Towards Continuous Variable Quantum Computation of Lattice Gauge Theories

The calculation of physical quantities in a relativistic quantum field theory (rQFT) is a computationally demanding task due to the presence of an infinite number of degrees of freedom. This problem carries over to discretized versions of these theories, i.e. lattice field theories, where the Hilbert space size increases exponentially with the size of the lattice. Despite the success of some classical techniques such as Monte Carlo, their applicability is limited. For instance, Monte Carlo is associated with a sign problem that makes real-time evolution and high-fermion-density systems particularly challenging to compute. Quantum computation is a promising avenue thanks to the fact that quantum computers are quantum by nature and can efficiently simulate such systems. However, lattice gauge theories pose additional complications such as the demand for gauge invariance and the infinite Hilbert spaces corresponding to every bosonic degree of freedom. One way to address the latter is through continuous variables quantum computation, whose fundamental units of quantum information are the bosonic ``qumodes.” In this dissertation, I will discuss the quantum computation of lattice field theories in both qubit and qumode settings, with a focus on methods applicable to lattice gauge theories and systems with phase structure. I will review our qubit quantum computations of an interacting fermionic model and the lattice Schwinger model, and then present CV quantum computing techniques that can more efficiently address bosonic degrees of freedom in interacting scalar field theories as well as non-linear sigma models. These algorithms make effective use of the “easy” Gaussian operations and photon number measurements, and provide setups for more complicated models such as SU(2) non-Abelian gauge theory.