Toward a Definition of Complexity for Quantum Field Theory States

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization...

Full description

Saved in:
Bibliographic Details
Published in:Physical review letters 2018-03, Vol.120 (12), p.121602-121602, Article 121602
Main Authors: Chapman, Shira, Heller, Michal P, Marrochio, Hugo, Pastawski, Fernando
Format: Article
Language:English
Subjects:
Complexity
Field theory
Geodesy
Quantum entanglement
Quantum field theory
Quantum theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form su(1,1) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.120.121602