Within tensor network theory, matrix product operators (MPOs) are a class of many-body operators acting on finite-dimensional lattice quantum systems that admit efficient classical description and do not create a large amount of entanglement. In this talk, we discuss an ansatz for continuous matrix product operator (cMPO) 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. As an application, we use this ansatz to construct the continuum limit of matrix product unitaries beyond quantum cellular automata, and we conclude with some future directions.
Erickson Tjoa (Garching): Continuous matrix product operators for quantum fields
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