Error correction and entanglement dynamics in systems with programmable geometries

Summary: Quantum error correction (QEC) is a key ingredient towards realizing scalable quantum computation and is at the center of intense theoretical and experimental efforts. QEC hides information redundantly in a non-local way, thereby protecting it against the corrupting effects of noise. To date, the leading approach for QEC employs the surface code, which is experimentally attractive for its comparatively lenient error threshold and for its convenience of implementation in a two-dimensional lattice with local interactions. The surface code is simultaneously one of the best studied model of topological order, so we also have a deep physical understanding of the properties of this code, in particular how the underlying topological order endows robustness to the encoded information. The surface code encodes a single quantum bit’s worth of information into a block comprised of n physical qubits arranged in a √n x √n square grid. Its code distance, the size of the smallest error that can go undetected, grows with the block size as  d ~ √n, ensuring protection against noise. However, the number of logical qubits encoded, k, is independent of n, so this protection comes at the cost of a large qubit overhead. Developing new conceptual approaches to QEC, motivated by rapidly evolving and varied experimental capabilities, is therefore of utmost importance.