Digital Quantum Simulation of Dynamics in Interacting Fields

Abstract

Matter under extreme conditions behaves as a non-equilibrium, strongly-interacting quantum system. One example is the quark-gluon plasma, which briefly filled the early universe and is now recreated in particle accelerators like the Large Hadron Collider. Such systems are in the non-perturbative regime of quantum chromodynamics (QCD), where their time evolution is classically intractable. Quantum computing offers a promising tool for simulating their real-time dynamics directly. Present-day noisy intermediate-scale quantum (NISQ) hardware is limited in qubit count and circuit depth, so developing efficient formulations and algorithms is key both to current demonstrations and to scaling toward experimentally relevant QCD simulations. This dissertation spans different formulations of the SU(2) lattice gauge theory as well as the scalar field theory, constructing scalable quantum circuits for these formulations and introducing physics-aware truncation methods. All proposed simulations are validated on quantum hardware, with results in agreement with classical benchmarks. A scalable framework is established for simulating energy loss and hadronization in 1+1-dimensional SU(2) lattice gauge theory, in which a heavy quark traverses a lattice of light quarks. Classical lattice QCD methods are translated into physics-informed quantum circuits to prepare the interacting ground state. The evolution is run on IBM's quantum processor ibm_pittsburgh, and observables including charge distribution and energy loss are measured on the hardware. A further study develops the quantum simulation of the fully gauge-fixed SU(2) Hamiltonian in a mixed basis, a formulation that is expected to remain efficient at all gauge couplings. The continuous gauge fields can be digitized with as few as three qubits per plaquette to reproduce low-energy observables with 10^{-3} precision. Progress to larger systems on present-day hardware is limited by resource overhead, which motivates truncations that preserve the relevant observables. Sequency Hierarchy Truncation (SeqHT) exploits the hierarchy in the contributions of basis operators. Demonstrated on the adiabatic preparation of the λϕ4 ground state on ibm_sherbrooke, SeqHT reduces circuit depth by ~30%, suppressing hardware noise in the extracted observables. Together, these studies contribute toward quantum simulations of real-time QCD dynamics inaccessible to classical computation.