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Open Quantum Systems Decoherence

Computational tameness of classical non-causal models

arXiv

Authors: Ämin Baumeler, Stefan Wolf

Year

2016

Paper ID

42359

Status

Preprint

Abstract Read

~2 min

Abstract Words

135

Citations

N/A

Abstract

We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity class operatorname{mathsf{UP}}capoperatorname{mathsf{coUP}}. An example of a problem in that class is factorization. Our result implies that classical deterministic closed timelike curves (CTCs) cannot efficiently solve problems that lie outside of that class. Thus, in stark contrast to other CTC models, these CTCs cannot efficiently solve operatorname{mathsf{NP-complete}} problems, unless operatorname{mathsf{NP}}=operatorname{mathsf{UP}}capoperatorname{mathsf{coUP}}=operatorname{mathsf{coNP}}, which lets their existence in nature appear less implausible. This result gives a new characterization of operatorname{mathsf{UP}}capoperatorname{mathsf{coUP}} in terms of fixed points.

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This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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We show that the computational power of the non-causal circuit model, i.e., the circuit model where the assumption of a global causal order is replaced by the assumption of...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1611.05641 [2] arXiv https://arxiv.org/abs/1611.05641 [3] Publisher https://arxiv.org/abs/1611.05641

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