Quantum Gravity Computers: On the Theory of Computation with Indefinite Causal Structure View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2009

AUTHORS

Lucien Hardy

ABSTRACT

A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is non-fixed. In quantum theory non-fixed quantities are subject to quantum uncertainty. It is therefore likely that, in a theory of quantum gravity, we will have indefinite causal structure. This means that there will be no matter of fact as to whether a particular interval is time-like or not. We study the implications of this for the theory of computation. Classical and quantum computations consist in evolving the state of the computer through a sequence of time steps. This will, most likely, not be possible for a quantum gravity computer because the notion of a time step makes no sense if we have indefinite causal structure. We show that it is possible to set up a model for computation even in the absence of definite causal structure by using a certain framework (the causaloid formalism) that was developed for the purpose of correlating data taken in this type of situation. Corresponding to a physical theory is a causaloid, Λ (this is a mathematical object containing information about the causal connections between different spacetime regions). A computer is given by the pair {Λ,S} where S is a set of gates. Working within the causaloid formalism, we explore the question of whether universal quantum gravity computers are possible.We also examine whether a quantum gravity computer might be more powerful than a quantum (or classical) computer. In particular, we ask whether indefinite causal structure can be used as a computational resource. More... »

PAGES

379-401

References to SciGraph publications

Book

TITLE

Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle

ISBN

978-1-4020-9106-3
978-1-4020-9107-0

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4020-9107-0_21

DOI

http://dx.doi.org/10.1007/978-1-4020-9107-0_21

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1011726315


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