Reducing T Gates with Unitary Synthesis
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910000335552512 |
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| author | Hao, Tianyi Xu, Amanda Tannu, Swamit |
| author_facet | Hao, Tianyi Xu, Amanda Tannu, Swamit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reducing T Gates with Unitary Synthesis Hao, Tianyi Xu, Amanda Tannu, Swamit Quantum Physics Emerging Technologies 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. |
| title | Reducing T Gates with Unitary Synthesis |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2503.15843 |