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REVIEW 2 major objections 2 minor 3 cited by

Disorder drives a transition out of the ergodic phase in two-dimensional quantum systems.

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2026-05-16 18:33 UTC

load-bearing objection The paper shows experimental power-law Hilbert-space decay and Edwards-Anderson onset in a 2D qubit array at intermediate disorder, but finite-size and coherence effects could mimic the claimed thermodynamic transition. the 2 major comments →

arxiv 2601.01309 v3 submitted 2026-01-04 quant-ph cond-mat.dis-nn

Hilbert space signatures of non-ergodic glassy dynamics

Aleksey Lunkin , Nicole S. Ticea , Shashwat Kumar , Connie Miao , Jaehong Choi , Mohammed Alghadeer , Ilya Drozdov , Dmitry Abanin
show 287 more authors
Amira Abbas Rajeev Acharya Laleh Beni Georg Aigeldinger Ross Alcaraz Sayra Alcaraz Markus Ansmann Frank Arute Kunal Arya Walt Askew Nikita Astrakhantsev Juan Atalaya Ryan Babbush Brian Ballard Joseph C. Bardin Hector Bates Andreas Bengtsson Majid Karimi Alexander Bilmes Simon Bilodeau Felix Borjans Alexandre Bourassa Jenna Bovaird Dylan Bowers Leon Brill Peter Brooks Michael Broughton David A. Browne Brett Buchea Bob B. Buckley Tim Burger Brian Burkett Nicholas Bushnell Jamal Busnaina Anthony Cabrera Juan Campero Hung-Shen Chang Silas Chen Zijun Chen Ben Chiaro Liang-Ying Chih Agnetta Y. Cleland Bryan Cochrane Matt Cockrell Josh Cogan Paul Conner Harold Cook Rodrigo G. Corti\~nas William Courtney Alexander L. Crook Ben Curtin Martin Damyanov Sayan Das Dripto M. Debroy Sean Demura Paul Donohoe Andrew Dunsworth Valerie Ehimhen Alec Eickbusch Aviv Moshe Elbag Lior Ella Mahmoud Elzouka David Enriquez Catherine Erickson Lara Faoro Vinicius S. Ferreira Marcos Flores Leslie Burgos Sam Fontes Ebrahim Forati Jeremiah Ford Brooks Foxen Masaya Fukami Alan Wing Fung Lenny Fuste Suhas Ganjam Gonzalo Garcia Christopher Garrick Robert Gasca Helge Gehring Robert Geiger William Giang Dar Gilboa James E. Goeders Edward C. Gonzales Raja Gosula Stijn J. Graaf Alejandro Dau Dietrich Graumann Joel Grebel Alex Greene Jonathan A. Gross Jose Guerrero Lo\"ick Guevel Tan Ha Steve Habegger Tanner Hadick Ali Hadjikhani Michael C. Hamilton Monica Hansen Matthew P. Harrigan Sean D. Harrington Jeanne Hartshorn Stephen Heslin Paula Heu Oscar Higgott Reno Hiltermann Jeremy Hilton Hsin-Yuan Huang Mike Hucka Christopher Hudspeth Ashley Huff William J. Huggins Evan Jeffrey Shaun Jevons Zhang Jiang Xiaoxuan Jin Cody Jones Chaitali Joshi Pavol Juhas Andreas Kabel Dvir Kafri Hui Kang Kiseo Kang Amir H. Karamlou Ryan Kaufman Kostyantyn Kechedzhi Julian Kelly Tanuj Khattar Mostafa Khezri Seon Kim Paul V. Klimov Can M. Knaut Bryce Kobrin Alexander N. Korotkov Fedor Kostritsa John Mark Kreikebaum Ryuho Kudo Ben Kueffler Arun Kumar Vladislav D. Kurilovich Vitali Kutsko Tiano Lange-Dei Brandon W. Langley Pavel Laptev Kim-Ming Lau Emma Leavell Justin Ledford Joonho Lee Joy Lee Kenny Lee Brian J. Lester Wendy Leung Lily Li Wing Yan Li Ming Li Alexander T. Lill William P. Livingston Matthew T. Lloyd Laura Lorenzo Erik Lucero Daniel Lundahl Aaron Lunt Sid Madhuk Aniket Maiti Ashley Maloney Salvatore Mandr\`a Leigh S. Martin Orion Martin Eric Mascot Paul Das Dmitri Maslov Melvin Mathews Cameron Maxfield Jarrod R. McClean Matt McEwen Seneca Meeks Anthony Megrant Kevin C. Miao Zlatko K. Minev Reza Molavi Sebastian Molina Shirin Montazeri Charles Neill Michael Newman Anthony Nguyen Murray Nguyen Chia-Hung Ni Murphy Yuezhen Niu Logan Oas William D. Oliver Raymond Orosco Kristoffer Ottosson Alice Pagano Agustin Paolo Sherman Peek David Peterson Alex Pizzuto Elias Portoles Rebecca Potter Orion Pritchard Michael Qian Chris Quintana Ganesh Ramachandran Arpit Ranadive Matthew J. Reagor Rachel Resnick David M. Rhodes Daniel Riley Gabrielle Roberts Roberto Rodriguez Emma Ropes Lucia B. Rose Eliott Rosenberg Emma Rosenfeld Dario Rosenstock Elizabeth Rossi David A. Rower Robert Salazar Kannan Sankaragomathi Murat Can Sarihan Kevin J. Satzinger Max Schaefer Sebastian Schroeder Henry F. Schurkus Aria Shahingohar Michael J. Shearn Aaron Shorter Vladimir Shvarts Volodymyr Sivak Spencer Small W. Clarke Smith David A. Sobel Barrett Spells Sofia Springer George Sterling Jordan Suchard Aaron Szasz Alexander Sztein Madeline Taylor Jothi Priyanka Thiruraman Douglas Thor Dogan Timucin Eifu Tomita Alfredo Torres M. Mert Torunbalci Hao Tran Abeer Vaishnav Justin Vargas Sergey Vdovichev Guifre Vidal Benjamin Villalonga Catherine Heidweiller Meghan Voorhees Steven Waltman Jonathan Waltz Shannon X. Wang Brayden Ware James D. Watson Yonghua Wei Travis Weidel Theodore White Kristi Wong Bryan W. Woo Christopher J. Wood Maddy Woodson Cheng Xing Z. Jamie Yao Ping Yeh Bicheng Ying Juhwan Yoo Noureldin Yosri Elliot Young Grayson Young Adam Zalcman Ran Zhang Yaxing Zhang Ningfeng Zhu Nicholas Zobrist Zhenjie Zou Sergio Boixo Hartmut Neven Vadim Smelyanskiy Trond I. Andersen Pedram Roushan Mikhail V. Feigelman Lev B. Ioffe
This is my paper
classification quant-ph cond-mat.dis-nn
keywords non-ergodic dynamicsquantum glassmany-body localizationsuperconducting qubitsEdwards-Anderson order parameterHilbert space dynamicsspin diffusiondisordered spin systems
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper examines dynamics of a disordered interacting spin model realized in a two-dimensional superconducting qubit array at finite temperature. In an intermediate disorder window it finds glass-like features including broadly distributed observables, partial freezing of degrees of freedom, power-law decay of Hilbert space return probability, and emergence of Edwards-Anderson order while spin diffusion stops. At weaker disorder the system remains ergodic with finite diffusion. This establishes that a transition out of ergodicity occurs in two dimensions.

Core claim

In the two-dimensional disordered spin model realized on the qubit array, an intermediate non-ergodic regime appears over a broad disorder range, marked by broadly distributed observables, slow power-law decay of the Hilbert-space return probability, onset of a finite Edwards-Anderson order parameter, and loss of spin diffusion, while lower disorder permits nonzero diffusion coefficient and persistent transport.

What carries the argument

The Hilbert-space return probability combined with the Edwards-Anderson order parameter, which together detect partial freezing of degrees of freedom across the many-body state space.

Load-bearing premise

The measured power-law decay, broad distributions, and order parameter onset mark a true thermodynamic transition rather than finite-size or transient hardware effects.

What would settle it

A demonstration that the Edwards-Anderson parameter vanishes or the return probability decay turns exponential when system size increases at fixed disorder and temperature.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Spin diffusion coefficient drops to zero above a critical disorder strength.
  • Physical observables cease to be self-averaging and instead show broad distributions.
  • Only a subset of degrees of freedom freeze, leaving others active.
  • The system leaves the ergodic phase at finite disorder and finite temperature.

Where Pith is reading between the lines

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

  • The power-law return probability may remain a useful diagnostic for glassiness in the thermodynamic limit.
  • Analogous measurements on other two-dimensional platforms could test whether the transition is platform-independent.
  • The results suggest finite-temperature 2D many-body glasses may be experimentally accessible without requiring extreme isolation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 2 minor

Summary. The manuscript reports experiments on a two-dimensional array of superconducting qubits realizing a disordered interacting spin model at finite temperature. It identifies an intermediate non-ergodic regime with glass-like features: broadly distributed observables, power-law decay of the Hilbert-space return probability, onset of a finite Edwards-Anderson order parameter, and vanishing spin diffusion, while nonzero diffusion persists at weaker disorder. The authors conclude that these signatures establish a transition out of the ergodic phase in two-dimensional systems.

Significance. If the central interpretation is upheld, the result would be significant: it supplies experimental evidence for finite-temperature non-ergodic glassy dynamics in 2D, using both real-space transport and Hilbert-space return probabilities, thereby addressing a debated question in many-body localization and quantum glasses. The experimental platform and dual-space diagnostics constitute a concrete advance.

major comments (2)
  1. [Abstract and main results] Abstract and main results: the claim that the observed power-law return probability, broad distributions, Edwards-Anderson order-parameter onset, and vanishing diffusion constitute evidence of a thermodynamic transition out of the ergodic phase is load-bearing, yet the manuscript provides no finite-size scaling collapse or explicit coherence-time controls that would exclude transient dynamics cut off by hardware decoherence or finite-size localization that fails to survive the thermodynamic limit.
  2. [Results on Edwards-Anderson order parameter] The interpretation of the Edwards-Anderson order parameter as marking a true thermodynamic transition requires demonstration that its onset survives extrapolation to larger system sizes or longer coherence times; without such data the finite-size/hardware alternative remains viable.
minor comments (2)
  1. [Methods] Notation for the Hilbert-space return probability should be defined explicitly at first use with a clear equation reference.
  2. [Figures] Figure captions should state the number of disorder realizations and the precise fitting windows used for the power-law exponents.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their careful reading of the manuscript and for highlighting the need to strengthen the evidence for a thermodynamic transition. We address each major comment below, providing clarifications based on the experimental data and noting revisions where appropriate. Our responses focus on the multi-probe consistency of the observed signatures while acknowledging hardware constraints.

read point-by-point responses

  1. Referee: [Abstract and main results] Abstract and main results: the claim that the observed power-law return probability, broad distributions, Edwards-Anderson order-parameter onset, and vanishing diffusion constitute evidence of a thermodynamic transition out of the ergodic phase is load-bearing, yet the manuscript provides no finite-size scaling collapse or explicit coherence-time controls that would exclude transient dynamics cut off by hardware decoherence or finite-size localization that fails to survive the thermodynamic limit.

    Authors: We agree that a finite-size scaling collapse would provide more definitive support for a thermodynamic transition in the thermodynamic limit. The current experimental platform uses a fixed-size 2D qubit array, which precludes systematic variation of system size. Instead, we vary disorder strength and observe that the power-law Hilbert-space return probability, broad observable distributions, finite Edwards-Anderson parameter, and vanishing spin diffusion all onset at the same disorder threshold. Additional analysis of the return probability time series shows the power-law regime extends over the full accessible coherence window without premature cutoff by decoherence. We will revise the manuscript to include an expanded discussion of these hardware limitations and the rationale for interpreting the multi-observable crossover as evidence of the non-ergodic regime, consistent with theoretical expectations for 2D quantum glasses. revision: partial

  2. Referee: [Results on Edwards-Anderson order parameter] The interpretation of the Edwards-Anderson order parameter as marking a true thermodynamic transition requires demonstration that its onset survives extrapolation to larger system sizes or longer coherence times; without such data the finite-size/hardware alternative remains viable.

    Authors: The Edwards-Anderson order parameter is obtained from the long-time limit of the disorder-averaged local spin autocorrelations. Within the experimentally accessible coherence times, this parameter saturates to a nonzero value above the critical disorder, coinciding precisely with the suppression of spin diffusion. We have verified that the onset remains stable when varying the averaging window inside the coherence time. While direct extrapolation to infinite size or infinite coherence time is not feasible with the present hardware, the simultaneous disappearance of diffusion at the same disorder value provides independent corroboration that the order parameter reflects dynamical freezing. We will revise the manuscript to add supplementary figures displaying the time dependence of the order parameter and its disorder dependence with error bars to address this point explicitly. revision: yes

standing simulated objections not resolved
  • Finite-size scaling collapse cannot be performed because the superconducting qubit array has a fixed number of sites set by the experimental hardware.

Circularity Check

0 steps flagged

No significant circularity in experimental observations

full rationale

The paper reports direct experimental measurements on a 2D superconducting qubit array, including Hilbert-space return probabilities showing power-law decay, broad distributions of physical observables, onset of a finite Edwards-Anderson order parameter, and the disappearance of spin diffusion at higher disorder. These quantities are obtained as independent hardware observables rather than quantities fitted or defined in terms of each other within the paper. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps in the provided text to derive the central claim of a transition out of the ergodic phase; the results are presented as empirical evidence without reduction to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental paper; central claim rests on the interpretation of qubit measurements as thermodynamic signatures. No free parameters, axioms, or invented entities are stated in the abstract.

pith-pipeline@v0.9.0 · 6783 in / 1162 out tokens · 69320 ms · 2026-05-16T18:33:50.462977+00:00 · methodology

0 comments
read the original abstract

Disorder in quantum many-body systems can drive transitions between ergodic and non-ergodic phases, yet the nature--and even the existence--of these transitions remains intensely debated. Using a two-dimensional array of superconducting qubits, we study an interacting spin model at finite temperature in a disordered landscape, tracking dynamics both in real space and in Hilbert space. Over a broad disorder range, we observe an intermediate non-ergodic regime with glass-like characteristics: physical observables become broadly distributed and some, but not all, degrees of freedom are effectively frozen. The Hilbert-space return probability shows slow power-law decay, consistent with finite-temperature quantum glassiness. In the same regime, we detect the onset of a finite Edwards-Anderson order parameter and the disappearance of spin diffusion. By contrast, at lower disorder, spin transport persists with a nonzero diffusion coefficient. Our results show that there is a transition out of the ergodic phase in two-dimensional systems.

Figures

Figures reproduced from arXiv: 2601.01309 by Aaron Lunt, Aaron Shorter, Aaron Szasz, Abeer Vaishnav, Adam Zalcman, Agnetta Y. Cleland, Agustin Paolo, Alan Wing Fung, Alec Eickbusch, Alejandro Dau, Aleksey Lunkin, Alexander Bilmes, Alexander L. Crook, Alexander N. Korotkov, Alexander Sztein, Alexander T. Lill, Alexandre Bourassa, Alex Greene, Alex Pizzuto, Alfredo Torres, Alice Pagano, Ali Hadjikhani, Amira Abbas, Amir H. Karamlou, Andreas Bengtsson, Andreas Kabel, Andrew Dunsworth, Aniket Maiti, Anthony Cabrera, Anthony Megrant, Anthony Nguyen, Aria Shahingohar, Arpit Ranadive, Arun Kumar, Ashley Huff, Ashley Maloney, Aviv Moshe Elbag, Barrett Spells, Ben Chiaro, Ben Curtin, Benjamin Villalonga, Ben Kueffler, Bicheng Ying, Bob B. Buckley, Brandon W. Langley, Brayden Ware, Brett Buchea, Brian Ballard, Brian Burkett, Brian J. Lester, Brooks Foxen, Bryan Cochrane, Bryan W. Woo, Bryce Kobrin, Cameron Maxfield, Can M. Knaut, Catherine Erickson, Catherine Heidweiller, Chaitali Joshi, Charles Neill, Cheng Xing, Chia-Hung Ni, Chris Quintana, Christopher Garrick, Christopher Hudspeth, Christopher J. Wood, Cody Jones, Connie Miao, Daniel Lundahl, Daniel Riley, Dar Gilboa, Dario Rosenstock, David A. Browne, David A. Rower, David A. Sobel, David Enriquez, David M. Rhodes, David Peterson, Dietrich Graumann, Dmitri Maslov, Dmitry Abanin, Dogan Timucin, Douglas Thor, Dripto M. Debroy, Dvir Kafri, Dylan Bowers, Ebrahim Forati, Edward C. Gonzales, Eifu Tomita, Elias Portoles, Eliott Rosenberg, Elizabeth Rossi, Elliot Young, Emma Leavell, Emma Ropes, Emma Rosenfeld, Eric Mascot, Erik Lucero, Evan Jeffrey, Fedor Kostritsa, Felix Borjans, Frank Arute, Gabrielle Roberts, Ganesh Ramachandran, Georg Aigeldinger, George Sterling, Gonzalo Garcia, Grayson Young, Guifre Vidal, Hao Tran, Harold Cook, Hartmut Neven, Hector Bates, Helge Gehring, Henry F. Schurkus, Hsin-Yuan Huang, Hui Kang, Hung-Shen Chang, Ilya Drozdov, Jaehong Choi, Jamal Busnaina, James D. Watson, James E. Goeders, Jarrod R. McClean, Jeanne Hartshorn, Jenna Bovaird, Jeremiah Ford, Jeremy Hilton, Joel Grebel, John Mark Kreikebaum, Jonathan A. Gross, Jonathan Waltz, Joonho Lee, Jordan Suchard, Jose Guerrero, Joseph C. Bardin, Josh Cogan, Jothi Priyanka Thiruraman, Joy Lee, Juan Atalaya, Juan Campero, Juhwan Yoo, Julian Kelly, Justin Ledford, Justin Vargas, Kannan Sankaragomathi, Kenny Lee, Kevin C. Miao, Kevin J. Satzinger, Kim-Ming Lau, Kiseo Kang, Kostyantyn Kechedzhi, Kristi Wong, Kristoffer Ottosson, Kunal Arya, Laleh Beni, Lara Faoro, Laura Lorenzo, Leigh S. Martin, Lenny Fuste, Leon Brill, Leslie Burgos, Lev B. Ioffe, Liang-Ying Chih, Lily Li, Lior Ella, Logan Oas, Lo\"ick Guevel, Lucia B. Rose, Maddy Woodson, Madeline Taylor, Mahmoud Elzouka, Majid Karimi, Marcos Flores, Markus Ansmann, Martin Damyanov, Masaya Fukami, Matt Cockrell, Matthew J. Reagor, Matthew P. Harrigan, Matthew T. Lloyd, Matt McEwen, Max Schaefer, Meghan Voorhees, Melvin Mathews, Michael Broughton, Michael C. Hamilton, Michael J. Shearn, Michael Newman, Michael Qian, Mike Hucka, Mikhail V. Feigelman, Ming Li, M. Mert Torunbalci, Mohammed Alghadeer, Monica Hansen, Mostafa Khezri, Murat Can Sarihan, Murphy Yuezhen Niu, Murray Nguyen, Nicholas Bushnell, Nicholas Zobrist, Nicole S. Ticea, Nikita Astrakhantsev, Ningfeng Zhu, Noureldin Yosri, Orion Martin, Orion Pritchard, Oscar Higgott, Paula Heu, Paul Conner, Paul Das, Paul Donohoe, Paul V. Klimov, Pavel Laptev, Pavol Juhas, Pedram Roushan, Peter Brooks, Ping Yeh, Rachel Resnick, Raja Gosula, Rajeev Acharya, Ran Zhang, Raymond Orosco, Rebecca Potter, Reno Hiltermann, Reza Molavi, Robert Gasca, Robert Geiger, Roberto Rodriguez, Robert Salazar, Rodrigo G. Corti\~nas, Ross Alcaraz, Ryan Babbush, Ryan Kaufman, Ryuho Kudo, Salvatore Mandr\`a, Sam Fontes, Sayan Das, Sayra Alcaraz, Sean Demura, Sean D. Harrington, Sebastian Molina, Sebastian Schroeder, Seneca Meeks, Seon Kim, Sergey Vdovichev, Sergio Boixo, Shannon X. Wang, Shashwat Kumar, Shaun Jevons, Sherman Peek, Shirin Montazeri, Sid Madhuk, Silas Chen, Simon Bilodeau, Sofia Springer, Spencer Small, Stephen Heslin, Steve Habegger, Steven Waltman, Stijn J. Graaf, Suhas Ganjam, Tan Ha, Tanner Hadick, Tanuj Khattar, Theodore White, Tiano Lange-Dei, Tim Burger, Travis Weidel, Trond I. Andersen, Vadim Smelyanskiy, Valerie Ehimhen, Vinicius S. Ferreira, Vitali Kutsko, Vladimir Shvarts, Vladislav D. Kurilovich, Volodymyr Sivak, Walt Askew, W. Clarke Smith, Wendy Leung, William Courtney, William D. Oliver, William Giang, William J. Huggins, William P. Livingston, Wing Yan Li, Xiaoxuan Jin, Yaxing Zhang, Yonghua Wei, Zhang Jiang, Zhenjie Zou, Zijun Chen, Z. Jamie Yao, Zlatko K. Minev.

Figure 1
Figure 1. Figure 1: FIG. 1: Phase Diagram [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Evidence of glass formation in the frozen magnetization. a, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Signatures of glassy behaviour in the return probability. a, [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Disappearance of diffusion at strong disorder. a, [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Wavefunction statistics [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

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