Reducing T Gates with Unitary Synthesis

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 𝑈 3 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 𝑈 3 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×, and Clifford gates by 7×, resulting in up to 4× improvement in overall circuit infidelity.