A quantum circuit interpretation of evaporating black hole geometry
Ying Zhao
TL;DR
The paper presents a quantum-circuit interpretation of evaporating black hole geometry, tying the appearance and growth of the island to a sequence of transitions from two-sided to one-sided interiors driven by circuit uncomplexity. It employs a MERA-like tensor-network view and subregion uncomplexity to relate the evolution of the RT surface to how gates are allocated and scrambled between the radiation and the remaining black hole, with key quantities such as $S$, $S_{BH}$, $t_*$, and $t_{Page}$ organizing the dynamics. The analysis draws a parallel with perturbed thermofield double dynamics to show how interior information re-emerges in the radiation via repeated two-sided-to-one-sided transitions, providing a circuit-level bridge between bulk geometry and information transfer. This framework offers a concrete mechanism for interior accessibility and information recovery in evaporation, connecting holographic geometry with quantum information concepts in a tangible, stepwise manner.
Abstract
We give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes.