Design and Evaluation of Quantum Error Correction Protocols for Fault Tolerance, Coherent Noise, and Applications

Abstract

Quantum error correction (QEC) is widely regarded as a central requirement for realizing the full potential of quantum computing. The inherent noise of quantum hardware presents a major obstacle, and fault-tolerant QEC protocols introduce substantial overhead in both qubit count and circuit depth. In this thesis, we design and evaluate the efficiency of several QEC protocols under different noise models and application settings. Under stochastic circuit-level Pauli noise, we develop a distance-preserving fault-tolerant protocol with a lightweight ancillary structure, using only two ancilla qubits for the concatenated Steane code, and evaluate its performance. We further introduce an adaptive measurement protocol that significantly reduces the number of required syndrome extraction rounds. In the presence of coherent noise, we make progress toward establishing a constant lower bound for the surface code threshold by studying families of compass codes. These codes admit analytical characterization of their logical channels under coherent noise, and we complement this analysis with numerical studies of randomly generated code families. To facilitate the design and evaluation of quantum error-correcting codes, we combine the tensor-network framework of quantum LEGO with the hyperoptimized tensor contraction library Cotengra. This approach enables a substantial speedup in the computation of quantities derived from the weight enumerator polynomial of stabilizer codes. Finally, we investigate trade-offs in quantum error correction protocols designed to exploit local symmetries arising in lattice gauge theory simulations.