Reproducibility of a Seeded Bell-State Measurement Simulator

Ideal seeded classical emulation. Not a QPU result.

This is an ideal seeded classical emulation of quantum measurement probabilities. FARPY does not currently provide a production quantum service. No physical QPU was used.

External QPU: NO
External quantum SDK: NO
Network execution: NO
Production quantum capability: NO

Implementation: Python standard-library seeded ideal measurement simulator

Seeded Bell Phi-plus measurement simulator.

Can a frozen, seeded local simulator reproduce the measurement records of a two-qubit Bell Phi-plus fixture while preserving the distinction between deterministic circuit definition and probabilistic measurement outcomes?

• Frozen fixture: BELL-PHI-PLUS-V1.
• 2 qubits.
• 20 seeded runs.
• 4,096 shots per run.
• 81,920 total simulated measurements.
• Every shot must be 00 or 11.
• Each run must satisfy chi-square < 10.827566 with df=1 and alpha=0.001.

20 of 20 runs passed.

Mean proportion of 00: 0.50186767578125
Population standard deviation: 0.008084806280203916

• The frozen circuit definition remained identical across the base run and replay.
• All 20 seeded run records and runs.csv reproduced byte-for-byte.
• All 81,920 simulated measurements were either 00 or 11.
• Every run passed the frozen chi-square balance gate.
• Circuit definition determinism and measurement randomness are separate properties.
• Reproducibility applies only to the frozen implementation, seeds, shot count, and runtime.

This is not physical quantum hardware evidence.

• Physical entanglement.
• Physical quantum hardware behavior.
• Quantum fidelity.
• Noise tolerance.
• Quantum advantage.
• External provider integration.
• Production quantum service readiness.

• The simulator implements only the frozen Bell Phi-plus fixture.
• The simulator is an ideal seeded classical emulation of quantum measurement probabilities.
• The chi-square gate checks gross balance failure, not physical quantum fidelity.
• No density matrix, noise channel, tomography, entanglement witness, or hardware calibration was evaluated.
• No physical QPU or external provider was used.
• No quantum advantage or production readiness is established.

Does FARPY currently provide a production quantum service?
No. This candidate documents local simulator research only.

Was physical quantum hardware used?
No. No external QPU or provider was used.

What was simulated?
A frozen two-qubit Bell Phi-plus circuit with H, controlled-X, and measurement operations.

What was reproduced?
The circuit file, runs.csv, and all 20 seeded run records reproduced byte-for-byte.

Does this prove physical entanglement?
No. Statistical balance from an ideal local simulator is not evidence of physical entanglement.

What is the main finding?
The frozen seeded simulator is reproducible, while individual measurement outcomes remain probabilistic.

Trace the record.

Circuit SHA-256: d9e4befcdb7f19f161248e7b0267858eca85a781f31a7435bbbfcf04788c9557

Farpy Research Station. "Reproducibility of a Seeded Bell-State Measurement Simulator." FQR-2026-001, 2026.