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[12/20]Geometric Confinement of Decoherence in Connectivity-Engineered Networks

Wenjun Luo

Published Oct 26, 2026• 0 citations
Publisher

Abstract

The core challenge in quantum computing lies in decoherence and thermalization caused by environmental noise. Within the framework of connectivity engineering, this paper proposes a protection scheme based on pure geometric decoupling mechanisms. By separately calculating the dynamical evolution of both closed and open systems, the numerical results show that: in a closed system, the local network (k=1) thermalizes rapidly, while the decoupled network (k=3) exhibits long-time quantum oscillations. Under Lindblad dissipation, the Loschmidt echo of the k=1 network decays rapidly; while under the parameter conditions of L=10 and γ=0.5, the fidelity of the k=3 network still revives to 0.41 at t=12.5. This mechanism originates from geometric truncation, which fragments the long chain into independent sub-chains, forming "geometric confinement" and "Quantum Fast-Shutter Protection". After further introducing static disorder impurities, the revival peak remains stable, indicating that the mechanism possesses strong robustness against both dynamical dissipation and static disorder. This result establishes a connectivity criterion for suppressing decoherence and provides a solid discrete physical benchmark for designing noise-resistant NISQ quantum memory hardware.

DOI
10.5281/zenodo.23657116

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The core challenge in quantum computing lies in decoherence and thermalization caused by environmental noise. Within the framework of connectivity engineering, this paper proposes a protection scheme based on pure geometric decoupling mechanisms. By separately calculating the dynamical evolution of both closed and open systems, the numerical results show that: in a closed system, the local network (k=1) thermalizes rapidly, while the decoupled network (k=3) exhibits long-time quantum oscillations. Under Lindblad dissipation, the Loschmidt echo of the k=1 network decays rapidly; while under the parameter conditions of L=10 and γ=0.5, the fidelity of the k=3 network still revives to 0.41 at t=12.5. This mechanism originates from geometric truncation, which fragments the long chain into independent sub-chains, forming "geometric confinement" and "Quantum Fast-Shutter Protection". After further introducing static disorder impurities, the revival peak remains stable, indicating that the mechanism possesses strong robustness against both dynamical dissipation and static disorder. This result establishes a connectivity criterion for suppressing decoherence and provides a solid discrete physical benchmark for designing noise-resistant NISQ quantum memory hardware.
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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.
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.
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Stable quantum memories that capable of storing quantum information for long time scales are an essential building block for an array of potential applications. The long memory time are usually achieved via dynamical decoupling technique involving decoupling of the memory states from its local environment. However, because this process is strongly limited by the errors in the pulses, an noise-protected scheme remains challenging in the field of quantum memories. Here we propose a scheme to design a noise-resisted [Formula: see text] pulse, which features high fidelity exceeding [Formula: see text] under realistic situations. Using this [Formula: see text] pulse we can generate different dynamical decoupling sequences that preserve high fidelity for long time scales. The versatility, robustness, and potential scalability of this method may allow for various applications in quantum memories technology.