Discrimination of Unitary Transformations and Quantum Algorithms

TL;DR

This paper explores the ability to distinguish between different unitary transformations in quantum algorithms, focusing on the Deutsch-Jozsa problem, and develops algorithms that can discriminate these transformations with certainty.

Contribution

It introduces a framework for discriminating among oracle unitaries in quantum algorithms, providing a comprehensive set of algorithms for the Deutsch-Jozsa problem.

Findings

Developed algorithms for perfect discrimination of oracle unitaries.

Established the connection between discrimination and solving the Deutsch-Jozsa problem.

Provided an exhaustive collection of algorithms for certainty in discrimination.

Abstract

Quantum algorithms are typically understood in terms of the evolution of a multi-qubit quantum system under a prescribed sequence of unitary transformations. The input to the algorithm prescribes some of the unitary transformations in the sequence with others remaining fixed. For oracle query algorithms, the input determines the oracle unitary transformation. Such algorithms can be regarded as devices for discriminating amongst a set of unitary transformations. The question arises: "Given a set of known oracle unitary transformations, to what extent is it possible to discriminate amongst them?" We investigate this for the Deutsch-Jozsa problem. The task of discriminating amongst the admissible oracle unitary transformations results in an exhaustive collection of algorithms which can solve the problem with certainty.