Surface code quantum error correction incorporating accurate error propagation

Abstract

The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is obtained by repeat- edly measuring each syndrome qubit after appropriate interaction with its four nearest neighbor data qubits. Changes in the measurement value indicate the presence of chains of errors in space and time. The standard method of determining operations likely to return the code to its error-free state is to use the minimum weight matching algorithm to connect pairs of measurement changes with chains of corrections such that the min- imum tota..