Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Clifford+T approximation of single-qubit operators   We give an efficient randomized algorithm for approximating an arbitrary
element of $SU(2)$ by a product of Clifford+$T$ operators, up to any given
error threshold $\epsilon>0$. Under a mild hypothesis on the distribution of
primes, the algorithm's expected runtime is polynomial in $\log(1/\epsilon)$.
If the operator to be approximated is a $z$-rotation, the resulting gate
sequence has $T$-count $K+4\log_2(1/\epsilon)$, where $K$ is approximately
equal to $10$. We also prove a worst-case lower bound of
$K+4\log_2(1/\epsilon)$, where $K=-9$, so that our algorithm is within an
additive constant of optimal for certain $z$-rotations. For an arbitrary member
of $SU(2)$, we achieve approximations with $T$-count $K+12\log_2(1/\epsilon)$.
By contrast, the Solovay-Kitaev algorithm achieves $T$-count
$O(\log^c(1/\epsilon))$, where $c$ is approximately $3.97$.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math