Quantum algorithmic information theory

TL;DR

This paper explores the development of quantum algorithmic information theory, focusing on quantum halting amplitudes and quantum information content within a framework of universal quantum computation based on interferometers.

Contribution

It introduces a top-down approach to quantum algorithmic information theory, integrating quantum computation models with quantum information and Hilbert space quantum mechanics.

Findings

Defines quantum halting amplitude and quantum algorithmic information content.

Proposes a model of universal quantum computer using two-port interferometers.

Lays foundational concepts linking quantum computation with information theory.

Abstract

The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capable of arbitrary $U(2)$ transformations. Basic to all these considerations is quantum theory, in particular Hilbert space quantum mechanics.