Christopher Francis Kane, Physics Graduate Student

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**Abstract:** Flavor physics serves as a powerful method for constraining beyond the Standard Model physics. The hadronic contribution of these decays is described by Quantum Chromodynamics (QCD), which, at hadronic energy scales, requires a non-perturbative approach. By defining QCD on a Euclidean space-time lattice, the path integral can be solved numerically in a non-perturbative way using Monte Carlo methods. Using lattice QCD, theoretical predictions in flavor physics can be compared to experimental results. In the first part of this dissertation, we develop lattice QCD methods for high-precision studies of a class of decays known as radiative leptonic decays, where a pseudoscalar meson $H$ decays into a real photon and a pair of leptons.

Our methods are applicable to both the charged meson decays $H^+ \to \gamma \ell^+ \nu$, $H^- \to \gamma \ell^- \bar{\nu}$ and the neutral meson decays $H \to \gamma \ell^+ \ell^-$. Studying these decays will provide novel insight into tensions between experimental measurements and theoretical predictions present in $b \to s \ell^+ \ell^-$ decays.

While lattice QCD has revolutionized the understanding of hadronic non-perturbative physics in the Standard Model, as with any computational method, it has inherent limitations. In particular, due to the numerical sign problem, classes of non-perturbative physics, including real-time dynamics and finite density nuclear matter, cannot be studied using lattice QCD. One novel computational method that can in principle overcome the limitations of the sign problem is to perform the calculation using quantum computers. In the second part of this dissertation, I present several studies focused on developing methods for efficient quantum simulations of lattice field theories. In particular, we study how to overcome an exponential scaling in the cost of naively time-evolving a fully gauge-fixed formulation of a U(1) lattice gauge theory using Trotter methods. Turning to the crucial problem of initial state preparation, we study a recently developed ground state preparation algorithm based on the Quantum Eigenvalue Transformation for Unitary matrices (QETU). In addition to improving the original algorithm, we apply this algorithm to a particular formulation of a U(1) lattice gauge theory, as well as develop a new use case of QETU for the efficient preparation of Gaussian states. The final project in this dissertation focuses on comparing several time-evolution algorithms applied to general lattice field theory Hamiltonians. We derive general expressions for the cost of these algorithms that can be readily applied to a broad class of lattice field theories. Furthermore, we develop improved methods for block-encoding local bosonic operators for scalar field theories. Taken together, these results represent progress towards performing quantum simulations of lattice gauge theories on future quantum devices.