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A disorder-free mechanism, Fock space prethermalization, keeps a 72-qubit driven Ising chain from heating and sustains time-crystalline order for over 120 cycles.

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2026-08-04 07:50 UTC pith:NH3C5OAW

load-bearing objection A convincing 72-qubit DTC experiment with a useful new label, Fock space prethermalization, but the exponential-lifetime claim is asserted, not proven, and the data/code are not yet public. the 3 major comments →

arxiv 2510.24059 v2 pith:NH3C5OAW submitted 2025-10-28 quant-ph

Fock space prethermalization and time-crystalline order on a quantum processor

Zehang Bao , Zitian Zhu , Yang-Ren Liu , Zixuan Song , Feitong Jin , Xuhao Zhu , Yu Gao , Chuanyu Zhang
show 26 more authors
Ning Wang Yiren Zou Ziqi Tan Aosai Zhang Zhengyi Cui Fanhao Shen Jiarun Zhong Yiyang He Han Wang Jia-Nan Yang Yanzhe Wang Jiayuan Shen Gongyu Liu Yihang Han Yaozu Wu Jinfeng Deng Hang Dong Pengfei Zhang Hekang Li Zhen Wang Chao Song Chen Cheng Rubem Mondaini Qiujiang Guo Biao Huang H. Wang
This is my paper
classification quant-ph
keywords Fock space prethermalizationtime crystaldiscrete time-crystalline orderdomain wall conservationFloquet drivingergodicity breakingsuperconducting qubitsquantum thermalization
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.

This paper tries to establish that periodically driven quantum many-body systems can be protected from heating by a mechanism that needs neither disorder nor very high driving frequency. The protection comes from strong Ising interactions, which make the number of domain walls—the boundaries between up and down spins—nearly conserved, splitting the huge space of spin configurations into many small, weakly connected islands. Because a wavefunction stays on its original island for a long time, the system fails to thermalize, and a simple periodic drive produces period-doubled (time-crystalline) oscillations that survive for at least 120 drive cycles on a 72-qubit superconducting processor. If correct, this gives a new, experimentally accessible route to stable non-equilibrium phases in interacting quantum devices.

Core claim

For a kicked Ising model with Ising coupling J comparable to the drive frequency, and with generic single- and two-qubit perturbations λ1, λ2 much weaker than J, the Floquet eigenstates carry an almost well-defined domain-wall number w. The Ising energy gap 2J|w−w'| suppresses hybridization between sectors of different w, and within a sector only spin flips that locally conserve w are allowed. As a result, the Fock-space network of many-body states becomes sparse: the wavefunction D(w,t) stays exponentially localized around its initial domain-wall sector even when the initial state sits at high energy density. Measurements on rings of up to 72 qubits show the wave packet remaining far from t

What carries the argument

The approximately conserved domain-wall number W(s)=Σ_j [s_j(1−s_{j+1})+(1−s_j)s_{j+1}], enforced by the large Ising energy gap 2J|w−w'| between sectors of different W. Each Floquet eigenstate acquires a nearly good quantum number w at weak perturbation; inside a fixed-w sector, only flips of spins whose two neighbors are antiparallel are allowed, so the dense Fock-space network decomposes into linearly many sparse subnetworks, delaying ergodicity even at high energy density.

Load-bearing premise

The entire scheme rests on the assumption that for weak perturbations the domain-wall number of each Floquet eigenstate is exponentially well conserved, so that the wavefunction remains localized on its initial sector for very long times; the paper evidences this only for 120 cycles and up to 72 qubits and supplies no rigorous bound on the leakage time in the thermodynamic limit.

What would settle it

Measure the late-time leakage out of the initial domain-wall sector, i.e., D(w,t) for w≠w0, over several hundred drive cycles on a 72-qubit processor or in a large-scale numerical simulation; if the leakage grows with system size or reaches the density-of-states value dos(w) on timescales short compared with an exponential in J/λ1, the claimed robust ergodicity breaking would collapse.

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

If this is right

  • Discrete time-crystalline order can be stabilized without quenched disorder or high-frequency driving, using interaction strengths comparable to the drive frequency.
  • The thermalization rate becomes spatially controllable: initializing different spin patterns produces inhomogeneous light cones, enabling local management of heating in many-body devices.
  • Fock-space wave-packet dynamics are demonstrated as a sharp probe of Floquet eigenstructure, useful for diagnosing prethermal and ergodicity-broken regimes.
  • The mechanism is compatible with additional structures, opening routes to other non-equilibrium phases (e.g., time quasicrystals) and to protected quantum information processing.
  • Finite-size scaling in the crossover near λ1≈0.4 suggests the phenomenon is not a finite-size artifact and survives to large systems.

Where Pith is reading between the lines

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

  • The exponential localization D(w,t)∼e^{−|w−w0|} hints at an emergent sector structure that could be captured by an effective rotor or hard-constraint model; one testable extension is to check whether dynamics inside a single w-sector are integrable or thermal.
  • Because the mechanism is disorder-free, it could be ported to platforms where disorder is hard to engineer, such as photonic or ultracold-gas simulators; a concrete test would compare the measured butterfly velocity with the analytical expression in Eq. (S18) across platforms.
  • The claim that domain-wall conservation 'persists for exponentially long time' (SI §2C) is asserted without a rigorous derivation, and the experimental and numerical support covers only 120 cycles up to L=72; whether the thermodynamic-limit leakage time is truly exponential remains open.
  • One could test the stability of FSP against coupling to an environment, following recent ideas that strong Fock-space bottlenecks protect fragmented Hilbert spaces against thermal avalanches.

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

3 major / 4 minor

Summary. The paper proposes 'Fock space prethermalization' (FSP) as a disorder-free mechanism for suppressing heating in a periodically driven Ising chain with interaction strength J comparable to the drive frequency. The central idea is that strong Ising interactions split the Fock-space graph into sectors labeled by approximate domain-wall (DW) number, with inter-sector hybridization suppressed by the Ising gap and intra-sector connectivity limited by local DW-conserving moves. The authors support this with exact-diagonalization eigenstructure, a perturbative butterfly-velocity formula, and an experiment on up to 72 superconducting qubits showing wave-packet localization in Fock space, subharmonic time-crystalline oscillations persisting for 120 drive cycles, site-resolved light-cone dynamics, and finite-size scaling across L = 24, 40, 56, 72 that identifies a crossover near λ1 ≈ 0.4. The manuscript argues that FSP is distinct from conventional high-frequency Floquet prethermalization, MBL, and quantum scars.

Significance. If the central claim holds, FSP is a potentially important addition to the known mechanisms of ergodicity breaking: it requires no disorder, operates at interaction strengths comparable to the drive frequency, and organizes the entire Fock-space network into sparse sectors rather than a few scarred states. The experimental work is substantial: 72-qubit programmable circuits, 120-cycle dynamics, careful context-aware gate calibration, noisy simulations that reproduce the data, and an analytic butterfly velocity that matches the measured light cone without fitting parameters. The paper also gives explicit credit to prior work on Fock-space dynamics and prethermal DTCs. The main risk is that several statements about 'exponentially long' conservation and thermodynamic-limit robustness go beyond what the finite-time, finite-size evidence establishes.

major comments (3)
  1. [SI §2C, first bullet and Figs. S9, S10] The manuscript asserts that the DW number in FSP 'persists for exponentially long time' and uses this to distinguish FSP from U(1) prethermal DTCs. No derivation is provided for this exponential timescale. The evidence shown is finite-time and finite-size: experimental data extend to 120 cycles, ED is limited to L ≤ 18, and Fig. S9c gives a DTC lifetime that grows linearly with L (t0 ≈ 2.9 + 4.3L), not exponentially. The exponential localization in Fig. S8a is a statement about a fixed L = 18 system, not about the thermodynamic-limit lifetime. This is load-bearing for the abstract's 'robust mechanism for breaking ergodicity' and for the claimed separation from ordinary prethermalization. Either provide a rigorous perturbative bound with explicit λ- and L-dependence, or soften the claims to 'long-lived' and avoid stating an exponential timescale.
  2. [Main text, 'Scaling of FSP-thermal crossover', Fig. 4c,e] The finite-size scaling collapses are computed over fixed time windows: t ∈ [2T,20T] for the Fourier amplitude Fw and t ∈ [10T,30T] for ⟨Δx⟩/√L. Given the measured vB ≈ 0.074 sites/cycle and the linear fit t0 ≈ 2.9 + 4.3L in Fig. S9c, the light cone has not crossed even the L = 24 ring until t ≈ 100T, and for L = 72 it requires t ≈ 300T. Thus all plotted data lie in the transient local light-cone regime, where data collapse can occur even if the asymptotic dynamics is ergodic. To support the claim of a size-independent crossover and thermodynamic-limit FSP, the authors should show that the collapses remain stable when the time window is extended past the light-cone traversal time for at least the smaller systems, or provide a scaling argument that separates a genuine prethermal plateau from an algebraic transient.
  3. [Main text, Abstract and Conclusions] The wording 'FSP is a robust mechanism for breaking ergodicity' and 'robustly suppressing heating' is stronger than the presented evidence. The 72-qubit experiment demonstrates a long-lived (120-cycle) non-thermal transient for specific initial states and perturbations, and the eigenstructure calculations demonstrate approximate DW sectors at small L. But without either a rigorous theorem or a scaling analysis that extends beyond the light-cone time, the manuscript has not established that the mechanism persists in the thermodynamic limit as true ergodicity breaking. I recommend rewording the central claim to describe a long-lived prethermal regime, or adding the missing theoretical support.
minor comments (4)
  1. [Author list and front matter] There are encoding artifacts in the author list: 'Y ang-Ren Liu' and 'Y u Gao' should be 'Yang-Ren Liu' and 'Yu Gao'. Please proofread the PDF generation.
  2. [Eq. (S18), SI §2B] The formula for vB(1) contains an explicit i inside an absolute value. Define the notation as the complex modulus and state that the result is real; otherwise the expression appears to be complex. Also state the units of vB (sites per Floquet cycle).
  3. [Fig. 2f and Fig. 4 captions] The captions state that 'across all figures in the text' error bars come from 10 random samples of φ2, but the main text also describes averaging over five globally shifted initial patterns. Please clarify in each caption which averaging is used for the plotted quantity.
  4. [SI §2D, Eq. (S37)] The derivation of Δx ∝ L for the subspace-thermalized case is clear, but the subsequent bullet in the main text says that in the FSP regime Δx/√L 'exceeds 0.5 in late times' yet the idealized prediction is Δx ∝ L. Please explain the role of noise-induced depolarization more explicitly at the point where this comparison is made, since the reader is left to reconcile the two scalings.

Circularity Check

0 steps flagged

No significant circularity: the central FSP claim is supported by independent numerical and experimental benchmarks; self-citations are context, not load-bearing.

full rationale

I find no step where a prediction reduces by construction to a fitted input or to a self-citation. The FSP mechanism is defined by the model (Eq. 1) with strong Ising coupling J=1, and the DW-sector eigenstructure is computed numerically (Fig. 1d; SI §2B Figs. S7–S8) and then independently probed in 72-qubit experiments via site-resolved correlators (Fig. 3) and Fock-space dynamics (Figs. 2, 4). The analytical butterfly velocity in Eq. S18 is parameter-free and is derived from the conjectured local DW-conservation process, then compared with measured light-cone speeds; it is not fitted to the data, so agreement is genuine evidence rather than circularity. The finite-size scaling collapse in Fig. 4 and the Porter-Thomas/thermal-distribution benchmarks in SI §2D are external checks. The main self-citations (Refs. [S3], [S6]) supply context about cat scars and domain-wall physics, but the relevant derivation and experimental verification appear in this paper itself, so the citations are not load-bearing. The claim in SI §2C that DW number 'persists for exponentially long time' is an extrapolation beyond the demonstrated 120 cycles and L≤72 data—a legitimate correctness/rigor concern, but not a circular reduction, since the claim is not used as an input to derive the same claim. Overall, the paper is self-contained against experimental and numerical benchmarks; the circularity score is therefore low.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central claim rests primarily on the approximate conservation of domain-wall number under strong Ising interactions, plus standard thermalization and noise-model assumptions. The model parameters (λ1, λ2, J, φ1, φ2) are chosen by hand, not fitted to the target DTC signal. No new physical entities are introduced.

free parameters (4)
  • λ1 (single-qubit perturbation strength) = 0.1 (FSP), 0.4 (critical), 1.2 (thermal); λ1/λ2 = 2
    Chosen by hand to place the system in FSP/critical/thermal regimes; the observed crossover is a function of this parameter, although the value 0.4 is first identified numerically and then confirmed experimentally.
  • λ2 (two-qubit perturbation in Ising term) = λ2 = λ1/2
    Fixed relative to λ1; introduces generic two-qubit terms that break integrability without echo fine-tuning.
  • J (Ising interaction strength) = J = 1
    Sets the energy scale equal to the drive frequency (T=1); the FSP-vs-Floquet-prethermal distinction depends on J ~ ω.
  • φ1, φ2 (longitudinal field Euler angles) = not fitted; 10 random samples in (0, 2π) averaged
    Chosen to break integrability and avoid single-qubit echoes; averaging over samples is a modeling/error-mitigation choice, not a fit.
axioms (4)
  • domain assumption For λ1, λ2 ≪ J, inter-DW-sector hoppings are suppressed by the Ising gap and the total domain-wall number is approximately conserved.
    Central premise of FSP; enters via Eq. (S8) and Fig. S7/S8. Supported by perturbation theory and numerics, not by a rigorous theorem.
  • domain assumption Fully thermalized wavefunctions have Porter-Thomas Fock-space amplitudes and Gaussian distributions in d and w (central limit theorem).
    Used in SI §2D to define thermal benchmarks (Eq. S32) and to interpret experimental wavepackets.
  • domain assumption The 72-qubit device implements the ideal Floquet unitary with errors well captured by independent depolarizing and readout models after context-aware calibration.
    Needed to attribute observed dynamics to unitary FSP; supported by device benchmarking and noisy simulation, but not independently verifiable from the preprint.
  • domain assumption MPS with χmax = 256 and linear 1/χ extrapolation accurately represent the exact dynamics for L up to 72 over the studied times.
    Basis for finite-size scaling; benchmarked at L=24 against exact statevector and extrapolation, but remains an approximation at larger L.

pith-pipeline@v1.3.0-alltime-deepseek · 42664 in / 18096 out tokens · 177540 ms · 2026-08-04T07:50:35.242107+00:00 · methodology

0 comments
read the original abstract

Periodically driven quantum many-body systems exhibit a wide variety of exotic nonequilibrium phenomena and provide a promising pathway for quantum applications. A fundamental challenge for stabilizing and harnessing these highly entangled states of matter is system heating by energy absorption from the drive. Here, we propose and demonstrate a disorder-free mechanism, dubbed Fock space prethermalization (FSP), to suppress heating. This mechanism divides the Fock-space network into linearly many sparse sub-networks, thereby prolonging the thermalization timescale even for initial states at high energy densities. Using 72 superconducting qubits, we observe an FSP-based time-crystalline order that persists over 120 cycles for generic initial Fock states. The underlying kinetic constraint of approximately conserved domain wall (DW) numbers is identified by measuring site-resolved correlators. Further, we perform finite-size scaling analysis for DW and Fock-space dynamics by varying system sizes, which reveals size-independent regimes for FSP-thermalization crossover and links the dynamical behaviors to the eigenstructure of the Floquet unitary. Our work establishes FSP as a robust mechanism for breaking ergodicity, and paves the way for exploring novel nonequilibrium quantum matter and its applications.

Figures

Figures reproduced from arXiv: 2510.24059 by Aosai Zhang, Biao Huang, Chao Song, Chen Cheng, Chuanyu Zhang, Fanhao Shen, Feitong Jin, Gongyu Liu, Hang Dong, Han Wang, Hekang Li, H. Wang, Jia-Nan Yang, Jiarun Zhong, Jiayuan Shen, Jinfeng Deng, Ning Wang, Pengfei Zhang, Qiujiang Guo, Rubem Mondaini, Xuhao Zhu, Yang-Ren Liu, Yanzhe Wang, Yaozu Wu, Yihang Han, Yiren Zou, Yiyang He, Yu Gao, Zehang Bao, Zhengyi Cui, Zhen Wang, Ziqi Tan, Zitian Zhu, Zixuan Song.

Figure 1
Figure 1. Figure 1: Schematic illustration of Fock space prethermalization (FSP). a-b, Fock space network in the thermal (a) and FSP (b) regimes. The thickness of lines denotes the relative hopping strength |Ts1,s2 | of different bonds in each case, which is obtained numerically for the Floquet unitary without the perfect π-pulse, i.e., e −iJ P j σ˜ z j (λ2) ˜σ z j+1 (λ2)Up(φ1, λ1, φ2). Bonds with strength weaker than 4% of t… view at source ↗
Figure 2
Figure 2. Figure 2: FSP-induced time-crystalline wave packet dynamics. a-d, Measured dynamics of radial probability distribution Π(d, nT) in FSP regime at λ1 = 2λ2 = 0.1 (a, b) and thermal regime at λ1 = 2λ2 = 1.2 (c, d). The initial state |s0⟩ is prepared to the “1FM” pattern. e, Illustration of initial Fock states investigated in this work. ↑, ↓ denote s j = 1 and 0, respectively. “1FM” and “2FM” patterns differ from an ove… view at source ↗
Figure 3
Figure 3. Figure 3: Site-resolved dynamics of equal-time correlators. a, Snapshots of the measured equal-time correlator Cjk(t) at λ1 = 0.1 for the “1FM” initial state, with the flipped qubit Q36 highlighted in red. b, Measured dynamics of Aj(t) for the “1FM” initial state. Black dashed lines represent analytical predictions for light-cone propagation speed. c, Measured snapshots of Cjk(t) at t = 30T for λ1 = 0.2, 0.3, 0.4, a… view at source ↗
Figure 4
Figure 4. Figure 4: Finite-size scaling of FSP-thermalization crossover. a, Measured DW probability distribution D(w, nT) in the Fock space prether￾mal (λ1 = 0.1), critical (λ1 = 0.4), and thermal (λ1 = 1.2) regimes. b, Measured dynamics of the normalized averaged DW number ⟨w⟩/L as a function of perturbation strength λ1. c, Maximum amplitude of the Fourier spectra of DW dynamics for system sizes L = 24, 40, 56, and 72. Fouri… view at source ↗

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Forward citations

Cited by 1 Pith paper

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

  1. Discrete time crystals enabled by Floquet strong Hilbert space fragmentation

    quant-ph 2025-12 unverdicted novelty 7.0

    Floquet strong Hilbert space fragmentation stabilizes discrete time crystals in a disorder-free kicked XXZ spin chain, with lifetime independent of frequency and exponential in system size.

Reference graph

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