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arXiv:2605.14293

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, Ermal Rrapaj, David I. Santiago, Wibe de Jong, Norman Y. Yao, Joel E. Moore, Irfan Siddiqi

quant-phSubmitted May 14, 2026• Announced May 15, 2026• 0 citations
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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.

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Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple $π$-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.

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Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic $P$ -donor impurities in isotopically enriched $^{28}Si$ cooled below $10$ K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.

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Wei-Guo Ma, Heng Fan, Shi-Xin Zhang

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A Robust Large-Period Discrete Time Crystal and its Signature in a Digital Quantum Computer

Tianqi Chen, Shen, Ruizhe, Ching Hua Lee +2 more

Discrete time crystals (DTCs) are novel out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by period-doubling dynamics due to its natural occurrence in a system of periodically driven two-level, e.g., spin-1/2, particles. The realization of DTCs beyond period-doubling, including their generalizations termed discrete quasicrystals has also been made in recent years, though such experiments typically involve higher spin particles. Constructing and observing DTCs beyond period-doubling in systems of two-level particles are generally still considered an open challenge due to the latter's $\mathbb{Z}_2$ symmetry that natively only leads to period-doubling. In this work, we developed an intuitive interacting system of two-level particles (qubits) that supports the more non-trivial period-quadrupling DTCs ($4T$-DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such $4T$-DTCs in a quantum processor despite the presence of considerable noise and the small number of available qubits. Our findings extend the landscape of time crystalline behavior by demonstrating a distinct realization of time crystallinity beyond standard period-doubling dynamics with qubits (two-level particles) on a NISQ-era digital quantum computer, as well as the potential of existing noisy intermediate-scale quantum devices for simulating exotic non-equilibrium quantum states of matter.

arXiv:2309.11560•Sep 20, 2023•1 citation
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 Z2\mathbb{Z}_2Z2​ discrete time crystals realized with qubits. This owes, in part, to the challenge of stabilizing eigenstate order in higher discrete symmetry (Zn\mathbb{Z}_nZn​) time crystals, due to the presence of richer domain wall physics. Here, we demonstrate the realization of a Z3\mathbb{Z}_3Z3​ 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 Z3\mathbb{Z}_3Z3​ 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.
Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple πππ-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.
Observing a 3T3T3T discrete time crystal on a trapped-ion qudit quantum processor
Time crystals have been observed in various qubit-based quantum platforms. However, the realization of time-crystal behavior beyond period doubling has remained fairly unexplored, in part because established qubit architectures natively encode two-cycle dynamics. Qudits offer a natural route beyond this restriction. Here we propose a one-dimensional, disorder-free S=1S=1S=1 Floquet model with short-range interactions that realizes a discrete 3T3T3T time crystal and implement it on a trapped-ion qudit quantum processor. We observe period tripling dynamics in local observables and spin correlations, confirming the collective subharmonic response of the system in the experiment. The stabilization mechanism is analyzed by deriving the effective Floquet Hamiltonian and performing numerical simulations that demonstrate the existence of a prethermal phase over a wide range of parameters. We compute the phase diagram and verify the presence of multipartite entanglement through the Quantum Fisher Information, showing that this quantity gets enhanced at the crossover between ergodic and localized regimes in non-equilibrium.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic PPP -donor impurities in isotopically enriched 28Si^{28}Si28Si cooled below 101010 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.
We introduce a qudit-native framework for engineering rich and robust discrete time crystals (DTCs) by leveraging their internal multilevel structure. Unlike in qubit systems, qudit-based DTCs exhibit distinct dynamical mechanisms that arise only in multilevel systems, as supported by a dressed normal-form analysis in the heating-suppression regime. These mechanisms are manifested in representative systems: we show that subspace-selective embedded kicks stabilize higher-order subharmonic responses and suppress thermalization, as demonstrated in spin-1 chains; in spin-3/2 systems, extending embedded kicks to more levels enables different level partitions and reveals that DTC robustness is dictated by the symmetry of the partition; and in spin-2 platforms, we realize concurrent 2T and 3T DTCs under a unified drive. These findings establish a systematic, hardware-efficient methodology for designing stable and multifunctional Floquet phases of matter on modern qudit-based quantum processors.
Discrete time crystals (DTCs) are novel out-of-equilibrium quantum states of matter which break time translational symmetry. DTCs have been extensively realized in experiments, particularly their subclass that is characterized by period-doubling dynamics due to its natural occurrence in a system of periodically driven two-level, e.g., spin-1/2, particles. The realization of DTCs beyond period-doubling, including their generalizations termed discrete quasicrystals has also been made in recent years, though such experiments typically involve higher spin particles. Constructing and observing DTCs beyond period-doubling in systems of two-level particles are generally still considered an open challenge due to the latter's Z2\mathbb{Z}_2Z2​ symmetry that natively only leads to period-doubling. In this work, we developed an intuitive interacting system of two-level particles (qubits) that supports the more non-trivial period-quadrupling DTCs (4T4T4T-DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such 4T4T4T-DTCs in a quantum processor despite the presence of considerable noise and the small number of available qubits. Our findings extend the landscape of time crystalline behavior by demonstrating a distinct realization of time crystallinity beyond standard period-doubling dynamics with qubits (two-level particles) on a NISQ-era digital quantum computer, as well as the potential of existing noisy intermediate-scale quantum devices for simulating exotic non-equilibrium quantum states of matter.