Modeling the performance of the surface code with non-uniform error distribution: Part 1

At large code distances and for high-quality qubits, the estimation of the logical error rates of quantum codes by direct Monte-Carlo simulation is prohibitively expensive. We describe a simple bound for error rates in surface code memory experiments. This bound is used to derive an estimator for the error rate that is both sensitive to the geometric placement of error-prone qubits, and can be approximated numerically at polynomial cost in code distance at low error rates. Practical implementation and numerical benchmarking of this estimator is the subject of the following talk.