Theses and Dissertations

ORCID

0009-0006-6415-369X

Advisor

Rupak, Gautam

Committee Member

Novotny, Mark

Committee Member

Finke, Doug

Committee Member

Dutta, Dipangkar

Committee Member

Crider, Benjamin; Novotny, Mark

Date of Degree

8-12-2026

Original embargo terms

Embargo 6 months

Document Type

Dissertation - Open Access

Major

Physics

Degree Name

Doctor of Philosophy (Ph.D.)

College

College of Arts and Sciences

Department

Department of Physics and Astronomy

Abstract

This dissertation develops and analyzes quantum computational algorithms for structured Hamiltonians that arise in three physics settings — strongly interacting few-body nuclear systems, electron transport through condensed-matter nanodevices, and open quantum systems at finite temperature — and complements these algorithmic studies with a fault-tolerant resource-estimation analysis of the hardware required to execute them beyond the reach of classical simulation. For nuclear elastic scattering, the two-particle phase shift produced by a short-range interaction is obtained by trapping the particles in a harmonic potential and computing the resulting ground-state energy with a variational quantum eigensolver. A relaxation-based classical optimizer is paired with a Schmidt decomposition of the trial state so that circuits that nominally need many qubits are reduced to two-qubit operations, lowering the sensitivity to noise on near-term hardware. For electron transport, linear and nonlinear nanodevices known as quantum dragons are reformulated as the linear systems that arise from a non-equilibrium Green's-function description, then solved on a quantum platform using a variational quantum linear solver, a coherent variant augmented with fixed-point amplitude amplification, and an exact quantum linear-systems algorithm based on phase estimation. The framework is extended to a sixty-atom graphene nanoribbon represented as stacked three-site quantum-dragon slices, and a quantum-adapted Gauss–Seidel update is introduced as a physics-informed optimizer that aids convergence. For open quantum systems at finite temperature, two subspace-diagonalization schemes — a Krylov-based method and a prolate-spheroidal method built on the Hadamard test — are formulated to extract decoherence and thermalization observables for a one-dimensional harmonic oscillator on a lattice and for the spin-boson model. The algorithms are benchmarked on ideal and noisy simulators using standard depolarizing, thermal-relaxation, and readout error channels. A concluding outlook estimates the qubit counts, gate counts, and logical error rates that a fault-tolerant device would need to execute each algorithm, and applies hardware-specific cost models to current superconducting platforms. Together, the results connect algorithm design, near-term feasibility, and the longer-term hardware roadmap for quantum simulation in nuclear and condensed-matter physics.

Sponsorship (Optional)

This work was partially supported by grants DOE DESC00211, DOE DE-SC0024286 and NSF PHY-2209184.

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