Analog Quantum Simulation via Parametric Interactions in Superconducting Circuits

dc.contributor.authorBUSNAINA, JAMAL
dc.date.accessioned2023-09-19T13:16:19Z
dc.date.available2023-09-19T13:16:19Z
dc.date.issued2023-09-19
dc.date.submitted2023-09-15
dc.description.abstractWhile universal quantum computers are still years away from being used for simulating complicated quantum systems, analog quantum simulators have become an increasingly attractive approach to studying classically intractable quantum systems in condensed matter physics, chemistry, and high-energy physics. In this dissertation, we utilize superconducting cavities and qubits to establish analog quantum simulation (AQS) platforms to study systems of interest. An approach of AQS that has gained interest lately is the use of photonic lattices to simulate popular lattice models. These systems consist of an array of cavities or resonators arranged on a lattice with some couplings graph between modes. We propose an in situ programmable platform based on a superconducting multimode cavity. The unique design of the cavity allows us to program arbitrarily connected lattices where the coupling strength and phase of each individual coupling are highly programmable via parametrically activated interactions. Virtually, any quadratic bosonic Hamiltonian can be realized in our platform with a straightforward pumping scheme. The effectiveness of the cavity-based AQS platform was demonstrated by the experimental simulation of two interesting models. First, we simulated the effect of a fictitious magnetic field on a 4-site plaquette of a bosonic Creutz ladder, a paradigmatic topological model from high-energy physics. Under the right magnetic field conditions, we observed topological features such as emergent edge states and localized soliton states. The platform's ability is further explored by introducing pairing (downconversion) terms to simulate the Bosonic Kitaev chain (BKC), the bosonic version of the famous Fermionic Kitaev chain that hosts Majorana fermions. We observe interesting properties of BKC, such as chiral transport and sensitivity to boundary conditions. In the final part of the dissertation, we propose and implement a parametrically activated three-qubit interaction in a circuit QED architecture as the simplest building block to simulate lattice gauge theories (LGT). LGT is a framework for studying gauge theories in discretized space-time, often used when perturbative methods fail. The gauge symmetries lead to conservation laws, such as Gauss's law in electrodynamics, which impose constraints tying the configuration of the gauge field to the configuration of ''matter'' sites. Therefore, any quantum simulation approach for LGTs must maintain these conservation laws, with one strategy in AQS being to build them in at the hardware level. Here, the gauge constraints are explicitly included using a higher-order parametric process between three qubits. The simplest 2-site U(1) LGT building block is realized with two qubits as matter sites and a third qubit as the gauge field mediating the matter-matter interaction, which is crucial to maintain the symmetry of U(1) LGTs.en
dc.identifier.urihttp://hdl.handle.net/10012/19882
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectquantum simulationen
dc.subjectanalog quantum simulationen
dc.subjectqubiten
dc.subjectsuperconductingen
dc.subjectquantum computingen
dc.subjectnonHermitianen
dc.subjectlattice modelsen
dc.subjectlattice gauge theoriesen
dc.subjectparametric interactionen
dc.subjectquantum physicsen
dc.subjectthree body interactionen
dc.titleAnalog Quantum Simulation via Parametric Interactions in Superconducting Circuitsen
dc.typeDoctoral Thesisen
uws-etd.degreeDoctor of Philosophyen
uws-etd.degree.departmentElectrical and Computer Engineeringen
uws-etd.degree.disciplineElectrical and Computer Engineering (Quantum Information)en
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.embargo.terms0en
uws.contributor.advisorWilson, Christopher
uws.contributor.affiliation1Faculty of Engineeringen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Busnaina_Jamal.pdf
Size:
22.64 MB
Format:
Adobe Portable Document Format
Description:

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
6.4 KB
Format:
Item-specific license agreed upon to submission
Description: