, A. Kandala, and K. Temme, (2022), 10.48550/arXiv.2201.09866, arXiv:2201.09866 [quant-ph]

work page doi:10.48550/arxiv.2201.09866 2022
[21]

A. Mari, N. Shammah, and W. J. Zeng, Phys. Rev. A 104, 052607 (2021)

work page 2021
[22]

A. Lowe, M. H. Gordon, P. Czarnik, A. Arrasmith, P. J. Coles, and L. Cincio, Phys. Rev. Research 3, 033098 (2021)

work page 2021
[23]

Takagi, S

R. Takagi, S. Endo, S. Minagawa, and M. Gu, (2022), 10.48550/arXiv.2109.04457, arXiv:2109.04457 [quant-ph]

work page doi:10.48550/arxiv.2109.04457 2022
[24]

Tsubouchi, T

K. Tsubouchi, T. Sagawa, and N. Yoshioka, (2022), 10.48550/arXiv.2208.09385, arXiv:2208.09385 [quant- ph]

work page doi:10.48550/arxiv.2208.09385 2022
[25]

Takagi, H

R. Takagi, H. Tajima, and M. Gu, (2022), 10.48550/arXiv.2208.09178, arXiv:2208.09178 [quant- ph]

work page doi:10.48550/arxiv.2208.09178 2022
[26]

Verstraete, J

F. Verstraete, J. J. Garc´ ıa-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004)

work page 2004
[27]

Zwolak and G

M. Zwolak and G. Vidal, Phys. Rev. Lett. 93, 207205 (2004)

work page 2004
[28]

Cheng, C

S. Cheng, C. Cao, C. Zhang, Y. Liu, S.-Y. Hou, P. Xu, and B. Zeng, Phys. Rev. Research 3, 023005 (2021)

work page 2021
[29]

A. H. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert, and S. Montangero, Phys. Rev. Lett. 116, 237201 (2016)

work page 2016
[30]

Schollw¨ ock, Annals of Physics326, 96 (2011), january 2011 Special Issue

U. Schollw¨ ock, Annals of Physics326, 96 (2011), january 2011 Special Issue

work page 2011
[31]

Urbanek, B

M. Urbanek, B. Nachman, V. R. Pascuzzi, A. He, C. W. Bauer, and W. A. de Jong, Phys. Rev. Lett. 127, 270502 (2021)

work page 2021
[32]

Pfeuty, Annals of Physics 57, 79 (1970)

P. Pfeuty, Annals of Physics 57, 79 (1970)

work page 1970
[33]

T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002)

work page 2002
[34]

M. Heyl, A. Polkovnikov, and S. Kehrein, Phys. Rev. Lett. 110, 135704 (2013)

work page 2013
[35]

Heyl, Phys

M. Heyl, Phys. Rev. Lett. 113, 205701 (2014)

work page 2014
[36]

Heyl, Rep

M. Heyl, Rep. Prog. Phys. 81, 054001 (2018)

work page 2018
[37]

Heyl, Phys

M. Heyl, Phys. Rev. Lett. 115, 140602 (2015)

work page 2015
[38]

Karrasch and D

C. Karrasch and D. Schuricht, Phys. Rev. B 87, 195104 (2013)

work page 2013
[39]

Dborin, V

J. Dborin, V. Wimalaweera, F. Barratt, E. Ostby, T. E. O’Brien, and A. G. Green, Nat Commun 13, 5977 (2022)

work page 2022
[40]

J. C. Halimeh and V. Zauner-Stauber, Phys. Rev. B 96, 134427 (2017)

work page 2017
[41]

Homrighausen, N

I. Homrighausen, N. O. Abeling, V. Zauner-Stauber, and J. C. Halimeh, Phys. Rev. B 96, 104436 (2017)

work page 2017
[42]

J. Lang, B. Frank, and J. C. Halimeh, Phys. Rev. B 97, 174401 (2018). 6

work page 2018
[43]

Van Damme, J.-Y

M. Van Damme, J.-Y. Desaules, Z. Papi´ c, and J. C. Halimeh, (2022), 10.48550/arXiv.2210.02453, arXiv:2210.02453 [cond-mat, physics:quant-ph]

work page doi:10.48550/arxiv.2210.02453 2022
[44]

Van Damme, T

M. Van Damme, T. V. Zache, D. Banerjee, P. Hauke, and J. C. Halimeh, (2022), 10.48550/arXiv.2203.01337, arXiv:2203.01337 [cond-mat, physics:hep-lat, physics:quant-ph]

work page doi:10.48550/arxiv.2203.01337 2022
[45]

Jurcevic, H

P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Phys. Rev. Lett. 119, 080501 (2017)

work page 2017
[46]

L.-N. Wu, J. Nettersheim, J. Feß, A. Schnell, S. Bur- gardt, S. Hiebel, D. Adam, A. Eckardt, and A. Widera, (2022), 10.48550/arXiv.2208.05164, arXiv:2208.05164 [cond-mat, physics:quant-ph]

work page doi:10.48550/arxiv.2208.05164 2022
[47]

Kandala, K

A. Kandala, K. Temme, A. D. C´ orcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Nature 567, 491 (2019)

work page 2019
[48]

S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, J. Phys. Soc. Jpn. 90, 032001 (2021)

work page 2021
[49]

Giurgica-Tiron, Y

T. Giurgica-Tiron, Y. Hindy, R. LaRose, A. Mari, and W. J. Zeng, in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) (2020) pp. 306–316

work page 2020
[50]

LaRose, A

R. LaRose, A. Mari, S. Kaiser, P. J. Karalekas, A. A. Alves, P. Czarnik, M. E. Mandouh, M. H. Gordon, Y. Hindy, A. Robertson, P. Thakre, M. Wahl, D. Samuel, R. Mistri, M. Tremblay, N. Gardner, N. T. Stemen, N. Shammah, and W. J. Zeng, Quantum 6, 774 (2022)

work page 2022
[51]

R. L. Burden and J. D. Faires, Numerical Analysis (Cen- gage Learning, 2010)

work page 2010
[52]

Montangero, Introduction to Tensor Network Meth- ods: Numerical Simulations of Low-Dimensional Many- Body Quantum Systems (Springer International Publish- ing, Cham, 2018)

S. Montangero, Introduction to Tensor Network Meth- ods: Numerical Simulations of Low-Dimensional Many- Body Quantum Systems (Springer International Publish- ing, Cham, 2018)

work page 2018
[53]

Javanmard, D

Y. Javanmard, D. Trapin, S. Bera, J. H. Bardarson, and M. Heyl, New J. Phys. 20, 083032 (2018)

work page 2018
[54]

J. I. Cirac, D. P´ erez-Garc´ ıa, N. Schuch, and F. Ver- straete, Rev. Mod. Phys. 93, 045003 (2021)

work page 2021
[55]

Hatano and M

N. Hatano and M. Suzuki, Quantum Annealing and Other Optimization Methods , Lecture Notes in Physics, 37 (2005)

work page 2005
[56]

Qiskit: An open-source framework for quantum computing,

IBM-Quantum, “Qiskit: An open-source framework for quantum computing,” (2021)

work page 2021
[57]

Smith, M

A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, npj Quantum Information 5, 106 (2019)

work page 2019
[58]

Fauseweh and J.-X

B. Fauseweh and J.-X. Zhu, Quantum Inf Process 20, 138 (2021). 1 SUPPLEMENT AL MA TERIAL: QUANTUM SIMULA TION OF DYNAMICAL PHASE TRANSITIONS IN NOISY QUANTUM DEVICES We provide additional details and numerical results supplementing the conclusions from the main text. MA TRIX PRODUCT DENSITY OPERA TORS The vectorized Liouvillian is given by L# ≡−i(H⊗ I− I⊗...

work page 2021

[1] [1]

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010)

work page 2010

[2] [2]

R. P. Feynman, Int J Theor Phys 21, 467 (1982)

work page 1982

[3] [3]

D. A. Lidar. and T. A. Brun, Quantum Error Correction (Cambridge University Press, 2013)

work page 2013

[4] [4]

Lloyd, Science 273, 1073 (1996)

S. Lloyd, Science 273, 1073 (1996)

work page 1996

[5] [5]

Biamonte, P

J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Nature 549, 195 (2017)

work page 2017

[6] [6]

Kandala, A

A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Nature 549, 242 (2017)

work page 2017

[7] [7]

Wendin, Rep

G. Wendin, Rep. Prog. Phys. 80, 106001 (2017)

work page 2017

[8] [8]

C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Applied Physics Reviews 6, 021314 (2019)

work page 2019

[9] [9]

J. I. Cirac and P. Zoller, Phys. Rev. Lett.74, 4091 (1995)

work page 1995

[10] [10]

Blatt and C

R. Blatt and C. F. Roos, Nature Phys 8, 277 (2012)

work page 2012

[11] [11]

Jaksch, C

D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998)

work page 1998

[12] [12]

Bloch, J

I. Bloch, J. Dalibard, and S. Nascimb` ene, Nature Phys 8, 267 (2012)

work page 2012

[13] [13]

Burkard, T

G. Burkard, T. D. Ladd, J. M. Nichol, A. Pan, and J. R. Petta, (2021), 10.48550/arXiv.2112.08863, com- ment: Rev. Mod. Phys. - Corrections and comments welcome, arXiv:2112.08863 [cond-mat, physics:physics, physics:quant-ph]

work page doi:10.48550/arxiv.2112.08863 2021

[14] [14]

Slussarenko and G

S. Slussarenko and G. J. Pryde, (2019), 10.1063/1.5115814, comment: 21 pages, 3 ﬁgures. A brief review on some topics in photonic quantum computing with lots of references to longer specialist reviews. Close to published version, arXiv:1907.06331 [quant-ph]

work page doi:10.1063/1.5115814 2019

[15] [15]

Weedbrook, S

C. Weedbrook, S. Pirandola, R. Garc´ ıa-Patr´ on, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012)

work page 2012

[16] [16]

Preskill, Quantum 2, 79 (2018)

J. Preskill, Quantum 2, 79 (2018)

work page 2018

[17] [17]

Temme, S

K. Temme, S. Bravyi, and J. M. Gambetta, Phys. Rev. Lett. 119, 180509 (2017)

work page 2017

[18] [18]

S. Endo, S. C. Benjamin, and Y. Li, Phys. Rev. X 8, 031027 (2018)

work page 2018

[19] [19]

Li and S

Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017)

work page 2017

[20] [20]

van den Berg, Z

E. van den Berg, Z. K. Minev, A. Kandala, and K. Temme, (2022), 10.48550/arXiv.2201.09866, arXiv:2201.09866 [quant-ph]

work page doi:10.48550/arxiv.2201.09866 2022

[21] [21]

A. Mari, N. Shammah, and W. J. Zeng, Phys. Rev. A 104, 052607 (2021)

work page 2021

[22] [22]

A. Lowe, M. H. Gordon, P. Czarnik, A. Arrasmith, P. J. Coles, and L. Cincio, Phys. Rev. Research 3, 033098 (2021)

work page 2021

[23] [23]

Takagi, S

R. Takagi, S. Endo, S. Minagawa, and M. Gu, (2022), 10.48550/arXiv.2109.04457, arXiv:2109.04457 [quant-ph]

work page doi:10.48550/arxiv.2109.04457 2022

[24] [24]

Tsubouchi, T

K. Tsubouchi, T. Sagawa, and N. Yoshioka, (2022), 10.48550/arXiv.2208.09385, arXiv:2208.09385 [quant- ph]

work page doi:10.48550/arxiv.2208.09385 2022

[25] [25]

Takagi, H

R. Takagi, H. Tajima, and M. Gu, (2022), 10.48550/arXiv.2208.09178, arXiv:2208.09178 [quant- ph]

work page doi:10.48550/arxiv.2208.09178 2022

[26] [26]

Verstraete, J

F. Verstraete, J. J. Garc´ ıa-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004)

work page 2004

[27] [27]

Zwolak and G

M. Zwolak and G. Vidal, Phys. Rev. Lett. 93, 207205 (2004)

work page 2004

[28] [28]

Cheng, C

S. Cheng, C. Cao, C. Zhang, Y. Liu, S.-Y. Hou, P. Xu, and B. Zeng, Phys. Rev. Research 3, 023005 (2021)

work page 2021

[29] [29]

A. H. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert, and S. Montangero, Phys. Rev. Lett. 116, 237201 (2016)

work page 2016

[30] [30]

Schollw¨ ock, Annals of Physics326, 96 (2011), january 2011 Special Issue

U. Schollw¨ ock, Annals of Physics326, 96 (2011), january 2011 Special Issue

work page 2011

[31] [31]

Urbanek, B

M. Urbanek, B. Nachman, V. R. Pascuzzi, A. He, C. W. Bauer, and W. A. de Jong, Phys. Rev. Lett. 127, 270502 (2021)

work page 2021

[32] [32]

Pfeuty, Annals of Physics 57, 79 (1970)

P. Pfeuty, Annals of Physics 57, 79 (1970)

work page 1970

[33] [33]

T. J. Osborne and M. A. Nielsen, Phys. Rev. A 66, 032110 (2002)

work page 2002

[34] [34]

M. Heyl, A. Polkovnikov, and S. Kehrein, Phys. Rev. Lett. 110, 135704 (2013)

work page 2013

[35] [35]

Heyl, Phys

M. Heyl, Phys. Rev. Lett. 113, 205701 (2014)

work page 2014

[36] [36]

Heyl, Rep

M. Heyl, Rep. Prog. Phys. 81, 054001 (2018)

work page 2018

[37] [37]

Heyl, Phys

M. Heyl, Phys. Rev. Lett. 115, 140602 (2015)

work page 2015

[38] [38]

Karrasch and D

C. Karrasch and D. Schuricht, Phys. Rev. B 87, 195104 (2013)

work page 2013

[39] [39]

Dborin, V

J. Dborin, V. Wimalaweera, F. Barratt, E. Ostby, T. E. O’Brien, and A. G. Green, Nat Commun 13, 5977 (2022)

work page 2022

[40] [40]

J. C. Halimeh and V. Zauner-Stauber, Phys. Rev. B 96, 134427 (2017)

work page 2017

[41] [41]

Homrighausen, N

I. Homrighausen, N. O. Abeling, V. Zauner-Stauber, and J. C. Halimeh, Phys. Rev. B 96, 104436 (2017)

work page 2017

[42] [42]

J. Lang, B. Frank, and J. C. Halimeh, Phys. Rev. B 97, 174401 (2018). 6

work page 2018

[43] [43]

Van Damme, J.-Y

M. Van Damme, J.-Y. Desaules, Z. Papi´ c, and J. C. Halimeh, (2022), 10.48550/arXiv.2210.02453, arXiv:2210.02453 [cond-mat, physics:quant-ph]

work page doi:10.48550/arxiv.2210.02453 2022

[44] [44]

Van Damme, T

M. Van Damme, T. V. Zache, D. Banerjee, P. Hauke, and J. C. Halimeh, (2022), 10.48550/arXiv.2203.01337, arXiv:2203.01337 [cond-mat, physics:hep-lat, physics:quant-ph]

work page doi:10.48550/arxiv.2203.01337 2022

[45] [45]

Jurcevic, H

P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, and C. F. Roos, Phys. Rev. Lett. 119, 080501 (2017)

work page 2017

[46] [46]

L.-N. Wu, J. Nettersheim, J. Feß, A. Schnell, S. Bur- gardt, S. Hiebel, D. Adam, A. Eckardt, and A. Widera, (2022), 10.48550/arXiv.2208.05164, arXiv:2208.05164 [cond-mat, physics:quant-ph]

work page doi:10.48550/arxiv.2208.05164 2022

[47] [47]

Kandala, K

A. Kandala, K. Temme, A. D. C´ orcoles, A. Mezzacapo, J. M. Chow, and J. M. Gambetta, Nature 567, 491 (2019)

work page 2019

[48] [48]

S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, J. Phys. Soc. Jpn. 90, 032001 (2021)

work page 2021

[49] [49]

Giurgica-Tiron, Y

T. Giurgica-Tiron, Y. Hindy, R. LaRose, A. Mari, and W. J. Zeng, in 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) (2020) pp. 306–316

work page 2020

[50] [50]

LaRose, A

R. LaRose, A. Mari, S. Kaiser, P. J. Karalekas, A. A. Alves, P. Czarnik, M. E. Mandouh, M. H. Gordon, Y. Hindy, A. Robertson, P. Thakre, M. Wahl, D. Samuel, R. Mistri, M. Tremblay, N. Gardner, N. T. Stemen, N. Shammah, and W. J. Zeng, Quantum 6, 774 (2022)

work page 2022

[51] [51]

R. L. Burden and J. D. Faires, Numerical Analysis (Cen- gage Learning, 2010)

work page 2010

[52] [52]

Montangero, Introduction to Tensor Network Meth- ods: Numerical Simulations of Low-Dimensional Many- Body Quantum Systems (Springer International Publish- ing, Cham, 2018)

S. Montangero, Introduction to Tensor Network Meth- ods: Numerical Simulations of Low-Dimensional Many- Body Quantum Systems (Springer International Publish- ing, Cham, 2018)

work page 2018

[53] [53]

Javanmard, D

Y. Javanmard, D. Trapin, S. Bera, J. H. Bardarson, and M. Heyl, New J. Phys. 20, 083032 (2018)

work page 2018

[54] [54]

J. I. Cirac, D. P´ erez-Garc´ ıa, N. Schuch, and F. Ver- straete, Rev. Mod. Phys. 93, 045003 (2021)

work page 2021

[55] [55]

Hatano and M

N. Hatano and M. Suzuki, Quantum Annealing and Other Optimization Methods , Lecture Notes in Physics, 37 (2005)

work page 2005

[56] [56]

Qiskit: An open-source framework for quantum computing,

IBM-Quantum, “Qiskit: An open-source framework for quantum computing,” (2021)

work page 2021

[57] [57]

Smith, M

A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, npj Quantum Information 5, 106 (2019)

work page 2019

[58] [58]

Fauseweh and J.-X

B. Fauseweh and J.-X. Zhu, Quantum Inf Process 20, 138 (2021). 1 SUPPLEMENT AL MA TERIAL: QUANTUM SIMULA TION OF DYNAMICAL PHASE TRANSITIONS IN NOISY QUANTUM DEVICES We provide additional details and numerical results supplementing the conclusions from the main text. MA TRIX PRODUCT DENSITY OPERA TORS The vectorized Liouvillian is given by L# ≡−i(H⊗ I− I⊗...

work page 2021