Continuous matrix product operators for quantum fields

TL;DR

This paper introduces a new ansatz for continuous matrix product operators in quantum field theory, enabling a closed-form expression, continuum limit derivation, and entanglement law preservation, with applications to continuous unitaries.

Contribution

It presents the first continuous matrix product operator ansatz that is expressed in closed form, derived as a continuum limit, and preserves entanglement properties in quantum fields.

Findings

Closed-form expression for continuous matrix product operators.

They can be derived as a continuum limit of lattice operators.

They preserve the entanglement area law in the continuum.

Abstract

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