A bridge-based algorithm for simultaneous primal and dual defects compression on topologically quantum-error-corrected circuits

Topological quantum error correction (TQEC) using the surface code is among the most promising techniques for fault-tolerant quantum circuits. The required resource of a TQEC circuit can be modeled as a space-time volume of a three-dimensional diagram by describing the defect movement along the time axis. For large-scale complex problems, it is crucial to minimize the space-time volume for a quantum algorithm with a reasonable physical qubit number and computation time. Previous work proposed an automated tool to perform bridge compression on a large-scale TQEC circuit. However, the existing automated bridging compression is only for dual defects and not for primal defects. This paper presents an algorithm to perform bridge compression on primal and dual defects simultaneously. In addition, the automatic compression algorithm performs initialization/measurement simplification and flipping to improve the compression. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 47%.