The diagonalization method in quantum recursion theory

TL;DR

This paper explores how the classical diagonalization method in recursion theory can be adapted for quantum computing, utilizing unitary operators with specific eigenvalues to handle quantum parallelism.

Contribution

It introduces a modified diagonalization technique suitable for quantum recursion theory, expanding classical methods to quantum computational frameworks.

Findings

Quantum diagonalization involves unitary operators with eigenvalues not equal to one.

The method adapts classical diagonalization to quantum settings.

Potential implications for quantum algorithm design.

Abstract

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.