Hardness of Braided Quantum Circuit Optimization in the Surface Code

Large-scale quantum information processing requires the use of quantum error-correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates, as they can be implemented using only local interactions in a 2-D array of physical qubits. Procedures, such as defect braiding and lattice surgery, can […]

Quantum Approximate Optimization With Parallelizable Gates

The quantum approximate optimization algorithm (QAOA) has been introduced as a heuristic digital quantum computing scheme to find approximate solutions of combinatorial optimization problems. We present a scheme to parallelize this approach for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions. The protocol consists of single qubit operations […]

Decoding Quantum Error Correction Codes With Local Variation

In this article, we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local information is taken into account during the decoding process: the code distance associated with a given logical […]