Efficient Correlation Surface Search for Fault-Tolerant Quantum Computing

Surface codes are a leading candidate for quantum error correction in realizing fault-tolerant quantum computing (FTQC). Compiling a logical circuit to a surface code-encoded physical circuit is an involved, multi-step process. A less well-known step among them is the task of identifying correlation surfaces, which are stabilizers across spacetime in the computation. Correlation surfaces are a fundamental construct in FTQC, as they reveal the relationship between logical observables and physical measurements. In this work, we motivate the need to compute correlation surfaces efficiently by using the lattice-surgery-based surface code as an example, and propose the first effective algorithm for this task. Numerical experiments across diverse application circuits show that our algorithm is thousands of times faster than existing solutions and can process circuits of practical size at runtime. Our implementation is open-source and integrated into the FTQC design automation package, TQEC.