Quantum gravity computers: On the theory of computation with indefinite causal structure
Abstract
A quantum gravity computer is one for which the particular effects of quantum gravity are relevant. In general relativity, causal structure is nonfixed. In quantum theory nonfixed 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 timelike or not. We study the implications of this for the theory of computation. Classical and quantum computations consist in ivolving 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, Lambda (this is a mathematical object containing information about the causal connections between different spacetime regions). A computer is given by the pair {Lambda, 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2007
 DOI:
 10.48550/arXiv.quantph/0701019
 arXiv:
 arXiv:quantph/0701019
 Bibcode:
 2007quant.ph..1019H
 Keywords:

 Quantum Physics;
 General Relativity and Quantum Cosmology
 EPrint:
 24 pages. For proceedings of "Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle: An International Conference in Honour of Abner Shimony"