Physical Review Research

“Continuous matrix-product operators for quantum fields”

In this work, we introduce an ansatz for continuous matrix-product operators for quantum field theory. We show that (1) they admit a closed-form expression in terms of finite number of matrix-valued functions without reference to any lattice parameter; (2) they are obtained as a suitable continuum limit of matrix-product operators; and (3) they preserve the entanglement area law directly in the continuum, and in particular they map a continuous matrix-product state (cMPS) to another cMPS. As an application, we use this ansatz to construct several families of continuous matrix-product unitaries beyond quantum cellular automata.

Access to paper: https://journals.aps.org/prresearch/abstract/10.1103/d61y-cxx3