Remarks on controlled measurement and quantum algorithm for calculating Hermitian conjugate

TL;DR

This paper introduces controlled measurement techniques and a quantum algorithm for calculating the Hermitian conjugate of matrices, enhancing quantum matrix manipulation methods.

Contribution

It presents two novel aspects: controlled measurement to improve access probability and an algorithm for Hermitian conjugate calculation, supplementing existing quantum matrix algorithms.

Findings

Controlled measurement improves access probability in quantum algorithms.

The new algorithm efficiently computes Hermitian conjugates of matrices.

Presented circuits demonstrate practical implementation.

Abstract

We present two new aspects for the recently proposed algorithms for matrix manipulating based on the special encoding the matrix elements into the superposition state of a quantum system. First aspect is the controlled measurement which allows to avoid the problem of small access probability to the required ancilla state at the final step of algorithms needed to remove the garbage of the states. Application of controlled measurement to the earlier developed algorithm is demonstrated. The second aspect is the algorithm for calculating the Hermitian conjugate of an arbitrary matrix, which supplements the algorithms proposed earlier. The appropriate circuits are presented.