Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The block-ZXZ synthesis of an arbitrary quantum circuit   Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix
decomposition can be applied, leading to four different syntheses of a
$w$-qubit quantum circuit performing the unitary transformation. The
demonstration is based on a recent theorem by F\"uhr and Rzeszotnik,
generalizing the scaling of single-bit unitary gates ($w=1$) to gates with
arbitrary value of~$w$. The synthesized circuit consists of controlled 1-qubit
gates, such as NEGATOR gates and PHASOR gates. Interestingly, the approach
reduces to a known synthesis method for classical logic circuits consisting of
controlled NOT gates, in the case that $U$ is a permutation matrix.

11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg