Resource-Efficient Quantum Simulations of Lattice Gauge Theories

Future large-scale quantum computers (QCs) can be a revolutionary tool for first-principle calculations in strongly coupled quantum field theories, which are essential in many scenarios in particle physics. Meanwhile, due to the unique features of our problems, many theoretical and algorithmic challenges need to be addressed before particle physics can take advantage of the ongoing quantum revolution. This thesis discusses how to efficiently utilize QCs for real-time simulations of gauge interactions in quantum field theories, focusing on two aspects. The first aspect is the reduction of space-time discretization errors via renormalization and improved Hamiltonians. We show that trotterization entails renormalization of the temporal and spatial lattice spacings. Based on the tools of Euclidean lattice field theory, we propose two schemes to determine Minkowski lattice spacings, using Euclidean data and thereby overcoming the demands on quantum resources for scale setting. In addition, Hamiltonians with improved discretization errors will reduce the number of qubits required by a factor of $\gtrsim 2^d$ in quantum simulations for lattices with $d$ spatial dimensions. We consider $\mathcal{O}(a^2)$-improved Hamiltonians for pure gauge theories and design the corresponding quantum circuits for its real-time evolution in terms of primitive gates. Numerical demonstrations with real and classically simulated quantum computers are included. The second aspect concerns gauge symmetries, which can be either fixed or encoded as a redundancy of the Hilbert space in quantum simulations. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy enables quantum error corrections by checking and restoring Gauss's law. In this work, we consider generic finite gauge groups and design the quantum circuits to detect and correct the symmetry-violating errors. We calculate the error thresholds below which the gauge-redundant digitization with Gauss's law error correction has better fidelity than the gauge-fixed digitization. Our results provide guidance for fault-tolerant quantum simulations of lattice gauge theories.