We develop and analyze a fault-tolerant quantum algorithm for computing $ n $-th order
response properties necessary for analysis of non-linear spectroscopies of molecular and …

Estimating the eigenstate properties of quantum many-body systems is a long-standing,
challenging problem for both classical and quantum computing. For the task of eigenstate …

Efficient classical simulation of the Schrodinger equation is central to quantum mechanics,
as it is crucial for exploring complex natural phenomena and understanding the fundamental …

As a signal recovery algorithm, compressed sensing is particularly effective when the data
has low complexity and samples are scarce, which aligns natually with the task of quantum …

Solving quantum molecular systems presents a significant challenge for classical
computation. The advent of early fault-tolerant quantum computing (EFTQC) devices offers a …

We compare several quantum phase estimation (QPE) protocols intended for early fault-
tolerant (EFT) quantum computers in the context of models of their implementations on a …

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have
demonstrated remarkable efficiency in extracting key spectral information. However, the …

Spectral estimation is a fundamental task in signal processing. Recent algorithms in
quantum phase estimation are concerned with the large noise, large frequency regime of the …

ALGORITHMS AND NUMERICAL ANALYSIS IN QUANTUM COMPUTING A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MATHEMATICS AND THE COMMITT Page 1 …