We report on the first experimental observation of a non-equilibrium phase of matter, the discrete time crystal (DTC). A DTC breaks time-translational symmetry and displays spatio-temporal quantum order in all of its eigenstates, a feature dubbed “eigenstate order”. We implement Floquet dynamics on a 1D chain of 20 superconducting qubits [2]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing the non-equilibrium phase [3]. We carefully validate the phase structure of the DTC by probing the average response of all eigenstates belonging to the Floquet unitary. Using a suitable choice of order parameter, we further identify the location of the MBL-ergodicity crossover via experimentally observed finite-size effects. These results open a direct path to studying quantum phase transitions and critical phenomena on NISQ quantum processors.
We report on the first experimental observation of a non-equilibrium phase of matter, the discrete time crystal (DTC). A DTC breaks time-translational symmetry and displays spatio-temporal quantum order in all of its eigenstates, a feature dubbed “eigenstate order”. We implement Floquet dynamics on a 1D chain of 20 superconducting qubits [2]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing the non-equilibrium phase [3]. We carefully validate the phase structure of the DTC by probing the average response of all eigenstates belonging to the Floquet unitary. Using a suitable choice of order parameter, we further identify the location of the MBL-ergodicity crossover via experimentally observed finite-size effects. These results open a direct path to studying quantum phase transitions and critical phenomena on NISQ quantum processors.
Abstract Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9–15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.
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.
Floquet engineering, i.e. driving the system with periodic Hamiltonians, not only provides great flexibility in analog quantum simulation, but also supports phase structures of great richness. It has been proposed that Floquet systems can support a discrete time-translation symmetry (TTS) broken phase, dubbed the discrete time crystal (DTC). This proposal, as well as the exotic phase, has attracted tremendous interest among the community of quantum simulation. Here we report the observation of the DTC in an one-dimensional superconducting qubit chain. We experimentally realize long-time stroboscopic quantum dynamics of a periodically driven spin system consisting of 8 transmon qubits, and obtain a lifetime of the DTC order limited by the coherence time of the underlying physical platform. We also explore the crossover between the discrete TTS broken and unbroken phases via various physical signatures. Our work extends the usage of superconducting circuit systems in quantum simulation of many-body physics, and provides an experimental tool for investigating non-equilibrium dynamics and phase structures.
A discrete time crystal (DTC) is an out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Previous studies have been limited to a set of models with Ising-like couplings - and mostly only in one dimension - thus precluding our understanding of the existence (or not) of DTCs in models with more realistic interactions. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. We uncover a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, and identify the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.
Discrete Time Crystals (DTCs) are a non-equilibrium phase of matter that breaks the time-translation symmetry. This manifests as robust oscillations observed in driven Hamiltonians. Realizing DTCs on current Noisy Intermediate-Scale Quantum (NISQ) computers can be challenging due to the environmental noise, decoherence of qubits and computational errors. This thesis investigates the resilience and robustness of DTC and examines recent developments, and possible improvements of DTC stabilization using current quantum processors. Generally, an externally driven many-body system is expected to heat up to an infinite temperature state. This process, which is called thermalization, prevents the time-crystalline order. The two primary mechanisms that protect time-crystalline order are many-body localization (MBL) which has a strong disorder that prevents the thermalization, and Floquet prethermalization where its high frequency driving prevents the thermalization. These two processes allow us to realize and investigate the time crystals before a quantum system thermalizes.
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.