Approximate synthesis of general single-qubit unitaries over the Clifford+√T gate set
Abstract
For the standard Clifford+T gate set, deterministic, ancilla-free synthesis now attains the minimal T-count for general single-qubit unitaries (Morisaki et al., arXiv:2510.05816). The √T gate rotates by half the angle of T, generating a finer lattice of implementable operations. Access to this magic state is expected to lower the cost of deterministic and ancilla-free synthesis of general single-qubit unitaries (Kliuchnikov et al., arXiv:2203.10064), but no direct Clifford+√T algorithm existed for this case. We provide one by extending the integer lattice-point enumeration method of Morisaki et al. We adopt a resource state cost model based on the magic-state catalysis approach of Gidney and Fowler (arXiv:1812.01238). On Haar-random targets synthesized to precisions ranging from ε=10−3 to 10−8, the cost of Clifford+√T circuits scales as 2.4log2(1/ε) compared to 3.0log2(1/ε) for T-count-optimal Clifford+T circuits. Once a one-time catalyst state is amortized, the Clifford+√T circuits are never costlier than their Clifford+T counterparts.
Related
- Optimal Quantum-Circuit Synthesis and Implementation of General Unitaries with Parallelized Bitstring-Conditioned Rotations
- Efficient learning of Clifford disentanglers and typical t-doped unitaries with exponentially more T gates
- Efficient Fidelity Estimation of General Quantum Resource States via Clifford Circuits
- A General Composition Theorem for Approximate Degree
- Link-middle-cut lower bounds for Clifford circuit synthesis
BibTeX
@misc{weiden2026approximate,
title = {{Approximate synthesis of general single-qubit unitaries over the Clifford+$\sqrtT$ gate set}},
author = {Mathias Weiden and Jae Won Kim and Justin Kalloor and John Kubiatowicz and Costin Iancu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.16659},
eprint = {2609.16659},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16659},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Approximate synthesis of general single-qubit unitaries over the Clifford+√T gate set
AU - Mathias Weiden
AU - Jae Won Kim
AU - Justin Kalloor
AU - John Kubiatowicz
AU - Costin Iancu
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2609.16659
UR - https://arxiv.org/abs/2609.16659
AB - For the standard Clifford+T gate set, deterministic, ancilla-free synthesis now attains the minimal T-count for general single-qubit unitaries (Morisaki et al., arXiv:2510.05816). The √T gate rotates by half the angle of T, generating a finer lattice of implementable operations. Access to this magic state is expected to lower the cost of deterministic and ancilla-free synthesis of general single-qubit unitaries (Kliuchnikov et al., arXiv:2203.10064), but no direct Clifford+√T algorithm existed for this case. We provide one by extending the integer lattice-point enumeration method of Morisaki et al. We adopt a resource state cost model based on the magic-state catalysis approach of Gidney and Fowler (arXiv:1812.01238). On Haar-random targets synthesized to precisions ranging from ε=10^−3 to 10^−8, the cost of Clifford+√T circuits scales as 2.4log_2(1/ε) compared to 3.0log_2(1/ε) for T-count-optimal Clifford+T circuits. Once a one-time catalyst state is amortized, the Clifford+√T circuits are never costlier than their Clifford+T counterparts.
ER -