Spacetime Sentinels Game Shows Pauli Checks Boost Fidelity Only Above Depth-18 Break-Even in Qiskit Simulations

{"The open-source game lets players allocate ancilla qubits to qiskit-paulice-generated Pauli checks while injecting a fixed quota of T gates into noisy circuits. Every configuration is scored exactly via Qiskit Aer density-matrix simulation against a stabilizer reference and validated against 50,000-shot SamplerV2 runs under two noise models. Exhaustive enumeration of 5,412 legal moves across five random payloads isolates three non-obvious trade-offs between check overhead, magic placement, and post-selection survival.","Checks become net-positive only past a depth threshold: at depth 6 they reduce R, whereas at depth 18 the best four-check configuration improves R by 1.103. Each added check shrinks the safe T-gate locations from 90 to roughly 14, forcing the optimal check count to decline as the magic quota rises. Critically, a T gate that anticommutes with a check degrades fidelity below the unprotected baseline (0.158 versus 0.628), showing that broken checks are actively harmful.","Context from prior low-overhead detection literature (e.g., the 2023-2025 works on flag-based and spacetime checks) indicates the game quantifies a previously qualitative tension between magic-state injection and check commutation. The browser and terminal implementations lower the barrier for experimental teams to prototype check schedules before hardware deployment. Future extensions could incorporate real-device calibration data and larger code distances.","Next steps include integrating the scoring engine into Qiskit’s error-mitigation module and testing whether learned check-placement policies transfer to 100+ qubit devices within the next year."}