A thorough understanding of non-equilibrium quantum mechanical phenomena provides the means to develop advanced and novel technologies. With growing expertise and improving controllability of quantum systems, a plethora of use-cases has emerged that employ and exploit physical processes for technological benefit. In this cumulative dissertation, I present my work on some of such research directions, such as controlling the non-equilibrium transport properties of graphene, engineering a non-equilibrium superradiant phase in driven two-band solids coupled to cavities, non-local quantum algorithm optimization on the native Hamiltonian level, and dynamics of superfluids in the presence of particle-hole symmetry. We have devised a master equation approach for the driven dissipative electron dynamics in graphene, which recovers experimental non-equilibrium transport measurements. We have used this model to characterize the anomalous Hall response, in which the geometric contribution to the transversal current is determined by the non-equilibrium electron distribution across the light-induced topological Floquet-Bloch band structure. The light-induced gap at the Dirac point is often obscured in time-resolved angle-resolved photoelectron spectroscopy (trARPES) due to experimental limitations. I have predicted that strong driving leads to Floquet-Bloch band populations at the Dirac point which display an energy difference that extends far enough beyond Floquet replicas to overcome resolution limitations in trARPES setups. Similarly, I have studied the optical conductivity of driven graphene at terahertz frequencies, which displays the Floquet gap at the Dirac point in particular, due to resonant inter-band transitions across the Floquet-Bloch bands. In the presence of strong driving, the optical conductivity changes its sign and the system displays optical gain due to an effective population inversion of the Floquet-Bloch bands. This has motivated me to study a graphene-inspired quantum optical model, in which I have found that a non-equilibrium superradiant phase emerges due to the same mechanism of population inverted Floquet states which sustain a coherent state in a resonant cavity. I refer to this as the Floquet-assisted superradiant phase (FSP), and have studied its stability in the presence of environmental factors, such as inhomogeneous broadening, driving with finite decoherence, and dissipation. The FSP appears robust under realistic conditions, which suggests its utilization in a type of Floquet-assisted laser-like mechanism at terahertz frequencies in a graphene-cavity setup in future research. Quantum computing faces the challenge of meticulously controlling quantum information across scalable systems. The more pragmatic near-term utilization of noisy intermediate-scale quantum (NISQ) devices draws attention to the potential of hybrid quantum-classical optimization algorithms. I have identified benefits of non-local quantum algorithm optimization approaches which act on the underlying Hamiltonian level rather than in the circuit picture of variational quantum algorithms (VQAs). I have found that a parameterization that optimizes the Fourier coefficients of the control parameters of the Hamiltonian displays improved optimization behavior and indicates a mitigation of the barren plateau phenomenon which plagues conventional VQAs. Similarly, we have optimized high fidelity implementations of the controlled NOT gate in the quantum computing architecture of neutral atoms in tweezer arrays under realistic conditions. We have considered non-local restrictions on the control parameters, which do not affect the computational universality of the architecture. This motivates future proposals that involve less intricate and more easily constructed NISQ computers. Superfluid states of matter such as Bose-Einstein condensates (BECs) and BCS-like condensates of neutral fermions display dynamics that are relevant for quantum simulation, superconducting devices such as Josephson junctions, and atomtronics. The order parameter of such superfluid phases is captured in effective field theories. We have developed a two-dimensional numerical simulation of an effective field theory which includes terms that interpolate between the presence and absence of particle-hole symmetry. The presence of this symmetry is accompanied by an amplitude mode that is present in BCS-like systems, but not in BECs. This theory thus captures both BEC-like and BCS-like superfluids in a manner that connects them continuously. We have demonstrated how the dynamics of defects such as vortices and solitons are affected considerably by the presence of particle-hole symmetry and the imbalance between particles and holes.