Horizons Protect Church-Turing

TL;DR

This paper discusses potential violations of the quantum-Extended Church-Turing thesis near black hole horizons and suggests a reformulation involving holographic boundaries to preserve its validity.

Contribution

It proposes a new perspective on the quantum-Extended Church-Turing thesis by incorporating holographic principles to account for black hole horizon effects.

Findings

Black holes may allow observers to learn results of non-quantum-efficient calculations rapidly.

Horizon properties are crucial in protecting the validity of the thesis.

Reformulation limits the thesis to observers with access to holographic boundaries.

Abstract

The quantum-Extended Church-Turing thesis is a principle of physics as well as computer science. It asserts that the laws of physics will prevent the construction of a machine that can efficiently determine the results of any calculation which cannot be done efficiently by a quantum Turing machine (or a universal quantum circuit). In this note I will argue that an observer falling into a black hole can learn the result of such a calculation in a very short time, thereby seemingly violating the thesis. A viable reformulation requires that the thesis only applies to observers who have access to the holographic boundary of space. The properties of the horizon play a crucial a role in protecting the thesis. The arguments are closely related to, and were partially motivated by a recent paper by Bouland, Fefferman, and Vazirani, and by a question raised by Aaronson.