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.
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.
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.
The core of quantum error correction lies in how to isolate local errors to prevent them from contaminating the global system. Within the framework of connectivity engineering, this paper proposes a holographic quantum error correction mechanism based on pure geometric decoupling. Numerical results show that in a locally connected network (k=1), local errors rapidly diffuse globally through the increase of entanglement entropy; while in the decoupled network (k=3), long-range hopping constructs a graph-topological barrier, strictly locking the error within the isolated sub-chain where it was injected, and the mutual entanglement entropy between A and B remains strictly at its initial zero value. Since the physical hopping between subsystems is cut off, the injected error state cannot trigger global chaos, and the purity of boundary information remains stable. This mechanism does not rely on traditional redundant encoding, but rather utilizes the intrinsic graph-topological isolation property of geometric connectivity to achieve "physical-layer" fault tolerance. It provides a minimal discrete dynamical benchmark for understanding Bulk Locality in holographic duality and points the way for designing redundancy-free quantum memories.
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.
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 non-Hermitian open boundary systems, non-reciprocal hopping inevitably induces the non-Hermitian skin effect (NHSE). In this paper, we propose a purely geometric scheme to reconstruct this boundary accumulation pattern: by introducing a fixed step length k (where k < L), the system precisely decomposes into k independent sub-chains. Quantitative analysis shows that this geometric blockade strictly cuts off single-particle transport between sub-chains, and each sub-chain independently inherits the Hatano-Nelson type skin effect. Through boundary probability density and spatial distribution heatmaps, we demonstrate at the eigenstate ensemble level that the probability distribution is geometrically partitioned to the right ends of the k sub-chains. In the original coordinates, the probability peak is no longer dominated by a single lattice site but exhibits multi-site segmented accumulation. A single eigenstate only localizes in one of the sub-chains and does not distribute across the blockade. This isolation is strictly guaranteed by the block-diagonal structure of the Hamiltonian, independent of disorder or weak-coupling approximations. This mechanism provides a deterministic criterion for controlling geometric localization in non-Hermitian quantum networks.