Pre-Registered Finite-Size Predictions for Page-Curve Experiments on Near-Term Quantum Hardware

Abstract

The Page curve, the rise and fall of radiation entropy during unitary evaporation, is now measurable on quantum simulators: trapped-ion and superconducting platforms routinely prepare scrambled states of 10–50 qubits and estimate subsystem Rényi entropies by randomized measurements. Semiclassical gravity, including the quantum-extremal-surface and replica-wormhole machinery that derives the Page curve, is constructed in the G → 0 limit and makes no prediction at finite qubit number. We state a set of exact finite-N laws for a concrete evaporation protocol — the location and determinism of the fine-grained transition, its first-order (whole-island) character, a quantized entanglement barrier with a per-qubit mechanism identity, the barrier's monotone response to scrambling depth, and a one-particle "mode books" formula that predicts the transition time under partial (graybody) emission — together with the complete experimental design: register sizes, gate budgets (~84–348 two-qubit gates at 12–24 qubits), a one-line noise mitigation certified to 3× typical hardware error rates, a measurement plan in which no register larger than max(t, N_I − t + 1) qubits is ever measured, and a total shot budget of order 10⁵. Every prediction is stated with the condition that falsifies it. All numbers were fixed before any experiment; the reproduction package included with this deposit reproduces every claim, including the exact hardware-numbers table, in under a minute.