Algorithms and numerical analysis in quantum computing
Abstract/Contents
- Abstract
- This dissertation delves into multiple facets of quantum computing and quantum algorithms from the perspective of an applied mathematician or numerical analyst and is segmented into four parts: 1. Efficient and Robust Quantum Phase Estimation (QPE) Algorithms: The first part presents a suite of efficient and robust QPE algorithms, tailored for early fault-tolerant quantum devices in the sense that they (1) use a minimal number of ancilla qubits, (2) allow for inexact initial states with a significant residual, (3) achieve the Heisenberg limit for the total resource used, and (4) have a diminishing prefactor for the maximum circuit length when the residual approaches zero. 2. Advanced Hamiltonian Learning Techniques: The second part discusses two efficient algorithms that deal with the Hamiltonian learning problem for many-body Fermionic and Bosonic systems. 3. Block-encoding of Pseudo-Differential Operators: In the third chapter, the focus shifts to the development of novel algorithms for the encoding of pseudo-differential operators, enhancing the quantum computing toolkit with more explicit and effective block-encoding strategies. 4. Optimization algorithms for Variational Quantum Circuits: Concluding the dissertation, a reinforcement learning-based algorithm is presented, offering new avenues for solving the difficult optimization problem of variational circuits.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2024; ©2024 |
| Publication date | 2024; 2024 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Li, Haoya |
|---|---|
| Degree supervisor | Ying, Lexing |
| Thesis advisor | Ying, Lexing |
| Thesis advisor | Candès, Emmanuel J. (Emmanuel Jean) |
| Thesis advisor | Papanicolaou, George |
| Degree committee member | Candès, Emmanuel J. (Emmanuel Jean) |
| Degree committee member | Papanicolaou, George |
| Associated with | Stanford University, School of Humanities and Sciences |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Haoya Li. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2024. |
| Location | https://purl.stanford.edu/sy552gp7613 |
Access conditions
- Copyright
- © 2024 by Haoya Li
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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