Reducing T Gates with Unitary Synthesis

2025-03-20

AI Summary

To address the excessive resource overhead of non-Clifford gates—particularly T gates—in fault-tolerant quantum computation, which arises from reliance on magic state distillation, this paper proposes a native synthesis method for arbitrary single-qubit U3 unitaries, bypassing conventional indirect decomposition schemes that require prior Rz-gate synthesis. We introduce a novel tensor network–based search framework that jointly minimizes T-count, Clifford-count, and approximation error within a single optimization process, enabling concurrent resource-efficiency and fidelity optimization. Evaluated on 187 benchmark circuits, our method achieves up to a 3.5× reduction in T-count, a 7× reduction in Clifford-count, and a 4× improvement in circuit fidelity (i.e., reduced approximation error). This approach provides a more efficient and compact fault-tolerant implementation for arbitrary single-qubit rotations.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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 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 $3.5 imes$, and Clifford gates by $7 imes$, resulting in up to $4 imes$ improvement in overall circuit infidelity.

Problem

• Reduces T gate count in quantum circuits
• Minimizes Clifford gate count and approximation error
• Improves circuit infidelity through direct unitary synthesis

Innovation

• Direct synthesis of single-qubit unitaries
• Tensor network-based search for U3 synthesis
• Reduces T and Clifford gates significantly