Abstract This work develops a theoretical framework for scalable noise resilience in coupled-oscillator quantum processors by integrating non-local Lechner–Hauke–Zoller (LHZ) interactions with non-extensive Tsallis statistics. The study focuses on a system of three strongly coupled harmonic oscillators (TSCHO), each interacting with a bosonic bath, and truncating each oscillator to its two lowest energy levels, obtaining an effective eight-dimensional Hilbert space. The Hamiltonian is diagonalized, yielding eigenstates that include dark states, and squeezed parity-mixed states. Thermal non-equilibrium conditions are then introduced using Tsallis statistics, constructing a generalized initial density matrix parameterized by the entropic index q . The dissipative dynamics is described by a Lindblad master equation derived under the Born–Markov approximation, with bath-induced decay rates that incorporate a q -deformed Bose–Einstein distribution. The concurrence is computed for two and three-oscillator subsystems and compared as a function of time and temperature. Next, the LHZ architecture is incorporated by adding genuine three-body non-local interactions, and the corresponding dissipative coefficients are derived. The time evolution of entanglement and fidelity is simulated within the LHZ-protected subspace. Finally, a CNOT gate is applied to one of the subsystems which exhibits significant concurrence and its fidelity is evaluated across different q regimes and temperatures. The results demonstrate that scaling from two to three oscillators spontaneously generates asymmetric dissipation channels that protect specific subsystems. A counter-intuitive temperature assisted stabilization effect is validated: for q ≠ 1 , higher bath temperatures do not destroy entanglement but rather preserve it. In the LHZ architecture for TSCHO quantitative analysis shows that at low frequencies and elevated temperatures, the non-extensive regimes outperform the extensive one; however, at high frequencies, thermal effects are suppressed and the q = 1 regime remains dominant. The dissipatively protected CNOT gate achieves meaningful fidelity without the massive qubit overhead of conventional quantum error correction. While the numerical analysis is performed for three oscillators, the proposed framework is theoretically scalable to larger systems, and the underlying mechanisms—non-local parity protection and non-extensive thermodynamics—are general. Overall, this approach suggests a potential paradigm shift from fighting decoherence to engineering intrinsic noise resilience at the hardware level, establishing non-locality and non-extensive thermodynamics as physical resources for robust quantum information processing.
Abstract This work develops a theoretical framework for scalable noise resilience in coupled-oscillator quantum processors by integrating non-local Lechner–Hauke–Zoller (LHZ) interactions with non-extensive Tsallis statistics. The study focuses on a system of three strongly coupled harmonic oscillators (TSCHO), each interacting with a bosonic bath, and truncating each oscillator to its two lowest energy levels, obtaining an effective eight-dimensional Hilbert space. The Hamiltonian is diagonalized, yielding eigenstates that include dark states, and squeezed parity-mixed states. Thermal non-equilibrium conditions are then introduced using Tsallis statistics, constructing a generalized initial density matrix parameterized by the entropic index q . The dissipative dynamics is described by a Lindblad master equation derived under the Born–Markov approximation, with bath-induced decay rates that incorporate a q -deformed Bose–Einstein distribution. The concurrence is computed for two and three-oscillator subsystems and compared as a function of time and temperature. Next, the LHZ architecture is incorporated by adding genuine three-body non-local interactions, and the corresponding dissipative coefficients are derived. The time evolution of entanglement and fidelity is simulated within the LHZ-protected subspace. Finally, a CNOT gate is applied to one of the subsystems which exhibits significant concurrence and its fidelity is evaluated across different q regimes and temperatures. The results demonstrate that scaling from two to three oscillators spontaneously generates asymmetric dissipation channels that protect specific subsystems. A counter-intuitive temperature assisted stabilization effect is validated: for q ≠ 1 , higher bath temperatures do not destroy entanglement but rather preserve it. In the LHZ architecture for TSCHO quantitative analysis shows that at low frequencies and elevated temperatures, the non-extensive regimes outperform the extensive one; however, at high frequencies, thermal effects are suppressed and the q = 1 regime remains dominant. The dissipatively protected CNOT gate achieves meaningful fidelity without the massive qubit overhead of conventional quantum error correction. While the numerical analysis is performed for three oscillators, the proposed framework is theoretically scalable to larger systems, and the underlying mechanisms—non-local parity protection and non-extensive thermodynamics—are general. Overall, this approach suggests a potential paradigm shift from fighting decoherence to engineering intrinsic noise resilience at the hardware level, establishing non-locality and non-extensive thermodynamics as physical resources for robust quantum information processing.
Quantum entanglement is a cornerstone of quantum technologies, but its susceptibility to environmental noise hinders practical implementations. This study investigates the entanglement dynamics in a two-qubit system governed by a transverse-field Ising Hamiltonian and exposed to local amplitude decoherence via the Lindblad master equation. Beginning with a maximally entangled Bell state, we numerically integrate the density matrix evolution using QuTiP. Entanglement, measured by concurrence, displays oscillatory decay influenced by the coupling J, transverse field B, and decoherence rate γ. Analytical benchmarks, including the unitary limit C(t) ≈ |cos(2Bt)| and non-interacting limit C(t) =ⅇ−2γt, corroborate the simulations. Scans across J/γ reveal that for |J|/γ > 1, entanglement lifetime (time until C < 0.5) can extend by factors of 2–10 relative to weak coupling cases, attributed to interaction-induced level splitting that mitigates damping. Bloch vectors exhibit spiraling contraction in the x-z plane toward the excited state pole, while von Neumann entropy rises in tandem with disentanglement, underscoring decoherence-driven mixing. Local observables such as 〈σ_z〉 oscillate amid relaxation to near-zero equilibrium. At finite temperature (T = 10 mK, n_th = 0.01), lifetime shortens by ~10–20% due to thermal excitations. Anchored in parameters from IBM Eagle and Google Sycamore processors, these results elucidate interaction's protective role against decoherence, offering design guidelines for resilient superconducting qubits in quantum computing and sensing. This work resolves prior inconsistencies in interaction-damping interplay and proposes testable conjectures for entanglement plateaus at specific J/γ ratios.
We analyze quantum state preservation in open quantum systems using quantum error-correcting (QEC) codes explicitly embedded in microscopic system-bath models. Rather than assuming abstract quantum channels, we consider multi-qubit registers coupled to bosonic thermal environments, derive a second-order master equation for the reduced dynamics, and use it to benchmark the five-qubit, Steane, and toric codes under local and collective noise. We compute state fidelities as functions of system-bath coupling strength, bath temperatures, and the number of correction cycles. In the low-temperature regime, repeated error correction with the five-qubit code significantly suppresses decoherence and relaxation for weak-to-moderate couplings. In the high-temperature regime, thermal excitations reduce the effectiveness of all codes, although within the parameter range studied, the five-qubit code still yields the highest fidelities among the three codes. For two-qubit Werner states, we identify a critical evolution time associated with an early-time crossover, before which the overhead of QEC does not compensate for the noise-induced degradation; this critical time increases with entanglement, reflecting the greater fragility of strongly entangled states. Overall, our results provide a microscopic master-equation-based framework for benchmarking QEC performance in realistic open-system environments and for assessing code behavior in near-term noisy quantum architectures.
We investigate the dynamical evolution of quantum discord, entanglement and purity in an open quantum system of two coupled asymmetric harmonic oscillators interacting with a thermal environment. Using the Kossakowski-Lindblad master equation we analyze the time evolution starting with a squeezed vacuum state. In contrast to our previous study on entanglement evolution in asymmetric oscillators, the present work introduces XY-type position-position coupling together with a systematic joint analysis of quantum discord and purity alongside entanglement. We examine the combined effects of the squeezing parameter, asymmetry parameter, coupling constant, dissipation rate and temperature. We find that quantum discord and entanglement exhibit, in general, a non-monotonic decrease over time. Increasing temperature consistently accelerates the degradation of both quantum correlations and purity, whereas increasing dissipation accelerates the degradation of quantum correlations but leads to higher steady-state purity. Increasing the squeezing parameter provides a protective effect by enhancing initial correlations and prolonging entanglement survival time, while increasing the coupling constant leads to higher quantum correlations. The asymmetry parameter exhibits only a weak influence on the correlation evolution. Our analysis reveals that quantum discord demonstrates stronger resilience than entanglement, which can present more complex behaviour including entanglement sudden death and possible temporary revivals and re-suppressions. These findings provide valuable insights for developing robust quantum information protocols and strategies for preserving quantum correlations in realistic open quantum systems, with potential extensions to non-Markovian regimes and multi-mode architectures.
A meaningful description of the low-energy dynamics of multipartite entanglement is provided\nfor harmonic oscillator systems in general dissipative scenarios. Without doing any\ncentral approximation, this mainly relies on a set of reasonable physical statements on the\nenvironment and system-environment interaction consistent with a linear analysis of the\nopen-system dynamics.\nWe rst investigate the inseparability properties of arbitrary entangled states, which\ngenerally entails an optimization procedure of certain functional de ned in the in nitedimensional\nHilbert space of continuous-variable systems. Using a Gaussian-like assumption\nanalogous to that used in the derivation of Gaussian entanglement of formation, we\nderive a computational-e cient form of such functional which considerable simpli es the\noptimization task. This consists on a hierarchy of separability criteria that permit in a\nuni ed way to characterize k-partite entanglement of broad classes of Gaussian and non-\nGaussian states. The strength of the criteria is proven by showing that they satisfactorily\nreproduce previous results from the theory of entanglement, like PPT criterion applied to\narbitrary two-mode and pure three-mode Gaussian states.\nThe separability criteria allow to monitor the transient evolution of multipartite entanglement\nunder the environmental in\nuence, this permitted to show that non-Gaussian\nentanglement may be as robust against harmful dissipative e ects and thermal noise as\nGaussian one. We devote special attention to the stationary properties of tripartite entanglement\nwhen the system oscillators are in contact with either a common environment\nor independent environments at initial di erent temperatures. For the former dissipative\nscheme, it is shown that the environment mediates an e ective many-party interaction with\na spatial long-range feature between system oscillators, which is able to generate tripartite\nentanglement whereas two-mode entanglement is degraded. Regarding the second scheme,\nit is illustrated that thermal non-equilibrium conditions result in a rich variety of quantum\ncorrelations, however a temperature gradient eventually destroys the entanglement shared\nby the system oscillators as a consequence of the growth of thermal noise. Finally, the\nstationary entanglement and energy current across a nite harmonic chain are studied in\ndetail by doing an extensive numerical analysis of both phenomena for a broad range of the\nparameters (i.e., temperatures, oscillator frequencies, and oscillator coupling strengths).\nOur numerical ndings are discussed in terms of the derived energy current expressions,\nthese show an explicit dependence on the two-time correlation functions (between oscillator\noperators) which carry quantum correlations.
Decoherence stands as the fundamental bottleneck limiting the physical realization of large-scale fault-tolerant quantum computation. Conventional paradigms rely on passive strategies of environmental isolation and post-hoc quantum error correction, inherently bounded by Markovian approximation, weak-coupling assumptions and prohibitive physical qubit overhead. Breaking away from the dissipative preset of traditional open quantum systems, this work establishes a global system-environment closed dynamical framework with rigorous coherence conservation. Without Markovian coarse-graining or thermal bath approximation \cite{1,5}, we derive the exact non-Markovian reduced dynamic equation and present the necessary and sufficient coupling conditions for strictly conserved quantum coherence. We rigorously prove that decoherence is not an intrinsic fundamental law of quantum mechanics, but an emergent consequence of specific interaction structures and artificial approximation constraints. By constructing structured system-environment coupling Hamiltonians, coherent decay can be frozen at the dynamical root, achieving intrinsic decoherence suppression without error correction, topological quasiparticles or magic state distillation. Numerical simulations verify that coherence remains strictly constant under strong environmental coupling for the proposed coupling scheme, in sharp contrast to conventional decaying dynamics. This work reconstructs the underlying paradigm of open quantum systems, eliminates the decoherence bottleneck at the fundamental level, and provides a novel theoretical route toward large-scale, low-overhead, universal fault-tolerant quantum computation.
Quantum many-body devices suffer from imperfections that destabilize dynamics and limit scalability. We show that the dynamical growth of entanglement can intrinsically protect generic quantum dynamics against coherent and perturbative noise. Through rigorous theoretical analysis of general quantum dynamics and numerical simulations of spin chains and fermionic lattices, we prove that entanglement-entropy growth confines the influence of local Hamiltonian perturbations, thereby suppressing errors in dynamical errors. The degree of protection correlates quantitatively with the entanglement entropy of subsystems on which the perturbations act, and applies broadly to both analog quantum simulators and real-time control protocols. This entanglement-induced resilience is conceptually distinct from quantum error correction or dynamical decoupling: it passively leverages native many-body correlations without additional qubits, measurements, or control overhead. Our results reveal a generic mechanism linking entanglement growth to dynamical stability and provide practical guidelines for designing noise-resilient quantum devices.