Late Breaking Results: An Efficient Bridge-based Compression Algorithm for Topologically Quantum Error Corrected Circuits

Topological quantum error correction (TQEC) is a promising method for fault-tolerant quantum circuits. A TQEC circuit can be visualized as the defect movement along the time axis and modeled as a 3D space-time volume to estimate the required resource. A quantum algorithm must minimize the space-time volume for a feasible physical qubit number and computational time, especially for large-scale designs. Previous work presents quadratic-time simultaneous primal and dual bridge compression for a TQEC circuit, which is infeasible for large-scale problems. This paper presents an efficient divide-and-conquer approach to primal and dual bridge compression, which can support different code distances between qubits. Compared with the previous work, experimental results show that our algorithm is effective and efficient even for large-scale problems.