Quantum simulation with periodically driven superconducting circuits

Abstract

Superconducting quantum circuits have made tremendous advances in realizing engineered quantum dynamics for quantum simulation and quantum information processing over the past two decades. Technological developments in the field of superconducting circuits have raised them to be the leading platform for implementing many-qubit systems. This thesis introduces a sequence of concepts for engineering spin-lattice Hamiltonians in analog quantum simulation with superconducting circuits. Our approach to quantum simulation is to engineer driving schemes that lead to implementations of the desired models. The applications of this approach are in our work mainly centered around two types of systems: interesting many-body topological quantum systems, namely Kitaev’s toric code and honeycomb model and two-body systems that can be employed as building blocks of larger quantum simulators or quantum computers. In the first part of this thesis, we make a proposal for an analog implementation of the toric code in superconducting circuits. We also discuss a realistic implementation of this model on an eight qubit lattice. In the second part, we present our analog approach for implementing arbitrary spinspin interactions in linearly and nonlinearly coupled superconducting qubits. Our proposed toolbox has the potential of easy generalization to a variety of systems and interactions. Lastly, based on our two-body toolbox, we set forward two possible implementations of the Kitaev honeycomb model and show that the engineered two-body interactions work - with good accuracy - in this many-body model.