Year: 2019
Type: article
Abstract: We propose how to compute the complexity of operators generated by Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The Hamiltonians in QFT/QM and quantum circuit have a few essential differences, for which we introduce new principles and methods for complexity. We show that the complexity geometry corresponding to one-dimensional quadratic Hamiltonians is equivalent to AdS3 spacetime. Here, the requirement that the complexity is nonnegative corresponds to the fact that the Hamiltonian is lower bounded and the speed of a particle is not superluminal. Our proposal proves the complexity of the operator generated by a free Hamiltonian is zero, as expected. By studying a non-relativistic particle in compact Riemannian manifolds we find the complexity is given by the global geometric property of the space. In particular, we show that in low energy limit the critical spacetime dimension to ensure the ‘nonnegative’ complexity is the 3+1 dimension.
Source: Journal of High Energy Physics
Authors: Run-Qiu Yang, Keun-Young Kim
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Award: G2320880518
OpenAlex ID: W2897819341