Scattering with universal quantum computers

In high-energy physics, the limitations of computational time and memory capacity restrict the extent of simulations that can be performed using classical digital computers. This dissertation develops and demonstrates a practical framework for computing scattering observables using universal quantum computers. Motivated by the growing potential of quantum computation to address real-time dynamics in exponentially large Hilbert spaces, we present methods that map continuum and lattice scattering problems to efficiently implementable quantum circuits. Central to the approach is a time-domain protocol: by comparing real-time evolution with and without an interaction potential, scattering phase shifts are measured directly from time delays; these phase shifts are converted into transmission probabilities to identify resonances and validated against finite-volume spectroscopy. We describe state-preparation strategies, Hamiltonian simulation techniques, and optimized measurement primitives tailored to near-term processors and scalable to fault-tolerant devices.

Numerical studies and hardware-oriented implementations in IBM Qiskit illustrate the approach for few-body nonrelativistic scattering and simple field-theory models, with detailed error analysis and resource estimates that quantify discretization, Trotterization/qubitization, and readout overheads. The results demonstrate that quantum simulations can access dynamical regimes and resonance phenomena challenging for classical methods, offering potential quantum advantage for problems in particle, nuclear, and condensed-matter physics. This work establishes practical algorithms, benchmarks, and implementation targets that inform the progression from noisy intermediate-scale experiments to large-scale, fault-tolerant simulations of scattering processes.