A QuTiP-Based Framework forSimulating Noisy Grover Search withQuantum Error Correction

Sammanfattning

This work develops and tests a simulation framework based on Python and the Quantum Toolbox in Python (QuTiP), a library used to build quantum states, operators, and open-system time evolutions. The objective is to simulate noisy quantum circuits with Lindblad dynamics, a master-equation description in which coherent gate evolution and dissipative noise from the environment are treated to- gether. Grover’s search algorithm is used as a reference circuit. It is not used here to optimize the search algorithm itself, but to study how far a realistic numerical description can be pushed when finite-duration gates, local noise models, auxiliary work qubits called ancillas, encoded states, and recovery procedures are included. The first part of the work constructs a realistic unencoded noisy Grover model. In this model, the oracle, which marks the desired solutions, and the diffuser, which amplifies their probability, are decomposed into elementary gates, and noise acts during the execution of each gate. Three noise mechanisms are compared: dephasing, which destroys phase coherence; amplitude damping, which models relaxation from |1〉 to |0〉, and depolarizing noise, which represents a more symmetric loss of quantum information. Quantum Error Correction (QEC) is then studied as a way to protect logical information by encoding one logical qubit into several physical qubits. The QEC models are analyzed through a hierarchy of benchmarks designed to add realism progressively while keeping the simulations computationally feasible. These bench- marks include ideal recovery, recovery with an explicit time cost, semi-realistic oracle or diffuser dynamics, and the combined semi-realistic case. The results show that QEC can improve the marked-state probability in specific intermediate noise regimes, but that this benefit is strongly limited by recovery time, encoding cost, and the semi-realistic treatment of the Grover blocks. The phase-flip code gives the clearest improvement for dephasing noise, while amplitude-damping codes show more constrained gains, especially when success probability or larger encoded spaces are taken into account. Finally, the QuTiP solvers mesolve and mcsolve are compared. The first directly evolves the density matrix, while the sec- ond uses Monte Carlo wave-function trajectories. The trajectory approach reduces memory pressure but introduces statistical convergence costs. Overall, the project identifies both the physical regimes where QEC is informative and the numerical limits of realistic Python/QuTiP simulations.