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arxiv: 2605.14293 · v1 · submitted 2026-05-14 · 🪐 quant-ph

Recognition: 2 theorem links

· Lean Theorem

A Qutrit Time Crystal Stabilized with Native Chiral Interactions

Noah Goss , Nishchay Suri , Brian Marinelli , Larry Chen , Akel Hashim , Sajant Anand , Alexis Morvan , Ravi K. Naik
show 6 more authors
Ermal Rrapaj David I. Santiago Wibe de Jong Norman Y. Yao Joel E. Moore Irfan Siddiqi
Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:37 UTC · model grok-4.3

classification 🪐 quant-ph
keywords discrete time crystalqutritchiral clock modelFloquet dynamicssuperconducting processorperiod triplingnon-equilibrium phases
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The pith

A chain of 15 superconducting qutrits realizes robust Z3 time-crystalline order via chiral interactions.

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

The paper demonstrates that a periodically driven chain of qutrits with disordered nearest-neighbor chiral interactions can spontaneously break Z3 time-translation symmetry, producing subharmonic period tripling. This order persists across a wide range of drive strengths and does not depend on the initial state. The tunable chiral angle controls domain-wall dynamics and spectral properties, enabling the eigenstate order that is harder to stabilize in conventional settings. A sympathetic reader would care because it shows how qudit hardware can access higher-symmetry non-equilibrium phases beyond the usual qubit-based period doubling. The work highlights that chirality is essential, as removing it leads to initial-state-dependent dynamics dominated by domain walls.

Core claim

We implement a Floquet chiral clock model on 15 superconducting qutrits and observe robust subharmonic period tripling that is independent of initial state and persists over a wide range of drive strengths. The chiral angle governs domain wall dynamics and stabilizes the time-crystalline order. In the absence of chirality, the dynamics show marked initial state dependence due to domain wall degeneracies.

What carries the argument

The Floquet chiral clock model with tunable chiral angle, which controls domain-wall dynamics and spectral degeneracies to stabilize Z3 time-crystalline order.

Load-bearing premise

The subharmonic response is due to spontaneous breaking of Z3 time-translation symmetry in eigenstates rather than from hardware imperfections or transient domain wall motion.

What would settle it

If the period-tripling signal decays rapidly with increasing chain length or shows strong initial-state dependence even when the chiral angle is present, the claim of stable eigenstate order would fail.

Figures

Figures reproduced from arXiv: 2605.14293 by Akel Hashim, Alexis Morvan, Brian Marinelli, David I. Santiago, Ermal Rrapaj, Irfan Siddiqi, Joel E. Moore, Larry Chen, Nishchay Suri, Noah Goss, Norman Y. Yao, Ravi K. Naik, Sajant Anand, Wibe de Jong.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: We engineer disorder by choosing flux pulse pa￾rameters that randomly select spin-spin couplings with Jj ∈ [0.08, 0.25] and θj mod π/3 ∈ [0.125, 0.9]. We demonstrate a continuous tuning of our system from a thermal phase to the Z3-DTC phase In Fig. 2a, for a random initial trit-string state, we display the full chain spin-1 magnetization M = |0⟩⟨0|−|2⟩⟨2| response (which, unlike the clock Z, is hermitian a… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: a, we show the results for a tunable coupler flux calibration experiment, where we sweep the coupler flux to find a point with minimal α22 cross-Kerr. As the majority of our qutrits are not straddling, we do not generally find an α22 = 0 cancellation point, but notably, as demonstrated in Fig. 12b, we can achieve an average α22 nulling of 24.7 KHz averaged across all 30 qutrit-qutrit coupled pairs on our … view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18 [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19 [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. (a) Spectrum and definition of quasienergy gaps. (b) The average spectral gap between adjacent quasienergies ∆ [PITH_FULL_IMAGE:figures/full_fig_p025_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21 [PITH_FULL_IMAGE:figures/full_fig_p026_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22 [PITH_FULL_IMAGE:figures/full_fig_p027_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23 [PITH_FULL_IMAGE:figures/full_fig_p028_23.png] view at source ↗
read the original abstract

Periodically driven quantum many-body systems can spontaneously break discrete time-translation symmetry, realizing discrete time crystals. To date, both experimental and theoretical efforts have largely focused on the simplest case of spontaneous period-doubling in $\mathbb{Z}_2$ discrete time crystals realized with qubits. This owes, in part, to the challenge of stabilizing eigenstate order in higher discrete symmetry ($\mathbb{Z}_n$) time crystals, due to the presence of richer domain wall physics. Here, we demonstrate the realization of a $\mathbb{Z}_3$ discrete time crystal by implementing a Floquet chiral clock model in a chain of 15 superconducting qutrits. Unlike the conventional Ising setting, our system features a tunable chiral angle that governs domain-wall dynamics, spectral degeneracies, and crucially, the stability of time-crystalline order. Using disordered nearest-neighbor chiral interactions, we observe robust subharmonic period tripling that persists across a wide range of drive strengths and is independent of initial state. Finally, we highlight the special role that chirality plays in our $\mathbb{Z}_3$ discrete time crystal -- in its absence, the system's Floquet dynamics exhibit a marked initial state dependence governed by domain wall degeneracies. Our results establish native qudit hardware as a powerful platform to access a broader landscape of non-equilibrium phases.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental realization of a Z3 discrete time crystal in a chain of 15 superconducting qutrits using a Floquet chiral clock model with disordered nearest-neighbor chiral interactions. The central claim is the observation of robust subharmonic period tripling that persists across a wide range of drive strengths, is independent of initial state, and is stabilized by the tunable chiral angle; the non-chiral case instead shows marked initial-state dependence due to domain-wall degeneracies.

Significance. If the distinction between true Z3 eigenstate order and finite-size transients holds, the result is significant as the first experimental Z3 time crystal in native qudit hardware. It demonstrates how chirality can suppress domain-wall effects to stabilize higher-order discrete time-translation symmetry breaking, extending the DTC paradigm beyond Z2 systems and highlighting qudits as a platform for richer Floquet phases.

major comments (2)
  1. [Results on initial-state independence and drive-strength scans] The central claim of initial-state-independent Z3 eigenstate order (abstract and results section) rests on subharmonic Fourier peaks in a finite 15-qutrit chain. Without explicit long-time scaling of the order-parameter Fourier component or direct comparison of Floquet spectral degeneracies across initial states, the data cannot yet distinguish spontaneous symmetry breaking from long-lived prethermal transients or chiral-angle-tuned domain-wall suppression.
  2. [Drive-strength dependence and order-parameter analysis] The robustness across drive strengths is asserted, but the manuscript does not report quantitative bounds on the prethermal lifetime or explicit finite-size scaling of the subharmonic response (e.g., peak height vs. chain length or evolution time). This leaves open whether the observed tripling survives in the thermodynamic limit or is an artifact of the accessible timescales.
minor comments (2)
  1. [Figures 2-4] Figure captions should explicitly state the number of experimental repetitions and error-bar definitions for the subharmonic Fourier amplitudes.
  2. [Model and implementation section] The definition of the chiral angle and its mapping to the hardware pulse parameters could be clarified with an explicit equation in the methods.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We address the major comments point by point below, clarifying our claims and making revisions to strengthen the presentation of our results on the Z3 discrete time crystal.

read point-by-point responses

  1. Referee: [Results on initial-state independence and drive-strength scans] The central claim of initial-state-independent Z3 eigenstate order (abstract and results section) rests on subharmonic Fourier peaks in a finite 15-qutrit chain. Without explicit long-time scaling of the order-parameter Fourier component or direct comparison of Floquet spectral degeneracies across initial states, the data cannot yet distinguish spontaneous symmetry breaking from long-lived prethermal transients or chiral-angle-tuned domain-wall suppression.

    Authors: We acknowledge that our experimental data is on a finite chain and that long-time scaling is challenging. However, we demonstrate initial-state independence through explicit comparisons in the results section, showing consistent subharmonic peaks regardless of preparation. To address the referee's concern, we have added a new figure panel showing the time-dependent order parameter decay for different initial states and a discussion of how the chiral angle suppresses domain wall effects, as evidenced by the absence of degeneracies in our effective Floquet Hamiltonian analysis. We believe this supports the eigenstate order claim, though we agree that thermodynamic limit confirmation would require further theoretical work. revision: partial

  2. Referee: [Drive-strength dependence and order-parameter analysis] The robustness across drive strengths is asserted, but the manuscript does not report quantitative bounds on the prethermal lifetime or explicit finite-size scaling of the subharmonic response (e.g., peak height vs. chain length or evolution time). This leaves open whether the observed tripling survives in the thermodynamic limit or is an artifact of the accessible timescales.

    Authors: We have revised the manuscript to include quantitative analysis of the subharmonic peak height as a function of drive strength and evolution time, providing bounds on the lifetime within our experimental window. Explicit finite-size scaling with varying chain lengths is not feasible in the current setup due to hardware constraints, but we discuss the expected behavior based on our theoretical model. We have added text clarifying that while the results are robust for N=15, extrapolation to the thermodynamic limit remains an open question for future studies. revision: yes

standing simulated objections not resolved
  • Explicit finite-size scaling to the thermodynamic limit beyond the 15-qutrit chain
  • Direct long-time scaling of the order parameter to distinguish prethermal transients from eigenstate order

Circularity Check

0 steps flagged

No circularity: experimental demonstration with direct hardware measurements

full rationale

The paper is an experimental realization of a Z3 discrete time crystal in a 15-qutrit superconducting chain using a Floquet chiral clock model. All central claims (robust subharmonic period tripling independent of initial state, contrast with non-chiral case) rest on direct time-domain and Fourier measurements of the order parameter, not on any derivation, ansatz, or fitted parameter that is then relabeled as a prediction. No equations are presented that reduce by construction to their own inputs, and no load-bearing self-citation chain is invoked to establish the result. The work is self-contained against external benchmarks via hardware data.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the implemented Hamiltonian matches the theoretical Floquet chiral clock model and that the observed subharmonic response indicates true eigenstate order rather than transient or disorder-driven effects.

free parameters (2)
  • chiral angle
    Tunable parameter that governs domain-wall dynamics and spectral degeneracies; its value is set by hardware calibration.
  • drive strength range
    Experimental parameter scanned to demonstrate robustness; not derived from first principles.
axioms (1)
  • domain assumption The Floquet chiral clock model accurately captures the dynamics of the 15-qutrit superconducting chain under periodic driving.
    Invoked to interpret the subharmonic response as Z3 time-crystalline order.

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