# Hawking Inquiry: Executable Recovery Benchmark

Status: reference-architecture compilation and ideal verification. No hardware experiment, provider connection or black-hole simulation.

## Reproduce

Use Python 3.12 in a separate virtual environment:

```sh
python -m venv .venv
.venv/bin/pip install -r requirements.txt
.venv/bin/python build_benchmark.py
```

The script writes `results.json` and 12 OpenQASM 2 circuits in `circuits/`.
No API key, cloud account or paid quantum job is used. Circuit compilation uses Qiskit 2.6.2, a bidirectional line, a `{u3,cx}` basis, identity initial layout, basic routing and optimisation level 0. This is an abstract reference architecture, not a chosen QPU or the original paper's hardware reproduction.

The four arms are phase-corrected exchange, unconditional SWAP, the conditional Eq. (8) output-only channel at theta=pi and phi=0.6, and a global-access inverse-then-SWAP control. The last arm assumes access to all channel registers. The reference is q0, input q1 and logical output the last qubit. The measured classical bits are readout[0]=reference and readout[1]=output. After routing, measurement instructions carry the physical mapping.

The exchange candidate uses RXX(pi/2), RYY(pi/2) and a fixed S phase on the output. The QMM-labelled arm refers to the bounded ideal circuit audit of doi:10.1007/s11128-026-05292-0. It is not an audit of the authors' QASM or backend runs.

## What Is Verified

1. Logical full-operator equivalence after routing, accounting for layout, up to one global phase.
2. Every compiled two-qubit gate follows the line connectivity.
3. Physical-operator equivalence after standard OpenQASM export and re-import, up to one global phase.
4. Correlators obtained from the re-imported measured circuits agree with the ideal Bell-overlap predictions.

Unitary checks cover all input vectors through full matrix comparison; the measured predictions use the specified Bell input. The basis-rotation gates are included in each export's resources. The main arm's resource counts refer to Bell preparation plus the channel, excluding measurement-basis rotations and measurement.

## Prospective Decision Rule

Primary arm: exchange. Collect 4096 raw independent shots in each of XX, YY and ZZ. Compute Fhat=(1+XX-YY+ZZ)/4. For the one fixed primary claim, alpha=0.01 and a justified total additive witness-bias bound b<=0.02, require Fhat>0.562. SWAP must pass the same validation condition. Other arms are controls; additional discoveries require their own multiplicity plan.

The total planned measurement budget for four arms is 49,152 shots before calibration, diagnostic reruns or independent replication. No shots have been collected. A failure does not establish fundamental information loss.

The sufficient true-fidelity threshold for at least 99% success uses the rounded decision threshold plus one statistical radius and the assumed bias allowance. It is conditional on the raw-shot and calibration assumptions in the report, not a measured power estimate.

## Noise and Calibration Limits

The grid is a sufficient-bound calculation under a stochastic fault-event model. If n1 single-qubit operations and n2 CX operations each have bounded fault probabilities p1 and p2, a union bound gives F>=max(0,1-n1*p1-n2*p2) for the ideal-F=1 primary preparation/channel. These probabilities are not interchangeable with backend average gate infidelities. Coherent errors, idle noise and calibration drift need separate justified treatment. There is no device timing, cost or calibration claim.

A sufficient prospective calibration allocation is:

b_prep + (epsilon_XX+epsilon_YY+epsilon_ZZ)/4 + b_drift <= 0.02.

Here b_prep bounds trace distance from the intended reference input, each epsilon bounds the effective measured observable's operator-norm error and b_drift accounts for run-to-run changes. Establishing these requires suitable calibration data and confidence bounds. No allocation has been experimentally met. Mitigated quasi-probabilities require a new uncertainty analysis before using this raw-shot rule.

## Scope

This package specifies an operational quantum-information experiment. It does not provide a quantum-gravity Hamiltonian, a black-to-white transition, Hawking radiation, Planck-scale memory evidence or a resolution of the information paradox. Its ideal checks do not constitute independent expert review or hardware replication.

Prepared by u/NeuronsToNirvana with AI assistance, 6 November 2026.