Approximate synthesis of general single-qubit unitaries over the Clifford+$\sqrt{T}$ gate set

• URL: http://arxiv.org/abs/2609.16659v1
• Date: Tue, 15 Sep 2026 05:25:39 GMT
• Title: Approximate synthesis of general single-qubit unitaries over the Clifford+$\sqrt{T}$ gate set
• Abstract summary: We show that access to the $sqrtT$ gate rotates by half the angle of $T$, generating a finer lattice of implementable operations.<n>It was assumed that access to this magic state lowers the cost of deterministic and ancillafree synthesis of general single-qubit unitaries.
• Score: 3.460527115734753
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\sqrt{T}$ gate rotates by half the angle of $T$, generating a finer lattice of implementable operations. It was assumed that access to this magic state lowers the cost of deterministic and ancilla-free synthesis of general single-qubit unitaries, but no direct Clifford+$\sqrt{T}$ 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 $\varepsilon=10^{-3}$ to $10^{-8}$, the cost of Clifford+$\sqrt{T}$ circuits scales as $2.4\log_2(1/\varepsilon)$ compared to $3.0\log_2(1/\varepsilon)$ for the provably $T$-count-optimal Clifford+$T$ circuits. Once a one-time catalyst state is amortized, the Clifford+$\sqrt{T}$ circuits are never costlier than their Clifford+$T$ counterparts.

Related papers

• Sharp Minimax Regret for Infinite-Memory Logistic Prediction [55.29259818039367]
  Lag $j$ can affect prediction by scale $r_j$ and enters only $n_T,j=T-j+1$ prediction rounds.<n>For every summable envelope, a localized mixture proves $cR_T(r)leq C_T(r)$.<n>For exponential and envelopes, under the stated finite-sample condition, a Toeplitz-design converse proves $cR_T(r)geq c_T(r)$.
  arXiv  Detail & Related papers  (2026-08-27T01:31:46Z)
• pygridsynth: A fast numerical tool for ancilla-free Clifford+T synthesis [0.0]
  pygridsynth is a Python library for ancilla-free approximate Clifford+$T$ synthesis.<n>The library builds upon established efficient and high-precision synthesis routines.<n> pygridsynth is a Python-native platform for high-precision Clifford+T$ synthesis and for benchmarking unitary and mixed synthesis strategies.
  arXiv  Detail & Related papers  (2026-04-23T06:44:35Z)
• Optimal ancilla-free Clifford+T synthesis for general single-qubit unitaries [0.0]
  The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum $T$-count.<n>The second algorithm, called probabilistic synthesis, approximates any single-qubit unitary by a probabilistic mixture of single-qubit Clifford+$T$ circuits with the minimum $T$-count.
  arXiv  Detail & Related papers  (2025-10-07T11:37:02Z)
• Reducing T Gates with Unitary Synthesis [0.41873449350124814]
  This work presents a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries.<n>By leveraging tensor network-based search, our approach enables native $U3$ synthesis, reducing the $T$ count, Clifford gate count, and approximation error.
  arXiv  Detail & Related papers  (2025-03-20T04:53:54Z)
• Synthesis and Arithmetic of Single Qutrit Circuits [0.8192907805418581]
  We study qutrit circuits consisting of words over the Clifford$+D$ cyclotomic gate set.<n>The framework developed to formulate qutrit gate synthesis for Clifford$+D$ extends to qudits of arbitrary prime power.
  arXiv  Detail & Related papers  (2023-11-15T04:50:41Z)
• Exact Synthesis of Multiqubit Clifford-Cyclotomic Circuits [0.8411424745913132]
  We show that when $n$ is a power of 2, a multiqubit unitary matrix $U$ can be exactly represented by a circuit over $mathcalG_n$. We moreover show that $log(n)-2$ ancillas are always sufficient to construct a circuit for $U$.
  arXiv  Detail & Related papers  (2023-11-13T20:46:51Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• The Approximate Degree of DNF and CNF Formulas [95.94432031144716]
  For every $delta>0,$ we construct CNF and formulas of size with approximate degree $Omega(n1-delta),$ essentially matching the trivial upper bound of $n. We show that for every $delta>0$, these models require $Omega(n1-delta)$, $Omega(n/4kk2)1-delta$, and $Omega(n/4kk2)1-delta$, respectively.
  arXiv  Detail & Related papers  (2022-09-04T10:01:39Z)
• Low-degree learning and the metric entropy of polynomials [44.99833362998488]
  We prove that any (deterministic or randomized) algorithm which learns $mathscrF_nd$ with $L$-accuracy $varepsilon$ requires at least $Omega(sqrtvarepsilon)2dlog n leq log mathsfM(mathscrF_n,d,|cdot|_L,varepsilon) satisfies the two-sided estimate $$c (1-varepsilon)2dlog
  arXiv  Detail & Related papers  (2022-03-17T23:52:08Z)
• Improved Sample Complexity for Incremental Autonomous Exploration in MDPs [132.88757893161699]
  We learn the set of $epsilon$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps. DisCo is the first algorithm that can return an $epsilon/c_min$-optimal policy for any cost-sensitive shortest-path problem.
  arXiv  Detail & Related papers  (2020-12-29T14:06:09Z)
• An Optimal Separation of Randomized and Quantum Query Complexity [67.19751155411075]
  We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $ellsqrtbinomdell (1+log n)ell-1,$ sum to at most $cellsqrtbinomdell (1+log n)ell-1,$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant.
  arXiv  Detail & Related papers  (2020-08-24T06:50:57Z)
• Model-Free Reinforcement Learning: from Clipped Pseudo-Regret to Sample Complexity [59.34067736545355]
  Given an MDP with $S$ states, $A$ actions, the discount factor $gamma in (0,1)$, and an approximation threshold $epsilon > 0$, we provide a model-free algorithm to learn an $epsilon$-optimal policy. For small enough $epsilon$, we show an improved algorithm with sample complexity.
  arXiv  Detail & Related papers  (2020-06-06T13:34:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.