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Circuit complexity in quantum field theory

Jul 26, 2017

86 pages

Published in:

JHEP 10 (2017) 107

Published: Oct 16, 2017

e-Print:

1707.08570 [hep-th]

DOI:

10.1007/JHEP10(2017)107

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Abstract: (arXiv)

Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar field theory for general dimensions. Applying the geometric approach of Nielsen to this quantum circuit model, the complexity of the state becomes the length of the shortest geodesic in the space of circuits. We compare the complexity of the ground state of the free scalar field to the analogous results from holographic complexity, and find some surprising similarities.

Note:

Corrected typo in eqs. (1.1) and (3.35). Added footnote on pg. 33, and additional references. Author name change

AdS-CFT Correspondence
Effective Field Theories
Black Holes in String Theory
Lattice Quantum Field Theory
field theory: scalar
ground state
holography
geodesic

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Figures(11)

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