Universality and Optimal Architectures for Layered Programmable Unitary Decompositions

• URL: http://arxiv.org/abs/2510.19397v1
• Date: Wed, 22 Oct 2025 09:15:58 GMT
• Title: Universality and Optimal Architectures for Layered Programmable Unitary Decompositions
• Authors: Javier Álvarez-Vizoso, David Barral,
• Abstract summary: decomposition of arbitrary unitary transformations into sequences of simpler, physically realizable operations is a foundational problem in quantum information science.<n>We establish a 1D Quantum Field model for justifying the universality of a broad class of such factorizations.<n>This framework provides a unified method to verify the universality of various proposed architectures.
• Score: 2.879036956042182
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The decomposition of arbitrary unitary transformations into sequences of simpler, physically realizable operations is a foundational problem in quantum information science, quantum control, and linear optics. We establish a 1D Quantum Field Theory model for justifying the universality of a broad class of such factorizations. We consider parametrizations of the form $U = D_1 V_1 D_2 V_2 \cdots V_{M-1}D_M$, where $\{D_j\}$ are programmable diagonal unitary matrices and $\{V_j\}$ are fixed mixing matrices. By leveraging concepts like the anomalies of our effective model, we establish criteria for universality given the set of mixer matrices. This approach yields a rigorous proof grounded on physics for the conditions required for the parametrization to cover the entire group of special unitary matrices. This framework provides a unified method to verify the universality of various proposed architectures and clarifies the nature of the ``generic'' mixers required for such constructions. We also provide a geometry-aware optimization method for finding the parameters of a decomposition.

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