Inspired by the ER=EPR conjecture in holographic physics, we construct a minimal and exactly solvable geometrically decoupled spin network benchmark within the framework of connectivity engineering. The system consists of two geometrically decoupled subsystems (Universes A and B) connected by a throat C. By constructing a directed boundary using complex hopping phases to introduce a synthetic gauge field, we measure the effective light-cone information propagation speed to be approximately 0.51; this propagation speed can be tuned by the geometric topology of the throat, satisfying the bandwidth scaling relation where v_arrive is proportional to W_C. Furthermore, we numerically extract an empirical dual bound where I_max times v_arrive is less than or equal to K, revealing a fundamental trade-off limit between entanglement generation capacity and information propagation speed. This work abandons gravitational metric degrees of freedom while retaining the core geometric-topological structures of holographic duality, providing a tunable and deterministic discrete numerical benchmark for holographic information transport.
Inspired by the ER=EPR conjecture in holographic physics, we construct a minimal and exactly solvable geometrically decoupled spin network benchmark within the framework of connectivity engineering. The system consists of two geometrically decoupled subsystems (Universes A and B) connected by a throat C. By constructing a directed boundary using complex hopping phases to introduce a synthetic gauge field, we measure the effective light-cone information propagation speed to be approximately 0.51; this propagation speed can be tuned by the geometric topology of the throat, satisfying the bandwidth scaling relation where v_arrive is proportional to W_C. Furthermore, we numerically extract an empirical dual bound where I_max times v_arrive is less than or equal to K, revealing a fundamental trade-off limit between entanglement generation capacity and information propagation speed. This work abandons gravitational metric degrees of freedom while retaining the core geometric-topological structures of holographic duality, providing a tunable and deterministic discrete numerical benchmark for holographic information transport.
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.
Holographic duality suggests that continuous spacetime geometry can emerge from underlying quantum entanglement. Based on the connectivity engineering framework, we construct a purely geometric decoupled lattice model to explore the entanglement area law and the emergence mechanism of discrete Ryu-Takayanagi (RT)-type scaling. By tuning the nearest-neighbor coupling λ, the system evolves from a disconnected direct sum decomposition (λ=0) to a globally connected phase. Precise numerical results indicate that weak nearest-neighbor coupling can stitch the rigid fault lines in the information distance matrix, inducing the formation of a smooth and continuous effective geometry. The core result is that in the stitched connected phase, the subsystem entanglement entropy is dominated by the geometric boundary, satisfying a scaling relation primarily governed by a linear area law with logarithmic corrections. Through a hold-out test on irregular subregions, the RT-type scaling calibrated by square samples provides a controlled error estimate for rectangular subregions. The L-shaped concave subregion exhibits a systematic negative deviation, corresponding to the well-known corner correction effect in free-fermion systems, further distinguishing perimeter scaling from minimal-surface scaling. Combined with Kitaev-Preskill diagnostic analysis, the results support that the discrete RT-type scaling can emerge from a purely geometric discrete network. This model provides a clean, exactly solvable underlying benchmark for studying discrete spacetime geometry and holographic entanglement on quantum simulators.
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 core of the black hole information paradox lies in whether Hawking radiation leads to information loss. Based on connectivity engineering, we construct a minimal, gravity-free spin network. By calculating the mutual information and fidelity across different bipartition sizes, we reproduce the complete Page curve. Numerical results show that the peak of mutual information in the geometrically decoupled network (k=3) exhibits a non-trivial scaling behavior with the connectivity k, and reaches saturation at k=3 (with a peak approximately 1.49 times that of the normal network). This not only reveals the reshaping of entanglement capacity by geometric topology but also establishes a topological upper bound for the Page curve peak. Fidelity analysis further reveals that in the late stages of evaporation, the residual subsystem tends towards purification, with the target state fidelity significantly rising to approximately 0.52, which is weakly sensitive to k. This indicates that information is not completely thermalized but exists in a highly compressed global correlation form within the entanglement structure of the black hole residue and external radiation. This model provides a deterministic and strictly reproducible discrete physical benchmark for studying black hole information dynamics.
In this paper, we discover the topological quantization and phase transition mechanisms of holographic extremal surfaces in discrete tensor networks, providing a rigorous discrete dynamical benchmark for the proposition that "gravity is entanglement". Using a one-dimensional spin network with a fixed truncated hopping step k, we derive a rigorous analytical solution for the peak position of entanglement entropy, demonstrating that it is solely determined by the underlying connectivity step k. The perturbative phase diagram further reveals that this quantized gravity ladder is strongly protected by the topological gap below a critical perturbation V_c, exhibiting unique critical scaling behavior at the transition point. The fitted critical exponent beta approx 0.07 is significantly lower than the mean-field exponent of conventional phase transitions, revealing a unique "critical rigidity" characteristic of finite-size long-range topological networks. This model not only provides a rigorous graph-theoretical benchmark for a discrete analogue of the Ryu-Takayanagi area law but also, through the "geometric decoupling" mechanism, constructs an analytically solvable microscopic dynamical sandbox for the highly debated entanglement wedge disconnection in the black hole island formula.
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.