Designing Physics-Informed Quantum Simulations with Qubits and Qudits

Simulating the real-time dynamics of interacting quantum systems is a long-standing challenge for classical computation. This thesis studies how quantum computers can address this challenge in three settings from nuclear and particle physics: collective neutrino oscillations, low-energy nuclear dynamics, and lattice gauge theories coupled to matter. We examine how the choice of encoding, simulation algorithm, and error-correction strategy affects the resources needed to simulate each system. For collective three-flavour neutrino oscillations, we develop qubit and qutrit circuits and implement them on superconducting quantum processors. We compare their gate requirements and sensitivity to noise, and show that error mitigation yields flavour probabilities in agreement with theoretical predictions for several time steps. For nuclear dynamics described by pionless effective field theory, we formulate the problem in first quantization and derive explicit resource estimates for product-formula and quantum-signal-processing algorithms. In the dilute regime relevant to nuclear scattering, first-quantized methods reduce both logical-qubit and gate requirements relative to second-quantized approaches. Among the methods considered, generalized quantum signal processing gives the lowest estimated gate cost. These time-evolution estimates suggest that low-energy nuclear scattering could be a candidate application for early fault-tolerant quantum computers. Finally, we investigate how the local symmetries of lattice gauge theories can provide part of the redundancy needed for quantum error correction, helping to reduce the additional encoding overhead. For ZN gauge theories with prime N encoded on N-level qudits, we show that Gauss's law defines a code protecting against bit-flip errors. We identify its logical operators with gauge-invariant observables and use them to derive a bosonic dual description. We then extend the construction to qubit encodings of ZN gauge theories with N a power of 2, where the constraints require stabilizers beyond the Pauli group, and show how these constraints can still be used for error correction and gauge fixing. This paves the way to more efficient encodings, and introduces new tools for the study of lattice gauge theories. Together, these results show how physical structure can guide the choice of encodings, algorithms, and error-correction schemes for more resource-efficient quantum simulation.