Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving systems of linear algebraic equations via unitary
  transformations on quantum processor of IBM Quantum Experience   We propose a protocol for solving systems of linear algebraic equations via
quantum mechanical methods using the minimal number of qubits. We show that
$(M+1)$-qubit system is enough to solve a system of $M$ equations for one of
the variables leaving other variables unknown provided that the matrix of a
linear system satisfies certain conditions. In this case, the vector of input
data (the rhs of a linear system) is encoded into the initial state of the
quantum system. This protocol is realized on the 5-qubit superconducting
quantum processor of IBM Quantum Experience for particular linear systems of
three equations. We also show that the solution of a linear algebraic system
can be obtained as the result of a natural evolution of an inhomogeneous
spin-1/2 chain in an inhomogeneous external magnetic field with the input data
encoded into the initial state of this chain. For instance, using such
evolution in a 4-spin chain we solve a system of three equations.

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an