Developing techniques for Simulation of SU(3) Quantum Field Theories on State-of-the-Art Quantum Devices

Abstract

Quantum computing has long been an experimental technology with the potential to enablesimulation at scale of phenomena which on classical devices would be too expensive to simulate at any but the smallest scales. Over the last several years, however, it has entered the NISQ era, where the number of qubits are sufficient for quantum advantage but substantial noise on hardware stands in the way of this achievement. This thesis details improvements to techniques of quantum simulation of the out-of-equilbrium real-time dynamics of lattice quantum chromodynamics (LQCD) and of dense 3-flavor neutrino systems on digital quantum devices that I have contributed to as a Ph.D. student. LQCD has been numerically computed using classical Monte-Carlo methods for decades with applications to nuclear and particle physics. However, classical Monte-Carlo methods experience the numerical sign problem, which limits their ability to solve problems such as the simulation of out-of-equilibrium real-time evolution. These problems are an ideal place to look for quantum advantage. The first project in this part is a comparison of gradient descent and the Bayesian process as choices for the classical optimizer within a variational quantum eigensolver that initializes the ground state of an SU(3) plaquette-chain. The thesis then pivots to a 1+1D lattice of quarks interacting with an SU(3) gauge-field. A VQE-based statepreparation for the vacua and a Trotterized time-evolution circuit is designed and applied to the problems of simulating beta and neutrinoless double beta decay. The latter has been implemented on Quantinuum's H1-1 trapped ion device. Finally, these circuits are adapted to a version useable on quantum devices with nearest-neighbor connectivity with minimal overhead, with an eye towards utilizing the higher qubit count of such devices for hadron dynamics and scattering. Physical dense neutrino systems are both highly out-of-equilibrium and are characterized by a highly entangling interaction, neutral current exchange between neutrinos. This makes the dynamics of dense neutrino systems, particularly the relatively not-well-studied 3-flavor variety, an ideal problem to attempt to solve with quantum computers. In this part, Trotterization circuit-elements for the neutrino-neutrino interactions that happen in ultradense 3-flavor neutrino systems are designed and implemented on Quantinuum's H1-1 trapped ion device and IBM's ibm torino superconducting device. A circuit for Trotterizing this interaction on qutrits, which is substantially lower in depth than its qubit counterparts, is also created. Lastly, by the Gottesman-Knill theorem problems need to exhibit both high entanglement and high deviation from stabilizer states ("magic") in order to exhibit quantum advantage. Thus, the second-to-last chapter of the thesis detail results with implications for the Standard Model in general that the 3 flavor ultradense neutrino systems with the highest, most-persistent magic are those that start with neutrinos in all 3 flavors.