Computation with narrow CTCs

TL;DR

This paper explores computational models with restricted closed timelike curves (CTCs), demonstrating their power to enhance classical and quantum computation, including exponential speedups and the ability to perform CTC-based tasks without prior runtime knowledge.

Contribution

It provides a full characterization of language classes recognized by polynomial-time probabilistic and quantum computers with narrow CTCs, revealing their computational power and practical implementation advantages.

Findings

Narrow CTCs add limited nondeterminism to deterministic computers.

They enable exponential speedups in constant-space probabilistic and quantum computation.

CTC-based computations can be implemented without prior knowledge of runtime.

Abstract

We examine some variants of computation with closed timelike curves (CTCs), where various restrictions are imposed on the memory of the computer, and the information carrying capacity and range of the CTC. We give full characterizations of the classes of languages recognized by polynomial time probabilistic and quantum computers that can send a single classical bit to their own past. Such narrow CTCs are demonstrated to add the power of limited nondeterminism to deterministic computers, and lead to exponential speedup in constant-space probabilistic and quantum computation. We show that, given a time machine with constant negative delay, one can implement CTC-based computations without the need to know about the runtime beforehand.