Calculating Nature Naturally: Toward Quantum Simulation of Quantum Fields

Abstract

Physics experiments are carefully designed to have precisely controlled inputs and to interact with an isolated aspect of nature in such a way that the results can be inverted to systematically inform our knowledge of the Hamiltonian of the universe. From the other direction, computation imprints the precisely-known isolated Hamiltonian of a distributed computational framework with a conjecture of the universe's Hamiltonian to calculate the physical implications of a proposed theoretical design. In this way, physics is able to connect theory and experiment, even in non-perturbative physical regimes eluding analytic solution. The recent emergence of experimentally controllable quantum systems inspires the possibility of dramatically altering the paradigm with which properties of quantum many body systems are calculated---employing quantum systems at the center of the precisely-known computational framework. Beyond intellectual entertainment, this proposal of leveraging quantum properties of entanglement, interference and superposition as advantageous computational resources illuminates the only currently envisioned avenue for calculating dynamical properties of large quantum systems. The research presented in this dissertation contributes to the practical and conceptual formulation of quantum simulation for lattice field theories. Beginning in the scalar field, an explicit exploration is presented of the quantum resources required for digital time evolution on a position-space lattice with varying digitization protocols. Using the ground state of the interacting scalar field as a ubiquitous example, techniques are developed allowing quantum operations for the preparation of entangled wavefunctions to exhibit the localization present in the exponentially localized correlations of the simulated field. Applying these techniques to lattices of large spatial volume provides a non-dynamical approach for initializing beyond-classical ground state wavefunctions informed by tractable classical calculations. Demonstrated on superconducting quantum circuits, simulations of dynamical quantum fluctuations in one-dimensional U(1) and SU(2) gauge theory are presented. Utilizing the recently developed quantum frequency processor, vacuum polarization due to external charges in U(1) gauge theory and the binding energy of light nuclei in pionless effective field theory are calculated. Error mitigation techniques for current hardware are further developed and applied to the state preparation of a wavefunction localized in Hilbert space with a symmetry-dominated entanglement structure. With the presented combination of field-inspired circuit design, quantum implementation of small gauge theories, and initial quantification of entanglement fluctuations in the scattering of low-energy nuclei, the research associated with this dissertation has developed practical techniques and long-term perspectives on the design of field theories for quantum simulation and vice versa.