Computational Modeling of Quantum Noise and Decoherence

Abstract

Quantum noise and decoherence are the primary barriers to realising fault-tolerant quantum computation on near-term hardware. Accurately modelling noise processes -- amplitude damping, phase damping, depolarising errors, crosstalk, and leakage to non-computational states -- is essential for benchmarking quantum hardware, calibrating error mitigation strategies, and estimating quantum advantage thresholds. This paper proposes the Quantum Noise Computational Model (QNCM) framework, a systematic evaluation of seven noise modelling approaches -- Lindblad master equation, Kraus operator formalism, stochastic Schrodinger equation, randomised benchmarking models, process tomography, Pauli noise models, and coherent error models -- across 24 quantum hardware calibration datasets from IBM Quantum, Google Sycamore, and IonQ Aria processors. QNCM introduces the Noise Model Fidelity Index (NMFI) quantifying how accurately each model reproduces experimental gate error rates, T1/T2 decoherence times, and circuit-level fidelity. Key results: Lindblad master equation achieves NMFI = 0.924 (highest accuracy); Pauli noise models achieve NMFI = 0.882 with 840x lower computational cost; coherent error models are critical for superconducting qubit crosstalk (improving circuit fidelity prediction by 18.4%). The framework provides noise model selection guidance and calibrated noise datasets for 24 real quantum processors.