T-Gate Optimization through Non-Clifford Fusion and Scalable Unitary Synthesis

The fault-tolerant quantum programs are typically converted to the Clifford+RZ gate set, and these RZ gates are further synthesized into sequences of Clifford and T gates in fault-tolerant quantum computers, where the T-gate count and T-gate depth are critical performance metrics. Beyond RZ gate synthesis, several algorithms have been developed for synthesizing general single-qubit and multi-qubit unitaries. Although scalable synthesis methods have shown improvements over existing approaches, their practical use is limited by the frequency and structure of such unitaries in typical circuits.

In this paper, we propose Non-Clifford Fusion (NCF), a compilation framework that reduces both T-gate count and T-gate depth. NCF transforms quantum circuits into the Pauli rotation form and partitions Pauli strings into groups, where each group can be conjugated (i.e., transformed) into a set of Pauli strings acting on a restricted subset of qubits. This structure enables the simultaneous synthesis of the entire group, reducing both T-gate count and depth. Experimental results show that NCF significantly reduces T-gate count, T-gate depth, and Clifford count compared to state-of-the-art synthesis methods.