Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On an implementation of the Solovay-Kitaev algorithm   In quantum computation we are given a finite set of gates and we have to
perform a desired operation as a product of them. The corresponding
computational problem is approximating an arbitrary unitary as a product in a
topological generating set of $SU(d)$. The problem is known to be solvable in
time $polylog(1/\epsilon)$ with product length $polylog(1/\epsilon)$, where the
implicit constants depend on the given generators. The existing algorithms
solve the problem but they need a very slow and space consuming preparatory
stage. This stage runs in time exponential in $d^2$ and requires memory of size
exponential in $d^2$. In this paper we present methods which make the
implementation of the existing algorithms easier. We present heuristic methods
which make a time-length trade-off in the preparatory step. We decrease the
running time and the used memory to polynomial in $d$ but the length of the
products approximating the desired operations will increase (by a factor which
depends on $d$). We also present a simple method which can be used for
decomposing a unitary into a product of group commutators for $2<d<256$, which
is an important part of the existing algorithm.

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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys