The Universe as a Quantum Computer
 Citation data:

Mathematics Preprint Series
 Publication Year:
 2014

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 Repository URL:
 https://digitalcommons.du.edu/cgi/viewcontent.cgi?article=1011&context=math_preprints, https://digitalcommons.du.edu/math_preprints/12
 Author(s):
 Publisher(s):
 Tags:
 Quantum computers, ccauset, quantum sequential growth process, Computer Sciences, Mathematics
article description
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 ccauset. A ccauset is defined to be a causet that is independent of its labeling. We characterize ccausets 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 ccauset has precisely two ccauset offspring. It follows that there are 2n ccausets of cardinality n + 1. This enables us to classify ccausets of cardinality n + 1 in terms of nbits. We then quantize the model by introducing a quantum sequential growth process. This is accomplished by replacing the nbits by nqubits 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 rank1 qubit operators. Moreover, the converse of this result holds. Simplifications occur for completely stationary processes. We close with examples of precluded events