Simulation algorithms, Floquet phenomena and superconducting qubits

This thesis explores topics that span the abstraction stack of quantum computing: from physical properties of superconducting qubits to computational properties of algorithms for quantum simulation. In the introduction, we begin by reviewing the circuit model of quantum computing. We then introduce circuit quantum electrodynamics (QED), the framework by which superconducting electrical circuits are theoretically modeled, as well as Floquet physics. After a primer on numerical analysis of these systems, we conclude with a discussion of logical errors in physical qubits. In Chapter 2 we present the Floquet fluxonium molecule, a new highly coherent superconducting qubit which is stabilized against ambient noise effects with a strong drive. In Chapter 3 we discuss phenomena related to dispersive readout of fluxonium qubits. In that Chapter we present a new classical simulation algorithm for simulating Floquet dynamics of dispersive readout out to large photon populations using asymptotically fewer computational resources than the prior state of the art. In Chapter 4 we investigate the quantum computational complexity of preparing ground states of Hamiltonians, focusing on the role of frustration. We identify a class of Hamiltonians which are close to being frustration free and point out that they have interesting complexity properties. We give a quantum algorithm for preparing ground states of these Hamiltonians and show that the quantum query complexity is asymptotically improved compared to the general case.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Thibodeau, Matthew G.

Contributors dc:contributor

• Clark, Bryan K
• Stone, Michael
• Leditzky, Felix
• Kou, Angela

• quantum
• qubit
• qubits
• superconducting
• Floquet
• simulation

Statement dc:rights

• Copyright 2025 Matthew Thibodeau

Language dc:language

en

Handle dc:identifier

https://hdl.handle.net/2142/132466

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/132466