Circuit complexity in quantum field theory

Ro Jefferson; Robert C. Myers

doi:10.1007/JHEP10(2017)107

Circuit complexity in quantum field theory

Ro Jefferson, Robert C. Myers

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Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Article number	107
Pages (from-to)	1-81
Number of pages	81
Journal	JHEP
Volume	2017
DOIs	https://doi.org/10.1007/JHEP10(2017)107
Publication status	Published - 2017

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title = "Circuit complexity in quantum field theory",

abstract = "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.",

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AU - Myers, Robert C.

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AB - 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.

U2 - 10.1007/JHEP10(2017)107

DO - 10.1007/JHEP10(2017)107

M3 - Article

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VL - 2017

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JO - JHEP

JF - JHEP

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Circuit complexity in quantum field theory

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