Non-Gaussian operations are indispensable for simulating nonlinear dynamics on quantum computers, especially within the continuous-variable and photonic computing paradigms. However, the implementation of non-Gaussian gates remains a significant challenge, often relying on strong optical nonlinearities or probabilistic, ancilla-assisted protocols. Moreover, the procedures to describe dynamics in dissipative theories remain unexplored. This work focuses on the design and feasibility of non-Gaussian gate constructions aimed at solving Burgers' equation, offering broader insight into the practical realization of non-Gaussian resources for quantum simulation of nonlinear fluid dynamical systems. A central motivation for exploring continuous-variable quantum computing (CVQC) is its potential to represent and process physical systems in a manner that more naturally reflects their underlying continuity. In classical computational methods, accurately capturing shock waves and other discontinuities in nonlinear systems is notoriously challenging. In the CVQC framework, however, these difficulties may be alleviated. CVQC is a model of quantum computation that encodes information in continuous spectra. Thus, it supports high-dimensional encoding. CVQC is particularly well-suited for implementation in photonic systems, where light modes naturally carry quantum information. Combining CVQC with quantum optics will benefit from the low decoherence properties of photons, meaning that the quantum information carried by the photons remains stable, and photon-based gate operations are likely to preserve this information. Since qumodes operate in infinite-dimensional Hilbert spaces and natively encode continuous field amplitudes, CVQC offers the potential to represent steep gradients and discontinuities without the need for explicit grid-based resolution. Moreover, the intrinsic unitarity of quantum evolution may naturally preserve features such as entropy conditions and wavefront coherence, which are often problematic in classical solvers. While the practical implementation remains a subject of ongoing research, the photonic CVQC paradigm presents a fundamentally different approach—one that could offer significant advantages in modeling nonlinear phenomena involving shocks.