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Axioms 2015, 4(1), 102-119; doi:10.3390/axioms4010102

A Model for the Universe that Begins to Resemble a Quantum Computer

Department of Mathematics, University of Denver, Denver, CO 80208, USA
Academic Editor: James D. Malley
Received: 10 December 2014 / Revised: 19 February 2015 / Accepted: 2 March 2015 / Published: 9 March 2015
(This article belongs to the Special Issue Quantum Statistical Inference)
View Full-Text   |   Download PDF [429 KB, uploaded 9 March 2015]   |  

Abstract

This article presents a sequential growth model for the Universe that acts like a quantum computer. The basic constituents of the model are a special type of causal set (causet) called a c-causet. A c-causet is defined to be a causet that has a unique labeling. We characterize c-causets as those causets that form a multipartite graph or equivalently those causets whose elements are comparable whenever their heights are different. We show that a c-causet has precisely two c-causet offspring. It follows that there are 2n c-causets of cardinality n + 1. This enables us to classify c-causets of cardinality n + 1 in terms of n-bits. We then quantize the model by introducing a quantum sequential growth process. This is accomplished by replacing the n-bits by n-qubits and defining transition amplitudes for the growth transitions. We mainly consider two types of processes, called stationary and completely stationary. We show that for stationary processes, the probability operators are tensor products of positive rank-one qubit operators. Moreover, the converse of this result holds. Simplifications occur for completely stationary processes. We close with examples of precluded events. View Full-Text
Keywords: causal sets; discrete quantum gravity; transition amplitudes causal sets; discrete quantum gravity; transition amplitudes
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Gudder, S. A Model for the Universe that Begins to Resemble a Quantum Computer. Axioms 2015, 4, 102-119.

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