QuCT: A Framework for Analyzing Quantum Circuit by Extracting Contextual and Topological Features

In the current Noisy Intermediate-Scale Quantum era, quantum circuit analysis is an essential technique for designing high-performance quantum programs. Current analysis methods exhibit either accuracy limitations or high computational complexity for obtaining precise results. To reduce this tradeoff, we propose QuCT, a unified framework for extracting, analyzing, and optimizing quantum circuits. The main innovation of QuCT is to vectorize each gate with each element, quantitatively describing the degree of the interaction with neighboring gates. Extending from the vectorization model, we propose two representative downstream models for fidelity prediction and unitary decomposition. The fidelity prediction model performs a linear transformation on all gate vectors and aggregates the results to estimate the overall circuit fidelity. By identifying critical weights in the transformation matrix, we propose two optimizations to improve the circuit fidelity. In the unitary decomposition model, we significantly reduce the search space by bridging the gap between unitary and circuit via gate vectors. Experiments show that QuCT improves the accuracy of fidelity prediction by 4.2x on 5-qubit and 18-qubit quantum devices and achieves 2.5x fidelity improvement compared to existing quantum compilers [19, 55]. In unitary decomposition, QuCT achieves 46.3x speedup for 5-qubit unitary and more than hundreds of speedup for 8-qubit unitary, compared to the state-of-the-art method [87].