Restoring Quantum Signal Fidelity Under Decoherence: Echo Pulse Optimization and Relevance to MRI, Brain Tumor Classification, and Neurodiagnostic Accuracy

Decoherence is the primary obstacle separating today's noisy quantum devices from fault-tolerant quantum computers. When a qubit loses coherence, the quantum information it carries degrades and cannot be recovered. In applications such as MRI signal processing or quantum-assisted brain tumor classification, this loss can translate into diagnostic error. This study uses quantum circuit simulation to evaluate four echo-based dynamical decoupling pulse sequences as software methods for reducing decoherence in single-qubit systems. All simulations were implemented in Python 3.10 using Qiskit and modeled quantum states with density matrices. Monte Carlo analysis was conducted across 100 trials of 1,024 shots per trial to capture realistic measurement noise. The qubit was initialized in superposition and subjected to three noise types: low-frequency phase noise (T₂), high-frequency phase noise, and combined noise (T₁ + T₂). These noise types correspond to the relaxation processes that govern MRI signal quality. The four strategies tested were: an unprotected baseline, Hahn Echo, Carr-Purcell-Meiboom-Gill (CPMG), and a Mixed-Sync method. Under low-frequency noise, Hahn Echo restored fidelity to 100.00% from a baseline of 57.90%. Under high-frequency noise, CPMG recovered fidelity to 97.62% from 2.45%. Under combined T₁ + T₂ noise, Mixed-Sync improved fidelity only to 65.34% from 60.95%, demonstrating that T₁ energy relaxation causes irreversible loss that pulse sequences cannot overcome. These results are analogous to the T₁-limited signal ceiling in MRI and illuminate fundamental constraints relevant to quantum-assisted neuroimaging.