Circuit complexity for free fermions

By Lucas Hackl, R. Myers. Journal of High Energy Physics, 2018

225 citations recorded by the source corpus.

A bstractWe study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a right-invariant metric. After analyzing the differences and similarities to bosonic circuit complexity, we develop a comprehensive mathematical framework to compute circuit complexity between arbitrary fermionic Gaussian states. We apply this framework to the free Dirac field in four dimensions where we compute the circuit complexity of the Dirac ground state with respect to several classes of spatially unentangled reference states. Moreover, we show that our methods can also be applied to compute the complexity of excited energy eigenstates of the free Dirac field. Finally, we discuss the relation of our results to alternative approaches based on the Fubini-Study metric, the relevance to holography and possible extensions.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/0058511e2deb250857bfc23ce4307aacf19cd107

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Citations in the corpus

Holographic complexity in Vaidya spacetimes. Part II (2018, background): “In this case, the boundary of the WDW patch is defined by two timelike geodesics that originate at the past joint (30)We note that the logarithmic factor does not seem to arise for a free fermion [35, 57].”
Complexity and entanglement for thermofield double states (2018, methodology): “ group-theoretic structure if these operators form a closed algebra, i.e., a Lie algebra g with [Kb I;KbJ] = ifI;JKKbK. Recent studies of the complexity in free quantum eld theories (see, e.g., refs. [23,55,56,58,59]) focused on circuits which remain within the space of Gaussian states, and hence th”
Holographic complexity in Vaidya spacetimes. Part I (2018, unknown): “Another simple extension of this work would be to study the complexity for a mass quench of a free fermion, using the techniques of [44].”
Circuit complexity for coherent states (2018, methodology): “An interesting suggestion in [42] was to construct a family of new cost functions using the Schatten norm (e.”