Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Computation of the Permanent of Block Factorizable Matrices   We present an efficient algorithm for computing the permanent for matrices of
size N that can written as a product of L block diagonal matrices with blocks
of size at most 2. For fixed L, the time and space resources scale linearly in
N, with a prefactor that scales exponentially in L. This class of matrices
contains banded matrices with banded inverse. We show that such a factorization
into a product of block diagonal matrices gives rise to a circuit acting on a
Hilbert space with a tensor product structure and that the permanent is equal
to the transition amplitude of this circuit and a product basis state. In this
correspondence, a block diagonal matrix gives rise to one layer of the circuit,
where each block to a gate acting either on a single tensor component or on two
adjacent tensor components. This observation allows us to adopt matrix product
states, a computational method from condensed matter physics and quantum
information theory used to simulate quantum systems, to evaluate the transition
amplitude.

23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math