Non-causal computation

TL;DR

This paper introduces non-causal circuits, a new computation paradigm that relaxes fixed causal order assumptions, demonstrating they can outperform traditional causal circuits by leveraging logical consistency.

Contribution

It presents the concept of non-causal circuits, showing they can surpass causal circuits in computational tasks by removing the need for fixed causal structures.

Findings

Non-causal circuits can outperform causal circuits.

Suppressing loops is more restrictive than avoiding contradictions.

Extends non-causal advantages from correlations to computation.

Abstract

Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a novel computing paradigm beyond quantum computing, replacing this assumption by mere logical consistency: We study non-causal circuits, where a fixed time structure within a gate is locally assumed whilst the global causal structure between the gates is dropped. We present examples of logically consistent non- causal circuits outperforming all causal ones; they imply that suppressing loops entirely is more restrictive than just avoiding the contradictions they can give rise to. That fact is already known for correlations as well as for communication, and we here extend it to computation.