Circuit complexity in quantum field theory

By Ro Jefferson, R. Myers. 2017

455 citations recorded by the source corpus.

A bstractMotivated 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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/08d43b728e329f2d18fd60488d46a5f673723640

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Citations in the corpus

On the time dependence of holographic complexity (2017, background): “While only considering free scalars [11, 12], these calculations yield striking similarities to the results produced with holographic complexity.”
Circuit complexity for coherent states (2018, methodology): “Abstract: We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen’s geometric approach as in [1].”
Krylov complexity in conformal field theory (2021, methodology): “[36] Robert A Jefferson and Robert C Myers, “Circuit complexity in quantum field theory,” Journal of High Energy Physics 2017, 1–81 (2017).”
Circuit complexity in fermionic field theory (2018, methodology): “A candidate is the system with two lattice points parallel to the work for scalars considered in [4].”
Holographic complexity in Vaidya spacetimes. Part I (2018, background): “In [42, 43], it was suggested the dependence on M could be associated with dependence of the holographic complexity α, which seems to be traded for the dependence on scale `ct with the addition of the boundary counterterm [56].”
Holographic complexity in Vaidya spacetimes. Part II (2018, background): “We would like to review these changes and the leading UV divergences carefully here because it is relevant for the comparison of the holographic complexity with the complexity evaluated in quantum field theories [33, 34].”
Circuit complexity in interacting QFTs and RG flows (2018, methodology): “In [66–68] a geometric approach for circuit complexity was put forward which was studied in great detail in the context of free scalar field theories in [14].”
Complexity and entanglement for thermofield double states (2018, background): “The previous discussion in [23] did not require a gate scale because it only considered gates constructed with the generators PaQb, which are dimensionless in natural units.”