Operations with elements of transferred density matrix via unitary transformations at receiver side

Abstract

Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following: turning some matrix elements to zero, rearranging the matrix elements and preparing their linear combinations with required coefficients. We also propose a protocol for solving a system of linear algebraic equations with a system of two equations as an example. Such operations are numerically simulated on the basis of 42-node spin-1/2 chain with the two-qubit sender and receiver.

Solving systems of linear algebraic equations via unitary transformations on quantum processor of IBM Quantum Experience

“…We note that the unitary transformations at the receiver side were used in Ref. [15] for structural restoring the elements of the density matrix transferred through the spin chain from the sender to the receiver and to perform simple operations with the density matrix elements [16] [18]. Now we optimize such transformations for solving a particular algebraic problem.…”

Computing scalar products via a two-terminal quantum transmission line

“…The unitary transformations of this type have been used in [15] to partially recover the nondiagonal part of the transferred density matrix. They also can be used for simulating simple operations with the elements of the transferred density matrix [16].…”