Ph.D. Defense - Kaavya Sahay

Title: Non-local Surface Code Computation Abstract: Quantum error correction (QEC) is necessary to protect fragile quantum states during computation. The surface code is a widely studied QEC encoding that exhibits high thresholds and supports practical logical gates while maintaining 2D-local connectivity. Recently, there have been significant advances in non-local quantum architectures, including neutral atoms and trapped ions. These developments call into question the prioritization of locality while designing strategies for error correction. Crucially, there are substantial inefficiencies in both qubit count and time overhead when restricting surface code computation to local architectures. In this dissertation, we investigate the improvements possible in key surface code operations when non-local connectivity is available. We develop strategies for bias-preserving fusion-based constructions, efficient decoding of transversal gates, and low-overhead magic state preparation. In addition to providing a blueprint for realizing surface code computation in non-local platforms, our results quantify the improvement one may extract from a QEC system when, all other properties being known, non-locality is introduced.