Non-causal 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.

6 pages, 4 figures

References in corpus (6)

• Experimental Superposition of Orders of Quantum Gates
• Quantum superposition of the order of parties as a communication resource
• The simplest causal inequalities and their violation
• Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios
• The space of logically consistent classical processes without causal order
• Device-independent test of causal order and relations to fixed-points

Cited by in corpus (6)

• Quantum computation with indefinite causal structures
• Dynamics of quantum causal structures
• Observer-dependent locality of quantum events
• Computational tameness of classical non-causal models
• Composition rules for quantum processes: a no-go theorem
• Revisiting Integer Factorization using Closed Timelike Curves