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 $S=1$ Floquet model with short-range interactions that realizes a discrete $3T$ 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.
Observing a 3T 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=1 Floquet model with short-range interactions that realizes a discrete 3T 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.
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 discrete time crystals realized with qubits. This owes, in part, to the challenge of stabilizing eigenstate order in higher discrete symmetry (Zn) time crystals, due to the presence of richer domain wall physics. Here, we demonstrate the realization of a Z3 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 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.
The simulation of non-equilibrium quantum many-body systems on noisy intermediate-scale quantum (NISQ) processors represents a central challenge and opportunity in modern condensed matter physics. Periodically driven (Floquet) systems can host exotic phases of matter with no equilibrium counterpart, most notably discrete time crystals (DTCs) characterized by spontaneous breaking of discrete time-translation symmetry and robust subharmonic responses. However, the realization of DTCs faces fundamental obstacles: driven many-body systems generically absorb energy and thermalize to an infinite-temperature state, destroying time-crystalline order. Two primary mechanisms have been identified to stabilize DTCs—many-body localization (MBL) through strong disorder, and Floquet prethermalization wherein high-frequency driving suppresses heating over exponentially long timescales. This work investigates the digital quantum simulation of prethermal DTCs on current superconducting quantum processors, with a focus on understanding and mitigating the impact of hardware noise. Recent experiments on 133-qubit heavy-hexagonal devices have demonstrated the realization of clean two-dimensional DTCs and incommensurately modulated DTCs (IM-DTCs) using kicked Ising models, observing period-doubling oscillations persisting for up to 100 Floquet cycles . Crucially, these simulations reveal that quantum noise, often perceived as detrimental, can in certain regimes stabilize novel prethermal DTC phases—a phenomenon identified as noise-induced DTCs supported by symmetry charge pumping or random gate fluctuations . The heavy-hexagonal lattice geometry, compared to square lattices, exhibits significantly slower quantum scrambling, thereby extending the prethermal plateau and enhancing DTC stability. We address two key challenges limiting the scalability of DTC simulations: limited qubit connectivity and environmental noise. By leveraging the universality of native gate sets, we demonstrate how to implement effective couplings among physically disconnected qubits at the cost of increased circuit depth, enabling the study of interaction-range effects on DTC stabilization—a phenomenon previously unobserved experimentally . Furthermore, we benchmark the performance of error mitigation protocols based on depolarising noise models, achieving excellent agreement between error-mitigated hardware data and tensor-network simulations in regimes where classical computations remain tractable . Our results highlight the complementary roles of quantum hardware and classical simulation: quantum processors provide access to regimes where entanglement growth outpaces tensor-network methods, while careful validation against classical benchmarks ensures the reliability of quantum outcomes. This study establishes a concrete pathway for using NISQ devices as experimental platforms for synthesizing and probing novel non-equilibrium quantum phases, advancing both our fundamental understanding of Floquet many-body dynamics and the practical capabilities of quantum simulation. The identification of noise as an active ingredient in phase stabilization suggests new directions for quantum engineering of spatiotemporal orders on near-term hardware.
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 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.
Abstract Discrete time crystals (DTCs) are 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 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 (4 T -DTCs). Remarkably, by utilizing a variational algorithm, we are able to observe clear signatures of such 4 T -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.
Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.