[Paper Review] Non-causal computation avoiding the grandfather and information antinomies.

Ämin Baumeler, Stefan Wolf|arXiv (Cornell University)|Jan 25, 2016

Quantum Computing Algorithms and Architecture12 references3 citations

TL;DR

This paper introduces non-causal circuits that relax the traditional requirement of fixed causal order in computation, replacing it with logical consistency. By allowing global non-causal structures while preserving local causality within gates, the model enables logically consistent circuits that outperform all causal counterparts, demonstrating that avoiding contradictions is less restrictive than eliminating loops entirely.

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, 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.

Motivation & Objective

• To investigate whether computation can be enhanced by relaxing the fixed causal order traditionally assumed in algorithm design.
• To address the grandfather and information antinomies that arise in non-causal systems by enforcing logical consistency instead of causal structure.
• To demonstrate that non-causal circuits can achieve superior computational performance compared to causal ones when logical consistency is preserved.
• To extend the principle that avoiding contradictions is less restrictive than eliminating loops, previously known in correlations and communication, to the domain of computation.

Proposed method

• Modeling computation as circuits where local gate operations assume a fixed time order, but the global order between gates is not constrained.
• Defining non-causal circuits as those where the global causal structure is dropped, but logical consistency across all computation steps is required.
• Using logical consistency as the primary constraint instead of causal ordering to determine valid computation outcomes.
• Constructing examples of non-causal circuits that are logically consistent and outperform all possible causal circuits.
• Analyzing the computational advantage by comparing the performance of logically consistent non-causal circuits against all causal alternatives.
• Extending known results from quantum correlations and communication to computational models, showing that loop avoidance is overly restrictive compared to contradiction avoidance.

Experimental results

Research questions

• RQ1 Can computation be performed more efficiently by relaxing the requirement of a fixed global causal order?
• RQ2 How can logical consistency be used as a substitute for causal ordering in circuit design?
• RQ3 What is the computational advantage of non-causal circuits that are logically consistent but not globally causal?
• RQ4 Why is suppressing loops entirely more restrictive than merely avoiding the contradictions they can cause in computation?
• RQ5 To what extent can non-causal computation outperform causal computation when logical consistency is enforced?

Key findings

• Non-causal circuits that are logically consistent can outperform all causal circuits, demonstrating a computational advantage.
• The suppression of loops is more restrictive than necessary, as long as logical consistency is maintained.
• Logical consistency alone is sufficient to avoid the grandfather and information antinomies, even in the absence of a fixed causal order.
• The framework extends principles known in quantum correlations and communication to the domain of computation.
• The results show that avoiding contradictions is less restrictive than eliminating loops, suggesting a broader design space for future computing models.
• The model provides a new paradigm for computation where logical consistency replaces causal order as the fundamental constraint.