Surface code quantum error correction incorporating accurate error propagation

The surface code is a powerful quantum error correcting code that can be defined on a2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and dataqubits form a checkerboard pattern. Information about errors is obtained by repeat-edly measuring each syndrome qubit after appropriate interaction with its four nearestneighbor data qubits. Changes in the measurement value indicate the presence of chainsof errors in space and time. The standard method of determining operations likely toreturn the code to its error-free state is to use the minimum weight matching algorithmto connect pairs of measurement changes with chains of corrections such that the min-imum total number of corrections is used. Prior work has not taken into account thepropagation of errors in space and time by the two-qubit interactions. We show thattaking this into account leads to a quadratic improvement of the logical error rate.