Title: Numerical Methods in Simulating Quantum Error Correction Code and Quantum Devices

Abstract: Quantum computing is a revolutionary way to do computation. It uses quantum mechanics to process information significantly faster than classical computers. Among various technologies, superconducting qubits stand out due to their scalability and rapid gate operations. Yet, significant obstacles remain on the path to fault-tolerant quantum computing, including scaling qubit counts, enhancing coherence times, achieving high-fidelity qubit readouts, and implementing quantum error correction (QEC). In this presentation, I will address several of these challenges using various numerical techniques, primarily focusing on quantum error correction. QEC detects and corrects errors occurring during computation, thus extending the qubit coherence time. Using the tensor network methods, I explore how the error correction toric code responds to external noise and elucidate its deep connection to topological order in mixed quantum states. I will also briefly discuss my other projects, such as the numerical studies of Josephson junction dynamics and the optimization of Josephson parametric amplifiers.