Reducing T Gates with Unitary Synthesis

Abstract

Quantum error correction is essential for achieving practical quantum computing but has a significant computational overhead. Among fault-tolerant (FT) gate operations, non-Clifford gates, such as $T$, are particularly expensive due to their reliance on magic state distillation. These costly $T$ gates appear frequently in FT circuits as many quantum algorithms require arbitrary single-qubit rotations, such as $R_x$ and $R_z$ gates, which must be decomposed into a sequence of $T$ and Clifford gates. In many quantum circuits, $R_x$ and $R_z$ gates can be fused to form a single $U3$ unitary. However, existing synthesis methods, such as Gridsynth, rely on indirect decompositions, requiring separate $R_z$ decompositions that result in a threefold increase in $T$ count. This work presents TensoR-based Arbitrary unitary SYNthesis (trasyn), a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries, avoiding the overhead of separate $R_z$ decompositions. By leveraging tensor network-based search, our approach enables native $U3$ synthesis, reducing the $T$ count, Clifford gate count, and approximation error. Compared to Gridsynth-based circuit synthesis, for 187 representative benchmarks, our design reduces the T count by up to 3.5$\times$, and Clifford gates by 7$\times$, resulting in up to 4$\times$ improvement in overall circuit infidelity.