Patchwork: automated lattice surgery and space-time partitioning for real-time decoding

Abstract

We introduce patchwork, a lattice-surgery compiler for arbitrary multi-qubit Pauli measurements on a prescribed narrow-corridor two-dimensional surface-code layout. Systematic geometric rules simplify stabilizer placement and gate scheduling, including for logical $Y$ measurements implemented using twist defects. We introduce measurement circuits and schedules that, together with protruding lobes of $Y$-extension patches, preserve the full effective code distance for all numerically tested code distances. To support parallel decoding, we develop a wavefront algorithm that partitions merged lattice-surgery patches into space-time commit, buffer, and cleanup regions. Simulations of three sequential multi-qubit Pauli measurements acting on ten logical qubits show that staged decoding achieves total failure probabilities close to those of monolithic decoding over the parameters tested. These methods provide an automated framework for fault-tolerant lattice surgery and a route toward scalable, real-time decoding.