Towards A Theory Of Quantum Computability

TL;DR

This paper introduces a formal framework for quantum computable functions, defining them as limits of quantum Turing machine computations, and establishes their foundational properties for developing a quantum computability theory.

Contribution

It proposes a rigorous definition of quantum computable functions and demonstrates their recursive enumerability, bridging classical computability concepts with quantum computation.

Findings

Quantum computable functions are defined as limits of quantum Turing machine computations.

The class of quantum computable functions is recursively enumerable.

This work lays the groundwork for a formal quantum computability theory.

Abstract

We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum Turing machine. The class of quantum computable functions is recursively enumerable, thus opening the door to a quantum computability theory which may follow some of the classical developments.