Modeling Superconducting Circuits for Quantum Computing and Quantum Sensing Applications

Abstract

Superconducting circuits are at the forefront of quantum computing and quantum sensing technologies, where accurate modeling and simulation are crucial for understanding and optimizing their performance. In this dissertation, we study modeling techniques and novel device designs to advance these technologies, focusing on efficient simulations, direct velocity measurement, and nonreciprocal devices for quantum information processing. First, we investigate the use of discrete variable representations~(DVRs) to numerically represent superconducting circuits, exploring their use and effectiveness in several prototypical examples. We find that not only are these DVRs capable of achieving decoherence-accurate simulation, i.e., accuracy at the resolution of experiments subject to decay, decoherence, and dephasing, they also demonstrate improvements in efficiency with smaller basis sizes and better convergence over current standard approaches, showing that DVRs are an advantageous alternative for representing superconducting circuits.

We then consider a specific quantum sensing application, direct velocity measurement in superconducting circuits. We propose and characterize theoretical models for backaction evading, direct velocity measurement that utilize traditional electric and magnetic transducers. We consider the readout of this signal via electric or magnetic field sensing by creating generic models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme --- voltage or current --- for each mechanical detector configuration implies access to either the position or velocity of the mechanical sub-system.

Finally, we explore the application of superconducting circuits in nonreciprocal devices, such as circulators. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large magnetic fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order --- such as the $XY$ model --- can be realized at much lower magnetic fields by using arrays of superconducting islands connected by Josephson junctions. Here we show that the quantum-coherent motion of a single vortex in such an array suffices to induce nonreciprocal behavior, enabling a small-scale, moderate-bandwidth, and low insertion loss circulator at very low magnetic fields and at microwave frequencies relevant for experiments with qubits.