Periodically driven quantum systems face a bottleneck of many-body heating, which destabilizes discrete time crystals (DTC). This paper proposes a purely geometric connectivity design: by reconstructing the network topology with fixed-step hopping, the system strictly decomposes into disconnected periodic ring components when g = gcd(L, k) > 1. At zero boundary leakage (ε = 0), the system undergoes strict direct product decomposition, absolutely prohibiting cross-component energy exchange. Numerical simulations show that within a finite time window, subsystems exhibit a stable 2T sub-harmonic response (a quasi-steady DTC phase); introducing weak boundary coupling ε causes controlled cross-component heating. Quantitative lifetime analysis reveals that the DTC lifetime τ scales with leakage strength as τ ∝ ε⁻¹, which directly corresponds to the ε²t² perturbative growth law of the OTOC in our previous connectivity engineering framework. This scheme requires no random disorder, providing a deterministic principle for modular wiring in decoherence-resistant quantum devices.
Periodically driven quantum systems face a bottleneck of many-body heating, which destabilizes discrete time crystals (DTC). This paper proposes a purely geometric connectivity design: by reconstructing the network topology with fixed-step hopping, the system strictly decomposes into disconnected periodic ring components when g = gcd(L, k) > 1. At zero boundary leakage (ε = 0), the system undergoes strict direct product decomposition, absolutely prohibiting cross-component energy exchange. Numerical simulations show that within a finite time window, subsystems exhibit a stable 2T sub-harmonic response (a quasi-steady DTC phase); introducing weak boundary coupling ε causes controlled cross-component heating. Quantitative lifetime analysis reveals that the DTC lifetime τ scales with leakage strength as τ ∝ ε⁻¹, which directly corresponds to the ε²t² perturbative growth law of the OTOC in our previous connectivity engineering framework. This scheme requires no random disorder, providing a deterministic principle for modular wiring in decoherence-resistant quantum devices.
In ordinary nearest-neighbor connected networks, local perturbations usually spread globally. This paper proposes a purely geometric scheme: by reconstructing the topology with a fixed step length k, the system decomposes into g disconnected periodic ring components when g = gcd(L, k). When ε = 0 and operators are taken from different components, the cross-component out-of-time-order correlator (OTOC) is strictly zero, down to machine precision. At numerically accessible system sizes, the saturated entanglement entropy averaged over random product states within components grows approximately linearly and approaches the half-chain Page value upper bound. Introducing a very weak single-boundary coupling, the cross-component OTOC leakage is consistent with the ε² scaling law in a finite early-time window. This mechanism requires no complex quantum error correction or strong disorder, providing a testable deterministic wiring principle for crosstalk isolation in quantum chips.
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 many-body scars are a core mechanism of weak ergodicity breaking, but deterministically protecting and scaling these fragile coherent states remains a great challenge. We propose a purely geometric scheme based on connectivity engineering: by reconstructing the network topology with fixed-step hopping, the parent system is strictly decoupled into multiple equal-length independent sub-chains. We validate this mechanism in the PXP model featuring scar states. Numerical results demonstrate that within the decoupled network, the sub-chain interiors not only independently inherit the many-body scar properties of the parent (manifested as long-lived staggered magnetization oscillations and finite-size revivals of entanglement entropy), but also, due to the geometric blockades, the cross-channel quantum mutual information is strictly blocked at the machine precision limit. This mechanism requires no complex external fine-tuning, providing a minimal and deterministic blueprint for multi-channel quantum memory multiplexing in quantum chips.
Krylov complexity is a central metric for characterizing quantum chaos and operator scrambling. Here, we propose a purely geometric connectivity-engineering scheme: by reconstructing the spin chain topology with a fixed hopping step, the parent system is strictly decoupled into multiple independent sub-chains. Numerically, the complexity of local operators in the normal chain grows rapidly, whereas in the decoupled network, it is strictly bounded and undergoes periodic revivals at low dimensions. The rapid decay of Lanczos coefficients and the drop in Krylov entropy confirm that the geometric-induced direct sum decomposition of the Hilbert space causes the Lanczos generation chain to truncate sharply beyond a finite order (the "wall effect"). This mechanism, analogous to a topological firewall in holographic gravity, challenges the connectivity assumption of the Universal Operator Growth Hypothesis and provides a minimalist deterministic benchmark for chaos isolation and information shielding in multi-core quantum chips.
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 (DTCs) represent a nonequilibrium phase of matter characterized by spontaneousbreaking of discrete time-translational symmetry under periodic driving. While Floquet topological phases offer apromising route to stabilizing DTC behavior, their persistence in realistic open quantum systems remains an openproblem. In this work, we numerically investigate a periodically driven one-dimensional Ising chain locally coupledto a dissipative two-level system (TLS) defect, motivated by microscopic defects commonly observed in superconductingcircuit-QED devices. Using Lindblad master-equation simulations implemented in QuTiP, we show that weaklydissipative TLS defects can dynamically synchronize with the Floquet edge mode and inherit its subharmonic oscillations.As the defect coupling and dissipation strength increase, the system undergoes a crossover toward decoherence andFloquet thermalization, accompanied by the suppression of edge-localized period doubling. By combining quasienergyspectroscopy, boundary-condition analysis, rigidity diagnostics, and entropy evolution, we characterize the stabilitylimits of Floquet topological time-crystalline phases in realistic noisy quantum hardware.