2025,
Urmia university of Technology, Iran,
Quantum fidelity serves as a fundamental measure of accuracy in the transfer. storage. and processing of quantum information. However. in realistic physical systems. perfect state transfer is hindered by the unavoidable interaction between a quantum system and its environment. leading to decoherence and dissipation. This thesis investigates the impact of decoherence on quantum fidelity within the framework of open quantum systems. emphasizing both theoretical modeling and computational approaches based on the Lindblad master equation and quantum-channel formalism.
The study begins by revisiting the postulates of quantum mechanics and the essential mathematical structures underlying qubit evolution. entanglement. and measurement. Two dominant decoherence mechanisms - energy relaxation and pure dephasing - are analyzed in detail. and their effects on the density matrix of a qubit are derived. The corresponding quantum channels - amplitude damping and dephasing - are formulated in the operator-sum representation. allowing a unified description of fidelity degradation processes. Furthermore. the combined amplitude-and-phase damping channel is developed as a comprehensive model encompassing both mechanisms.
To address the computational intractability of simulating multi-qubit open systems. the research employs Pauli and Clifford Twirl Approximations (PTA and CTA). which map complex noise channels into efficiently simulable Pauli-type channels without loss of physical validity. These twirling techniques enable the application of the Gottesman&ndashKnill theorem. Thus, allowing the simulation of error dynamics and the design of compatible quantum error-correcting codes (QECCs). The analysis extends to memoryless and correlated (Markovian) quantum channels. where temporal correlations between successive qubit errors are modeled through a correlation parameter &mu. providing insights into memory effects in realistic quantum media.
The results reveal that decoherence acts as the principal limitation to achieving high quantum fidelity. The rate of fidelity decay is governed by measurable physical quantities - relaxation time (T₁) and dephasing time (T₂) - which define the coherence lifetime of qubits. Twirling approximations were shown to preserve the essential statistical properties of decoherence while ensuring classical simulability. thereby bridging theoretical modeling with practical error correction.
Overall. this work deepens the understanding of decoherence phenomena and their quantitative influence on quantum fidelity. It offers a rigorous theoretical framework and computational strategy for mitigating fidelity loss in realistic quantum networks. memories. and computational architectures - contributing to the broader goal of developing scalable and noise-resilient quantum technologies.