Quantum memories are essential components in applications ranging from quantum computing to quantum communication networks. However, their practical utility is constrained by short coherence times, motivating the search for new physical systems that can inherently protect stored information. Discrete time crystals (DTCs)—periodically driven many-body systems exhibiting stable subharmonic oscillations that break discrete time-translation symmetry—offer a promising approach, as they are theoretically able to shield encoded information from local perturbations, making them compelling candidates for nextgeneration, passively protected quantum memories. In this work, we employ a tensor-network framework that models a quantum memory as a DTC. We employ the timeevolving block-decimation (TEBD) algorithm to perform both real- and imaginary-time evolution of a matrix-product-state (MPS) representation, thereby efficiently capturing the large many-body Hilbert space while tracking entanglement growth, sub-harmonic spectral responses, and memory-fidelity metrics over experimentally relevant timescales. By sweeping the drive strength, interaction range, and disorder, we map the phase diagram, pinpoint regimes that sustain time-crystalline order, and set the stage to model their coherence lifetimes.
Quantum memories are essential components in applications ranging from quantum computing to quantum communication networks. However, their practical utility is constrained by short coherence times, motivating the search for new physical systems that can inherently protect stored information. Discrete time crystals (DTCs)—periodically driven many-body systems exhibiting stable subharmonic oscillations that break discrete time-translation symmetry—offer a promising approach, as they are theoretically able to shield encoded information from local perturbations, making them compelling candidates for nextgeneration, passively protected quantum memories. In this work, we employ a tensor-network framework that models a quantum memory as a DTC. We employ the timeevolving block-decimation (TEBD) algorithm to perform both real- and imaginary-time evolution of a matrix-product-state (MPS) representation, thereby efficiently capturing the large many-body Hilbert space while tracking entanglement growth, sub-harmonic spectral responses, and memory-fidelity metrics over experimentally relevant timescales. By sweeping the drive strength, interaction range, and disorder, we map the phase diagram, pinpoint regimes that sustain time-crystalline order, and set the stage to model their coherence lifetimes.
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.
Discrete-Time Crystals (DTC) are a non-equilibrium phase of matter characterized by the breaking of time-translation symmetry in periodically driven quantum systems. In this work, we present a detailed thermodynamic analysis of a DTC in a one-dimensional spin-1/2 chain coupled to a thermal bath. We derive a master equation from the microscopic model, and we explore key thermodynamic quantities, such as work, heat, and entropy production. Our results reveal that the DTC signature inevitably decays in the presence of environmental noise, but we show that a periodic measurement scheme can mitigate the effects of decoherence, stabilizing the subharmonic oscillations of the DTC for extended periods. These findings provide insights into the robustness of time-crystalline phases and potential strategies for protecting them in experimental settings.
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.
Abstract Periodically driven (Floquet) many-body systems tend to absorb energy and approach an infinite-temperature state, yet can host emergent order such as discrete time crystals (DTCs). Here we realise a clean two-dimensional DTC and an incommensurately modulated DTC (IM-DTC) on the IBM Quantum Heron processor, a 133-qubit superconducting device with heavy-hexagonal connectivity, implementing a kicked Ising model and tracking magnetisation dynamics for up to 100 Floquet cycles. We observe robust period-doubling oscillations that persist over the accessible time window and are stable against perturbations of the transverse field, without invoking disorder-induced many-body localisation or high-frequency Floquet prethermalisation. Introducing a longitudinal field generates additional long-period amplitude modulations with frequencies incommensurate with the drive, realising an IM-DTC response. Comparison with state-vector and tensor-network simulations benchmarks the hardware and reveals regimes where entanglement growth makes classical simulation challenging, underscoring the utility of gate-based quantum processors for out-of-equilibrium dynamics in two dimensions.
We analyze the quantum dynamics of periodically driven, disordered systems in the presence of long-range interactions. Focusing on the stability of discrete time crystalline (DTC) order in such systems, we use a perturbative procedure to evaluate its lifetime. For 3D systems with dipolar interactions, we show that the corresponding decay is parametrically slow, implying that robust, long-lived DTC order can be obtained. We further predict a sharp crossover from the stable DTC regime into a regime where DTC order is lost, reminiscent of a phase transition. These results are in good agreement with the recent experiments utilizing a dense, dipolar spin ensemble in diamond [Nature (London) 543, 221 (2017)NATUAS0028-083610.1038/nature21426]. They demonstrate the existence of a novel, critical DTC regime that is stabilized not by many-body localization but rather by slow, critical dynamics. Our analysis shows that the DTC response can be used as a sensitive probe of nonequilibrium quantum matter.
Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are, however, only limited to realizing DTCs with period-doubling and period-tripling observable dynamics, forming only a very small subset of DTC phases. Creating larger periodic DTCs in the laboratory remains a longstanding challenge, yet it is necessary for developing the technological applications of DTCs, e.g., as a quantum memory for highly entangled qubits, or exploring interesting features beyond subharmonic dynamics, e.g., condensed matter phenomena in the time domain. By highlighting the connection between DTCs and quantum error correction, we devise a general and realistic scheme for building DTCs exhibiting any large-period observable dynamics, which are observable even at sufficiently small system sizes. Our proposal uses an array of spin-1/2 chains to simulate a repetition code at the hardware level, which has essential properties to realize robust observable dynamics. It is readily implemented with existing superconducting or trapped-ion quantum processors, making new families of DTCs experimentally accessible in the immediate future.