Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator

Bozhen Zhou; Cai-Ping Fang; Cheng-Lin Deng; Chi-Tong Chen; Da'er Feng; Dongning Zheng; Guangming Xue; Gui-Han Liang; Haifeng Yu; Hao Li

REVIEW 3 major objections 4 minor 2 cited by

Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that in a two-dimensional disordered XY model on 70 qubits, the apparent many-body localized regime is unstable: the imbalance keeps decaying as the system grows from 21 to 42 to 70 qubits, and the disorder strength…

desk verdict A solid finite-size scaling experiment that supports avalanche-driven delocalization in 2D, but the no-MBL-in-2D conclusion overreaches what power-law fits in a 250–1000 ns window can establish. read the letter →

arxiv 2507.16882 v1 pith:52K46DLS submitted 2025-07-22 quant-ph cond-mat.dis-nncond-mat.stat-mech

Tian-Ming Li , Zheng-Hang Sun , Yun-Hao Shi , Zhen-Ting Bao , Yong-Yi Wang , Jia-Chi Zhang , Yu Liu , Cheng-Lin Deng

show 30 more authors

Yi-Han Yu Zheng-He Liu Chi-Tong Chen Li Li Hao Li Hao-Tian Liu Si-Yun Zhou Zhen-Yu Peng Yan-Jun Liu Ziting Wang Yue-Shan Xu Kui Zhao Yang He Da'er Feng Jia-Cheng Song Cai-Ping Fang Junrui Deng Mingyu Xu Yu-Tao Chen Bozhen zhou Gui-Han Liang Zhong-Cheng Xiang Guangming Xue Dongning Zheng Kaixuan Huang Zheng-An Wang Haifeng Yu Piotr Sierant Kai Xu Heng Fan

This is my paper · ORCID

classification quant-phcond-mat.dis-nncond-mat.stat-mech

keywords many-bodylocalizationdelocalizationtwo-dimensionaldisorderedsystemssuperconductingquantumsimulatorimbalancerelaxationavalancheinstabilityfinite-sizescalingthermalization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Using a 70-qubit two-dimensional superconducting processor, the paper simulates a disordered 2D XY model and asks whether the finite-size many-body localized (MBL) regime, where disorder suppresses thermalization, remains stable as the system grows. Across three system sizes (21, 42, and 70 qubits) at disorder strengths where level statistics look localized, the measured imbalance decays as a power law and its relaxation exponent $\beta$ increases with system size. The disorder strength $W^*$ at which relaxation would practically halt grows roughly linearly with linear size $L$. From these extrapolations the authors conclude that what looks like MBL at finite size is unstable, that ergodicity is restored in sufficiently large systems, and that their data provide no evidence for an MBL phase at any disorder strength in two dimensions.

What carries the argument

The load-bearing object is the imbalance $I(t)$ and its power-law relaxation exponent $\beta$, extracted by fitting $I(t)\propto t^{-\beta}$ on the window $t\in[250,1000]$ ns; the paper uses the size dependence of $\beta$ and of the threshold $W^*(\beta=10^{-2})$ to distinguish a stable localized phase from a delocalizing regime. The interpretive mechanism is the avalanche instability of many-body localization, in which rare thermal regions spread through the localized system as its size grows, making the finite-size localized regime unstable in higher dimensions.

What would settle it

A direct falsifier would be a longer-time measurement on the same platform, or a larger lattice with better coherence, showing that the imbalance decay exponent $\beta$ stops growing with system size or that $I(t)$ saturates at a nonzero plateau for every $L$, either of which would invalidate the extrapolation that $W^*(\beta=10^{-2})$ grows without bound and that no MBL phase exists in 2D.

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Extended reading notes

Core claim

The central claim is that in a two-dimensional disordered many-body system, the finite-size MBL regime is not the beginning of a stable phase but a finite-size effect that gives way to slow thermalization as the system grows. On the 70-qubit simulator, evolving a checkerboard half-filled state under an XY Hamiltonian with random on-site potentials $h_i\in[-W,W]$, the authors find that the imbalance $I(t)\propto t^{-\beta}$ decays with an exponent $\beta$ that increases from 21 to 42 to 70 qubits at both $W/2\pi=50$ MHz and $100$ MHz, and that the fitted threshold $W^*(\beta=10^{-2})$ grows approximately linearly with $L$. They present this as evidence of many-body delocalization in two dimensions for the first time on a superconducting platform, interpret it as consistent with the avalanche instability of MBL beyond one dimension, and state that extrapolations of the data show no evidence for an MBL phase at any disorder strength in two-dimensional systems.

Load-bearing premise

The load-bearing premise is that fitting the measured imbalance decay to a power law over the 250-1000 ns window correctly captures the asymptotic dynamics, so the apparent strengthening of decay with system size is genuine long-time behavior rather than a finite-time transient or decoherence artifact.

Editorial extensions

If this is right

A finite-size 2D MBL regime seen at any fixed qubit number should not be read as a stable phase; the same Hamiltonian at larger $L$ is expected to show continued decay of imbalance.
At fixed disorder strength in 2D, the relaxation exponent $\beta$ rises with $L$, so the apparent localization threshold moves to higher disorder strengths as systems grow.
Extrapolating the near-linear growth of $W^*(\beta=10^{-2})$ with $L$ implies that no finite disorder strength protects localization in the thermodynamic limit.
In contrast, the 1D Anderson localized chain shows no comparable growth of $\beta$ with $L$, isolating the 2D many-body delocalization as an interaction-driven effect.
The numerical cost of benchmarking 2D disordered dynamics, with TDVP simulations at $W/2\pi=100$ MHz requiring bond dimensions above 1000, makes the analog quantum simulator the practical route to the data presented.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference. If the 2D localized phase is indeed absent, then quantum-hardware demonstrations of MBL in two dimensions should be described as finite-size or prethermal localization rather than evidence of an asymptotic phase.
Editorial inference. The same avalanche logic predicts that deliberately coupling a small thermal subsystem to a 2D localized region should cause faster delocalization for larger $L$, a test that could be performed directly on this processor.
Editorial inference. With improved coherence, tracking $I(t)$ past one microsecond would discriminate between a true power-law tail and a stretched-exponential decay; a persistent nonzero plateau at every size would challenge the paper's extrapolation.
Editorial inference. The near-linear growth of $W^*$ with $L$ is a quantitative prediction that could be compared with 2D quasiperiodic cold-atom experiments if the same threshold analysis were applied to their imbalance data.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The thing to know: this is a genuine finite-size scaling experiment, the first I know of that tracks imbalance decay across 21, 42, and 70 qubits in a 2D disordered XY simulator, with a 1D Anderson control and independent Krylov/TDVP benchmarks. The central observation—β grows with L in 2D while staying flat in 1D—looks solid. What is much less solid is the thermodynamic extrapolation: 'no MBL phase at any disorder strength in 2D' rests on power-law fits over 250–1000 ns and a hand-chosen threshold β=10^-2. The conditional verdict is right, and the stress-test concern is the one that matters.

What the paper does well: the hardware control is careful; the block-segment calibrations and on-resonant dynamics comparisons are thorough; the numerical benchmarks (Krylov for L=21, TDVP up to χ>1000 for L=42) are honest and actually show the simulations are hard. The citation pattern is appropriate—the authors engage both the numerical evidence for 2D MBL (Chertkov, Wahl) and the avalanche instability literature. The 1D Anderson control is a useful sanity check. There is no circularity: the observation is not fitted to the numerical conclusions.

The soft spots, in proportion:

1. The load-bearing step is assuming I(t)∝t^-β is the asymptotic form. All data stop around 1 µs. If the true long-time behavior is I∞ + A exp[-(t/τ)^γ] with I∞>0, or a stretched-exponential transient, a power-law fit in a fixed early window can produce exactly the reported β(L) trend without ergodicity restoration. The authors themselves flag this in the Discussion ("it is potential to observe a faster decay than the power law, or a stretched exponential behavior proposed for the MBL regime which eventually thermalizes"). So the gap is not hidden; it is stated.

2. The threshold β=10^-2 is calibrated from the 1D Anderson noise floor. That makes W*(β=10^-2) an operational crossover label, not a thermodynamic critical point. The linear growth of W* with L is evidence that the finite-size MBL regime is fragile, but it does not by itself establish that no MBL phase exists.

3. Minor framing issue: the Discussion says imbalance 'saturation' at nonzero values signifies MBL onset, then says increasing L induces 'persistent decay.' Within a 1 µs window, saturation and slow decay are hard to distinguish; the wording oversells the phase interpretation.

Who this is for: anyone tracking the MBL/avalanche debate and 2D quantum simulation. The data are worth taking seriously; the conclusion about the thermodynamic limit is an extrapolation and should be labeled as such.

Recommendation: send to peer review. A serious referee should ask for a fit-window robustness analysis, a test of alternative functional forms (including a nonzero asymptote), and a softened abstract. These are addressable revisions; the core experimental finding deserves referee time.

Referee Report

3 major / 4 minor

Summary. The paper reports an analog quantum simulation of a disordered two-dimensional XY model on a 70-qubit superconducting processor. For system sizes L = 21, 42, and 70, the authors measure the half-filling charge imbalance I(t) at disorder strengths W/2π = 50 and 100 MHz, observe that the fitted power-law relaxation exponent β = d ln I/d ln t increases with L, and compare the data against Krylov and TDVP benchmarks. They further fit β(W) as a power law, define a crossover disorder strength W*(β = 10^-2), and report that W* grows approximately linearly with L, leading to the conclusion that there is no MBL phase at any disorder strength in 2D and that the finite-size MBL regime is destabilized by many-body delocalization. The manuscript includes detailed device calibration, convergence checks for the TDVP simulations, a 1D Anderson-localization control, and a discussion of possible alternative decay forms.

Significance. If the thermodynamic-limit conclusion were established, this would be a major experimental contribution: it would provide the largest two-dimensional disordered many-body simulator to date and the first direct finite-size evidence for avalanche-induced delocalization in 2D. The paper has real strengths: the 70-qubit platform is well characterized, the Hamiltonian parameters are calibrated against independent single- and multi-qubit checks, the numerical benchmarks are carefully converged (including bond-dimension extrapolation to χ→∞ for L = 42), and the 1D Anderson control demonstrates a flat β ≈ 0.01. These elements make the finite-size observation of size-dependent imbalance decay credible. The central finite-window data and the numerical agreement are valuable; however, the extrapolation to 'no MBL phase at any disorder strength' rests on assumptions about the asymptotic decay form and the functional form of β(W) that the paper itself acknowledges are not settled.

major comments (3)

[Results of imbalance; Fig. 2(d,e); Discussion] The size-dependent relaxation exponent β is extracted from a single power-law fit on the window t ∈ [250, 1000] ns and is then used to infer W*(β = 10^-2) in Fig. 3(c). The manuscript's own Discussion states that improved coherence may reveal faster-than-power-law decay or stretched-exponential behavior (citing Ref. [50]), and the numerical benchmarks (21-qubit Krylov and 42-qubit TDVP with χ > 1000; Supp. §3B, §3C) also terminate near 1 μs. The data therefore do not establish that the fitted power law is the asymptotic long-time form of I(t). On a fixed early window, a state with I(t) = I_∞ + A exp[-(t/τ)^γ] and I_∞ > 0 can produce an apparent power-law exponent that increases as τ decreases with L, reproducing the reported trend without implying that ergodicity is restored. Consequently, the conclusion 'no evidence for the existence of an MBL phase at any disorder strength in two-dimensional systems' exceeds what the finite-window data and benchmarks currently support.
[Evidence of many-body delocalization; Fig. 3(a,c)] The extraction of W*(β = 10^-2) and its claimed linear growth with L depend on the assumed functional form β(W) = C W^{-γ}. The text says a power-law form fits better than an exponential and references the Supplementary Materials for the comparison, but the supplied SI contains no such comparison. Since the data cover only three system sizes and a limited disorder range, the choice of functional form is a load-bearing input to the extrapolation. Moreover, the threshold β = 10^-2 is an operational value calibrated to the measured 1D Anderson noise floor, not a physical criterion for the existence or absence of an MBL phase; an arbitrary threshold in a finite-time observable cannot by itself locate a thermodynamic phase boundary.
[Experimental setup and protocol; Fig. 1(a)] The three system sizes correspond to different lattice geometries and boundary conditions (a 3×7 block, a 6×7 block, and the full 70-qubit array from which Q65 and Q71 are excluded), not to a scaling at fixed aspect ratio and boundary-to-volume ratio. Some of the increase in β with L may therefore reflect geometry, aspect ratio, or boundary effects rather than a genuine thermodynamic-limit size trend. The authors should either restrict the claim to 'finite-size delocalization on the presented lattice geometries' or provide additional checks—for example, different subregions of the same device with the same shape—that separate size scaling from geometry effects.

minor comments (4)

[Abstract] The phrase 'for the first time, provide an evidence for the many-body delocalization in 2D disordered systems' is stronger than the evidence presented, given that earlier 2D cold-atom experiments (Refs. [21,22]) already observed slow relaxation and delocalization-related dynamics; suggest softening the claim.
[Results of imbalance; Fig. 2(d,e)] The error bars on β are statistical (one standard error from the linear fits), but no systematic-error analysis is given for the effect of pulse-calibration residuals or qubit decoherence on the extracted exponent; a brief discussion of expected systematic shifts would strengthen the interpretation.
[Supplementary Information §4A] The number of disorder realizations is stated for each L (60 for L=21, 30 for L=42, 30 for L=70), but it would be helpful to state explicitly whether the same disorder realizations are reused across the three sizes, since correlated disorder could inflate the apparent size trend.
[General] There are several typographical errors, e.g., 'stengths' in 'Results of imbalance', 'the the relaxation dynamics' in the paragraph after Fig. 3, and 'panned by' for 'spanned by' in Supp. §3B; these should be corrected in revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central size-dependent imbalance trend is directly measured and independently benchmarked against Krylov, TDVP, and POLFED numerical simulations.

full rationale

The derivation chain is observational rather than circular. The central claim is that at fixed disorder strengths W/2π = 50 and 100 MHz, the imbalance relaxation exponent β increases with system size for L = 21, 42, and 70 (Fig. 2d,e). That trend is extracted directly from measured I(t) decays, and the experimental curves are independently benchmarked by Krylov subspace simulations for L = 21 (Supp. §3B), MPS-TDVP simulations for L = 42 with bond-dimension convergence checks up to χ = 2100 (Supp. §3C), POLFED for the gap-ratio analysis (Supp. §3A), and a 1D Anderson localization control. The threshold β = 10^-2 used to define W* is calibrated to the measured 1D Anderson relaxation exponent, i.e., an external control rather than a quantity derived from the 2D target claim. W* is an operational crossover label extracted from a two-parameter power-law fit β = C W^-γ; its approximate linear growth with L is a presentation of the same measured β(L) data, not a prediction manufactured from an input that already contains the conclusion. The paper's own caveat that improved coherence might reveal faster-than-power-law or stretched-exponential decay [50] is a correctness and robustness concern about the asymptotic extrapolation, not a circularity: the finite-time data and numerical benchmarks stand independently of that extrapolation. Several citations are to the authors' own methods papers (POLFED, pulse calibration, Hilbert-space fragmentation), but none carries the load of the central size-scaling observation, which is supported by direct experimental and numerical evidence. No step reduces by construction to its own inputs.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new postulates or entities. The analysis rests on measurable experimental parameters, an empirical fitting form for the decay exponent, and standard domain assumptions about the relation between imbalance dynamics and MBL. No free parameters are hidden in a derivation, but the threshold and fitting form choices are the main non-derived inputs.

free parameters (4)

disorder strength W = 25, 30, 35, 40, 45, 50, 70, 90, 100 MHz
Tunable experimental control parameter. Not a fit parameter, but the central claim depends on the chosen range.
crossover threshold beta = 10^-2 = 0.01
A hand-chosen threshold defining W*, based on the measured 1D Anderson relaxation exponents. The value is not derived from theory.
fit window for power-law decay = t in [250, 1000] ns
The exponents beta are obtained by fitting a power law over this time interval. The choice is motivated by the experimental timescales but is not derived.
power-law form beta = C W^-gamma = C and gamma fitted per L
The paper states a power-law decay fits better than exponential, but the functional form is an empirical choice. The fitted values of gamma drive the W* extrapolation.

assumptions (4)

domain assumption The imbalance I(t) is a valid probe of ergodicity breaking in this model.
The paper equates slow imbalance decay with MBL behavior, following a large body of MBL literature. If the imbalance decay is dominated by other mechanisms (e.g., prethermalization, decoherence), the interpretation changes.
domain assumption The 2D XY Hamiltonian (1) is realized faithfully by the device.
The claim relies on the calibration of on-site potentials and couplings. The paper provides block-segment checks, but a perfect realization of the target Hamiltonian cannot be guaranteed.
domain assumption Power-law decay I(t) ~ t^-beta captures the relevant relaxation on the observed timescale.
The paper itself acknowledges that other functional forms (stretched exponential, faster decay) are possible for the eventual thermalization. The extraction of beta and W* depends on this assumption.
domain assumption The avalanche theory (cited Refs. [17-20, 26]) correctly describes the instability of MBL beyond 1D.
The interpretation of the data is framed as consistent with avalanche theory. The data do not directly measure rare thermal inclusions, so the connection to the avalanche mechanism is assumed.

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Cite this review

Pith. "Pith review of Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator." pith.science (2026). https://pith.science/paper/52K46DLS

@misc{pith2026250716882,
  author       = {Pith},
  title        = {Pith review of: Many-body delocalization with a two-dimensional 70-qubit superconducting quantum simulator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/52K46DLS}},
  note         = {Machine review of arXiv:2507.16882}
}

read the original abstract

Quantum many-body systems with sufficiently strong disorder can exhibit a non-equilibrium phenomenon, known as the many-body localization (MBL), which is distinct from conventional thermalization. While the MBL regime has been extensively studied in one dimension, its existence in higher dimensions remains elusive, challenged by the avalanche instability. Here, using a 70-qubit two-dimensional (2D) superconducting quantum simulator, we experimentally explore the robustness of the MBL regime in controlled finite-size 2D systems. We observe that the decay of imbalance becomes more pronounced with increasing system sizes, scaling up from 21, 42 to 70 qubits, with a relatively large disorder strength, and for the first time, provide an evidence for the many-body delocalization in 2D disordered systems. Our experimental results are consistent with the avalanche theory that predicts the instability of MBL regime beyond one spatial dimension. This work establishes a scalable platform for probing high-dimensional non-equilibrium phases of matter and their finite-size effects using superconducting quantum circuits.

Figures

Figures reproduced from arXiv: 2507.16882 by the authors.

**Figure 1.** a. A schematic representation of the analog quantum simulation is displayed in Fig. 1b. The high controllability of superconducting circuits allows the precise manipulation of the disorder, enabling us to tune the system between the ETH and MBL regimes. The scalability of the platform enables for the finite-size analysis of the ETH-MBL crossover. Recently, the robustness of the MBL regime has been experimentally s… view at source ↗

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

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Beyond the imbalance: site-resolved dynamics probing resonances in many-body localization
cond-mat.dis-nn 2026-01 conditional novelty 7.0 of 10

Histograms of site-resolved autocorrelators in the random-field XXZ chain expose few-body local resonances, reproduced by a two/three-site toy model, that control the initial-state-dependent finite-size scaling of the...
Stability of many-body localization in two dimensions
cond-mat.quant-gas 2025-08 conditional novelty 7.0 of 10

For random disorder, the 2D many-body localization crossover shifts to higher disorder with increasing system size, but for quasiperiodic disorder it is size-independent, suggesting MBL stability.

Reference graph

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Exploring Hilbert-Space Fragmentation on a Superconducting Processor,

Y ong-Yi Wang, Y un-Hao Shi, Zheng-Hang Sun, Chi-Tong Chen, Zheng-An Wang, Kui Zhao, Hao-Tian Liu, Wei-Guo Ma, Ziting Wang, Hao Li, Jia-Chi Zhang, Y u Liu, Cheng-Lin Deng, Tian-Ming Li, Y ang He, Zheng-He Liu, Zhen-Y u Peng, Xiaohui Song, Guangming Xue, Haifeng Y u, Kaixuan Hu...

2025
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Strongly correlated quantum walks with a 12-qubit superconducting processor,

Zhiguang Y an, Y u-Ran Zhang, Ming Gong, Y ulin Wu, Y arui Zheng, Shaowei Li, Can Wang, Futian Liang, Jin Lin, Y u Xu, Cheng Guo, Lihua Sun, Cheng-Zhi Peng, Keyu Xia, Hui Deng, Hao Rong, J. Q. Y ou, Franco Nori, Heng Fan, Xiaobo Zhu, and Jian-Wei Pan, “Strongly correlated quan...

2019
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High-precision pulse calibration of tunable couplers for high- ﬁdelity two-qubit gates in superconducting quantum proces- sors,

Tian-Ming Li, Jia-Chi Zhang, Bing-Jie Chen, Kaixuan Huang, Hao-Tian Liu, Y ong-Xi Xiao, Cheng-Lin Deng, Gui-Han Liang, Chi-Tong Chen, Y u Liu, Hao Li, Zhen-Ting Bao, Kui Zhao, Y ueshan Xu, Li Li, Y ang He, Zheng-He Liu, Yi-Han Y u, Si-Y un Zhou, Y an-Jun Liu, Xiaohui Song, Don...

2025
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Thermalization and criticality on an analogue–digital quantum simulator,

T. I. Andersen, N. Astrakhantsev, A. H. Karamlou, J. Berndts- son, J. Motruk, A. Szasz, J. A. Gross, A. Schuckert, T. Wester- hout, Y . Zhang, E. Forati, D. Rossi, B. Kobrin, A. Di Paolo, A. R. Klots, I. Drozdov, V . Kurilovich, A. Petukhov, L. B. Ioffe, A. Elben, A. Rath, V ....

2025
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Quantum Simulation of Topological Zero Modes on a 41-Qubit Superconducting Pro- cessor,

Y un-Hao Shi, Y u Liu, Y u-Ran Zhang, Zhongcheng Xiang, Kaixuan Huang, Tao Liu, Y ong-Yi Wang, Jia-Chi Zhang, Cheng-Lin Deng, Gui-Han Liang, Zheng-Y ang Mei, Hao Li, Tian-Ming Li, Wei-Guo Ma, Hao-Tian Liu, Chi-Tong Chen, Tong Liu, Y e Tian, Xiaohui Song, S. P . Zhao, Kai Xu, D...

2023
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Quantum simulation of Hawking radiation and curved space- time with a superconducting on-chip black hole,

Y un-Hao Shi, Run-Qiu Y ang, Zhongcheng Xiang, Zi-Y ong Ge, Hao Li, Y ong-Yi Wang, Kaixuan Huang, Y e Tian, Xiaohui Song, Dongning Zheng, Kai Xu, Rong-Gen Cai, and Heng Fan, “Quantum simulation of Hawking radiation and curved space- time with a superconducting on-chip black ho...

2023
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Anomalous Diffusion and Grifﬁths Effects Near the Many-Body Localization Transi- tion,

Kartiek Agarwal, Sarang Gopalakrishnan, Michael Knap, Markus M ¨uller, and Eugene Demler, “Anomalous Diffusion and Grifﬁths Effects Near the Many-Body Localization Transi- tion,” Phys. Rev. Lett. 114, 160401 (2015)

2015
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Ex- tended slow dynamical regime close to the many-body local- ization transition,

David J. Luitz, Nicolas Laﬂorencie, and Fabien Alet, “Ex- tended slow dynamical regime close to the many-body local- ization transition,” Phys. Rev. B 93, 060201 (2016)

2016
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Many-body localization in spin chain systems with quasiperi- odic ﬁelds,

Mac Lee, Thomas R. Look, S. P . Lim, and D. N. Sheng, “Many-body localization in spin chain systems with quasiperi- odic ﬁelds,” Phys. Rev. B 96, 075146 (2017)

2017
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Challenges to observation of many-body localization,

Piotr Sierant and Jakub Zakrzewski, “Challenges to observation of many-body localization,” Phys. Rev. B 105, 224203 (2022)

2022
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Observation of Slow Dynamics near the Many-Body Local- ization Transition in One-Dimensional Quasiperiodic Systems,

Henrik P . L ¨uschen, Pranjal Bordia, Sebastian Scherg, Fabien Alet, Ehud Altman, Ulrich Schneider, and Immanuel Bloch, “Observation of Slow Dynamics near the Many-Body Local- ization Transition in One-Dimensional Quasiperiodic Systems,” Phys. Rev. Lett. 119, 260401 (2017)

2017
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Observation of energy-resolved many-body local- ization,

Qiujiang Guo, Chen Cheng, Zheng-Hang Sun, Zixuan Song, Hekang Li, Zhen Wang, Wenhui Ren, Hang Dong, Dongn- ing Zheng, Y u-Ran Zhang, Rubem Mondaini, Heng Fan, and H. Wang, “Observation of energy-resolved many-body local- ization,” Nature Physics 17, 234–239 (2021)

2021
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Probing spin hydrodynamics on a superconducting quantum simulator,

Y un-Hao Shi, Zheng-Hang Sun, Y ong-Yi Wang, Zheng-An Wang, Y u-Ran Zhang, Wei-Guo Ma, Hao-Tian Liu, Kui Zhao, Jia-Cheng Song, Gui-Han Liang, Zheng-Y ang Mei, Jia-Chi Zhang, Hao Li, Chi-Tong Chen, Xiaohui Song, Jieci Wang, Guangming Xue, Haifeng Y u, Kaixuan Huang, Zhongcheng ...

2024
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Localization of inter- acting fermions at high temperature,

V adim Oganesyan and David A. Huse, “Localization of inter- acting fermions at high temperature,” Phys. Rev. B 75, 155111 (2007)

2007
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Many-body localization phase transition,

Arijeet Pal and David A. Huse, “Many-body localization phase transition,” Phys. Rev. B 82, 174411 (2010)

2010
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Critical Properties of the Many-Body Localization Transition,

V edika Khemani, S. P . Lim, D. N. Sheng, and David A. Huse, “Critical Properties of the Many-Body Localization Transition,” Phys. Rev. X 7, 021013 (2017)

2017
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Many- body localization edge in the random-ﬁeld heisenberg chain,

David J. Luitz, Nicolas Laﬂorencie, and Fabien Alet, “Many- body localization edge in the random-ﬁeld heisenberg chain,” Phys. Rev. B 91, 081103 (2015)

2015
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Two Uni- versality Classes for the Many-Body Localization Transition,

V edika Khemani, D. N. Sheng, and David A. Huse, “Two Uni- versality Classes for the Many-Body Localization Transition,” Phys. Rev. Lett. 119, 075702 (2017)

2017
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Emergent ergodicity at the tran- sition between many-body localized phases,

Rahul Sahay, Francisco Machado, Bingtian Y e, Chris R. Lau- mann, and Norman Y . Y ao, “Emergent ergodicity at the tran- sition between many-body localized phases,” Phys. Rev. Lett. 126, 100604 (2021)

2021
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Stability of many-body localization in ﬂo- quet systems,

Piotr Sierant, Maciej Lewenstein, Antonello Scardicchio, and Jakub Zakrzewski, “Stability of many-body localization in ﬂo- quet systems,” Phys. Rev. B 107, 115132 (2023)

2023
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Time dynamics with matrix product states: Many-body localization transition of large systems revisited,

Titas Chanda, Piotr Sierant, and Jakub Zakrzewski, “Time dynamics with matrix product states: Many-body localization transition of large systems revisited,” Phys. Rev. B 101, 035148 (2020)

2020
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Real- ization of hilbert space fragmentation and fracton dynamics in two dimensions,

Melissa Will, Roderich Moessner, and Frank Pollmann, “Real- ization of hilbert space fragmentation and fracton dynamics in two dimensions,” Phys. Rev. Lett. 133, 196301 (2024)

2024
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Observa- tion of Hilbert space fragmentation and fractonic excitations in 2D,

Daniel Adler, David Wei, Melissa Will, Kritsana Srakaew, Su- chita Agrawal, Pascal Weckesser, Roderich Moessner, Frank Pollmann, Immanuel Bloch, and Johannes Zeiher, “Observa- tion of Hilbert space fragmentation and fractonic excitations in 2D,” Nature 636, 80–85 (2024)

2024
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Roughening dynamics of interfaces in the two-dimensional quantum Ising model,

Wladislaw Krinitsin, Niklas Tausendpfund, Matteo Rizzi, Markus Heyl, and Markus Schmitt, “Roughening dynamics of interfaces in the two-dimensional quantum Ising model,” (2024), arXiv:2412.10145 [quant-ph]

2024 arXiv
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Roughening Transition in Quantum Circuits,

Hyunsoo Ha, David A. Huse, and Grace M. Sommers, “Roughening Transition in Quantum Circuits,” (2025), arXiv:2506.11187 [quant-ph]

2025
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Quantum and classical coarsening and their interplay with the Kibble-Zurek mecha- nism,

Rhine Samajdar and David A. Huse, “Quantum and classical coarsening and their interplay with the Kibble-Zurek mecha- nism,” (2024), arXiv:2401.15144 [quant-ph]

2024 arXiv
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Quantum coarsening and collective dynam- ics on a programmable simulator,

Tom Manovitz, Sophie H. Li, Sepehr Ebadi, Rhine Samaj- dar, Alexandra A. Geim, Simon J. Evered, Dolev Bluvstein, Hengyun Zhou, Nazli Ugur Koyluoglu, Johannes Feldmeier, Pavel E. Dolgirev, Nishad Maskara, Marcin Kalinowski, Subir Sachdev, David A. Huse, Markus Greiner, Vladan V...

2025
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Automatic qubit bringing-up 4
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Automatic allocation of qubit idle points 8
[59]

Precise calibration for aiming Hamiltonian 11

Automatic synchronization of control pulses 10 B. Precise calibration for aiming Hamiltonian 11
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Calibrate speciﬁc resonant frequency using time-domain Rabi oscillation 11
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Numerical methods and data 15 A

Block segment of multi-qubit on-resonant experiment 13 Section 3. Numerical methods and data 15 A. POLFED method 15 B. Krylov subspace method 17 C. Matrix-product-state based time dependent variational principle 17 D. Additional numerical data for 1D disordered systems 18 Sect...
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S7: • Qubit spectroscopy, which establishes the relationship between ﬂux bias and transition frequency

Automatic qubit bringing-up Following a round of initial calibration across the entire processor, we obtain some basic information, typical data of which is displayed in Fig. S7: • Qubit spectroscopy, which establishes the relationship between ﬂux bias and transition frequency...
[63]

If the idle frequency is placed too near its sweet point, achieving this non-realistic target frequency might fail due to ﬁtting errors in qubit spectroscopy

Automatic allocation of qubit idle points Based on the fundamental information (particularly qubit spectroscopy and spectrally resolved T1) obtained in Section 2 A 1, we establish a series of constraints for conﬁguring the idle energy levels of qubits: • The idle frequency sho...
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We provide an automated timing procedure (pseudo-code see Algorithm

Automatic synchronization of control pulses Differences in the lengths of the transmission lines used for distributing trigger signals to various electronic devices, as well as slight timing variations in the control signals transmitted through coaxial cables and microwave com...
[65]

single-qubit timing calibration

which consists of the following steps: • [Fig. S9(c)] Align XY and Z signals for each individual qubit (named as "single-qubit timing calibration"). • [Fig. S9(a)] Construct breadth-ﬁrst search (BFS) [ 11] based on the chip topology, starting from its center. This algorithm no...
[66]

UP” mode), all surrounding qubits are biased above the target frequency, whereas in the second conﬁguration (named as “DOWN

Calibrate speciﬁc resonant frequency using time-domain Rabi oscillation Due to residue Z crosstalk and parasitic couplings, the qubit frequency may slightly deviate from its expected bare frequency when all the qubits are simultaneously biased and thus dressed [ 13]. To addres...
[67]

1D” and “sub

Block segment of multi-qubit on-resonant experiment We precisely calibrate the resonant working points for all 70 qubits by time-domain Rabi oscillations (detailed in Section 2 B 1). Additionally, we ﬁne-tune the effective coupling strengths to approximately 3 MHz via measurin...
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Y .-H. Shi, R.-Q. Y ang, Z. Xiang, Z.-Y . Ge, H. Li, Y .-Y . Wang, K. Huang, Y . Tian, X. Song, D. Zheng, K. Xu, R.-G. Cai, and H. Fan, Quantum simulation of Hawking radiation and curved spacetime with a superconducting on-chip black hole, Nature Communications 14, 3263 (2023)

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E. A. Sete, A. Q. Chen, R. Manenti, S. Kulshreshtha, and S. Poletto, Floating Tunable Coupler for Scalable Quantum Computing Archi- tectures, Physical Review Applied 15, 064063 (2021)

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M. Boissonneault, J. M. Gambetta, and A. Blais, Improved superconducting qubit readout by qubit-induced nonlinearities, Physical Review Letters 105, 100504 (2010)

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Z. Y an, Y .-R. Zhang, M. Gong, Y . Wu, Y . Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y . Xu, C. Guo, L. Sun, C.-Z. Peng, K. Xia, H. Deng, H. Rong, J. Q. Y ou, F. Nori, H. Fan, X. Zhu, and J.-W. Pan, Strongly correlated quantum walks with a 12-qubit superconducting processor, S...

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T.-M. Li, J.-C. Zhang, B.-J. Chen, K. Huang, H.-T. Liu, Y .-X. Xiao, C.-L. Deng, G.-H. Liang, C.-T. Chen, Y . Liu, H. Li, Z.-T. Bao, K. Zhao, Y . Xu, L. Li, Y . He, Z.-H. Liu, Y .-H. Y u, S.-Y . Zhou, Y .-J. Liu, X. Song, D. Zheng, Z. Xiang, Y .-H. Shi, K. Xu, and H. Fan, High...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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Phenomenology of the Prethermal Many- Body Localized Regime,

David M. Long, Philip J. D. Crowley, V edika Khemani, and Anushya Chandran, “Phenomenology of the Prethermal Many- Body Localized Regime,” Phys. Rev. Lett. 131, 106301 (2023)

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Many-body localiza- tion and thermalization in quantum statistical mechanics,

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Many-body localization and quantum thermal- ization,

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