Continuous matrix-product operators for quantum fields
Abstract
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.
Fields of Study & Subjects
Quantum many-body systems
Quantum Computing Algorithms and Architecture
Advanced Operator Algebra Research
Publication details
- Journal / source
- Physical Review Research
- Publisher
- American Physical Society (APS)
- Volume
- 8
- Issue
- 2
- Publication date
- 21 March 2026
- Language
- EN