Temporally encoded lattice surgery protocols for hybrid error detection and correction schemes

Abstract

Techniques for performing temporally encoded lattice surgery (TELS) protocols to reduce space-time costs of lattice surgery measurements are disclosed. A given quantum algorithm may be represented using Pauli-based computation, and associated multi-qubit Pauli operators may be encoded into codewords of a given classical error-correcting code. A hybrid error detection and correction scheme may then be applied during a given TELS protocol in which classical error syndromes corresponding to errors with weights up to a certain weight limit may be corrected while other classical error syndromes corresponding to errors with higher weights may cause given lattice surgery measurements to be remeasured. The weight limit for the hybrid scheme may be chosen based, at least in part, on a number of codewords used, a size of a parallelizable Pauli set used to represent the quantum algorithm, and a distance parameter of the chosen classical error-correcting code.