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arXiv · 1801.07620

Circuit Complexity in Fermionic Field Theory

Rifath Khan·Chethan Krishnan·Sanchita Sharma
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Abstract

We define and calculate versions of complexity for free fermionic quantum field theories in 1+1 and 3+1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits. We do this both by discretizing and identifying appropriate classes of Bogoliubov-Valatin transformations, and also directly in the continuum by defining squeezing operators and their generalizations. As a closely related problem, we consider cMERA tensor networks for fermions: viewing them as paths in circuit space, we compute their path lengths. Certain ambiguities that arise in some of these results because of cut-off dependence are discussed.

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Rifath Khan, Chethan Krishnan, Sanchita Sharma. 2018-01-23. Circuit Complexity in Fermionic Field Theory. https://doi.org/10.1103/physrevd.98.126001

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