A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computer

TL;DR

This paper proposes a quantum-information-theoretic communication protocol to enhance a relativistic beyond-Turing computer, potentially impacting the understanding of the physical Church-Turing thesis and the foundations of quantum theory and gravity.

Contribution

It introduces a novel quantum communication approach to complement a relativistic beyond-Turing computer, linking quantum information, physics, and computational theory.

Findings

Quantum protocols can facilitate communication with beyond-Turing computers.

Quantum information may influence the validity of the physical Church-Turing thesis.

Foundations of quantum theory and quantum gravity could impact computational limits.

Abstract

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istv\'an N\'emeti and Gyula D\'avid (2006) have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this essay, I will honour Istv\'an's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in N\'emeti and D\'avid (2006) might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis.