A Bridge-Based Compression Algorithm for Topological Quantum Circuits

Topological quantum error correction (TQEC) is promising for scalable fault-tolerant quantum computation. The required resource of a TQEC circuit can be modeled as its space-time volume of a three-dimensional geometric description. Implementing a quantum algorithm with a reasonable physical qubit number and computation time is challenging for large-scale complex problems. Therefore, it is desirable to minimize the space-time volume for large-scale TQEC circuits. Previous work proposed bridge compression, which can significantly compress a TQEC circuit, but it was performed manually. This article presents the first automated tool that can perform bridge compression on a large-scale TQEC circuit. Our proposed algorithm applies the bridge compression technique to compactify TQEC circuits with modularization. Besides, we offer a time-ordering-aware 2.5-D placement for compacting TQEC circuits and satisfying time-ordered measurement constraints. On the other hand, we suggest friend net-aware routing to effectively reduce the required routing resource under topological deformation. Compared with the state-of-the-art work, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 84%.