Reconfigurable boson sampling

Theory • Introduction to Quantum Theory Introduction to quantum theory, Fock state, quadrature operator, and the related phase-space relations, including the Wigner function. • Gaussian Information Theory Gaussian information theory, squeezed states, symplectic phase space, and the associated transformations for the boson sampling components (beam splitter, phase shifter, Asymmetric MZI). • SPDC (Spontaneous Parametric Down-Conversion) SPDC with the relationship between squeezing and entanglement. Graph Theory • Introduction to Graph Theory Introduction to graph theory and the adjacency matrix. • Symmetric Matrix and Complexity Theory Symmetric matrices and the relationship between the determinant, permanent, Pfaffian, and Hafnian, along with complex algorithm theory and its relation to the complexity of linear optical circuits. • Decomposition Autonne-Takagi decomposition and unitary matrix decomposition. Boson Sampling • Classical Boson Sampling Classical boson sampling, the structure of the experiment, and a general explanation. • Gaussian Boson Sampling (GBS) Gaussian boson sampling, analysis of the relationship between phase-space relations and Hafnian theory, and a comparison of scattershot boson sampling to GBS. • Applications of GBS Encoding of the unitary matrix on an interferometric circuit with explanation of applications, particularly the use of GBS for finding perfect matchings in graphs, along with other applications. • Conclusion Concluding remarks on boson sampling, including an explanation of the state-of-the-art developments. Design of a TM Waveguide Crosser for a Bipartite Boson Sampling Circuit • Design Choices and Characterization Explanation of the design choices and characterization process. Characterization of the Unitary Matrices of a reconfigurable 10x10 interferometric circuit(on-going) • Experiment Explanation Detailed explanation of the experiment and the expected results. • Results Analysis Analysis of the results, followed by explanations and conclusions.