Quantum Computation as Gravity
High Energy Physics - Theory
2019-06-19 v2 Quantum Physics
Abstract
We formulate Nielsen's geometric approach to complexity in the context of two dimensional conformal field theories, where series of conformal transformations are interpreted as unitary circuits. We show that the complexity functional can be written as the Polyakov action of two dimensional gravity or, equivalently, as the geometric action on the coadjoint orbits of the Virasoro group. This way, we argue that gravity sets the rules for optimal quantum computation in conformal field theories.
Keywords
Cite
@article{arxiv.1807.04422,
title = {Quantum Computation as Gravity},
author = {Pawel Caputa and Javier M. Magan},
journal= {arXiv preprint arXiv:1807.04422},
year = {2019}
}
Comments
v2 includes major text revision and clarifications. Appendices added with a summary of our setup, discussion on different complexity metrics and Euler-Arnold approach to Virasoro circuits