A Bridge-based Compression Algorithm for Topological Quantum Circuits

The topological quantum error correction (TQEC) scheme is promising for scalable and reliable quantum computing. A TQEC circuit can be modeled by a three-dimensional diagram, and the implementation resource of a TQEC circuit is abstracted to its space-time volume. Implementing a quantum algorithm with a reasonable physical qubit number and reasonable computation time is challenging for large-scale practical problems. Therefore, minimizing the space-time volume of a TQEC circuit becomes a crucial issue. Previous work shows that bridge compression can greatly compress TQEC circuits, but it was performed only manually. It is desirable to develop automated compression techniques for TQEC circuits to achieve low-overhead, large-scale quantum computations. In this paper, we present the first work that can automatically perform bridge compression on TQEC circuits. Compared with the state-of-the-art method, experimental results show that our proposed algorithm can averagely reduce space-time volumes by 83%.