  Broadly speaking, this thesis is about nonlinear optics, quantum mechanics,
and computing. More specifically, it covers four main topics: Coherent LQG
Control, Free-Carrier Oscillations, Optical Ising Machines and Pulsed OPO
Dynamics. Tying them all together is a theory of open quantum systems called
the SLH model, which I introduce in Chapters 1-2. The SLH model is a general
framework for open quantum systems that interact through bosonic fields, and is
the basis for the quantum circuit theory developed in the text. Coherent LQG
control is discussed in Chapters 3-4, where I demonstrate that coherent
feedback outperforms measurement-based feedback for certain linear
quadratic-Gaussian (LQG) problems, and explain the discrepancy by the former's
simultaneous utilization of both light quadratures. Semiclassical
truncated-Wigner techniques for quantum-optical networks are discussed in
Chapter 5, leading to a thorough discussion of quantum noise in systems with
free-carrier nonlinearities (Chapter 6), comparison to the Kerr nonlinearity,
and potential applications for analog computing based on limit cycles and
amplification (Chapters 7-8). Ising machines based on optical parametric
oscillators (OPOs) are discussed in Chapters 9-10, the former focusing on large
1D and 2D networks of OPOs, and the latter on the dynamics of a single OPO in
the ultrafast, synchronously-pumped regime. Optical properties and design
considerations for silicon photonic waveguides are are treated in Chapter 11.
