Simple factorization of unitary transformations

2017/08/31 by Hubert de Guise, Olivia Di Matteo, L. L. Sánchez-Soto +1 · 73 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Beam splitter #Classical mechanics #Factorization #Hinge #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Neural Networks and Reservoir Computing #Optical Network Technologies #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Simple (philosophy) #Unique factorization domain #Unitary state #Unitary transformation #Variety (cybernetics) #quant-ph

paper · pdf · doi:10.1103/physreva.97.022328

published in Physical Review A 97(2) (American Physical Society) · 5 pages, 4 figures. Comments welcome!

openalex publication_date 2018/02/20 · arxiv created 2018/03/06 · arxiv updated 2018/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We demonstrate a method for general linear optical networks that allows one to factorize any SU(n) matrix in terms of two SU(n\ensuremath-1) blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in a straightforward way, ending in a tidy arrangement of SU(2) transformations. The method hinges only on a linear relationship between input and output states, and can thus be applied to a variety of scenarios, such as microwaves, acoustics, and quantum fields.

Citations

• Direct dialling of Haar random unitary matrices
• Representations of the Weyl group and Wigner functions for SU(3)
• Randomizing Quantum States: Constructions and Applications
• Coherent states: Theory and some applications
• Boson Sampling on a Photonic Chip
• Realization of Quantum Walks with Negligible Decoherence in Waveguide Lattices
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,\mathbb C)SL(N,C) Clebsch–Gordan coefficients
• Elementary gates for quantum computation
• Synthesis of Quantum Logic Circuits
• Reducing quantum computations to elementary unitary operations
• Quantum Theory of Angular Momentum

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