Quantum algorithms for learning and learning algorithms for quantum
Abstract/Contents
- Abstract
- Machine learning has established itself as one of the most successful computational paradigms of the 21st century. Quantum computation is attempting to be the next one. What algorithmic and theoretical insights can each of these fields gain from the other? We first apply the tools of machine learning and its theoretical counterpart, computational learning theory, to a famously resource-intensive operation at the heart of quantum experiments: quantum state tomography. It is the following task: given many identically-prepared copies of the same n-qubit quantum state, output an approximation of its density matrix, which has 2^n numbers. We consider performing adaptive measurements on the state. We design a neural network that `learns to learn' the correct measurement, which also speeds up a previous proposal for adaptive Bayesian updates in tomography by a factor of a million for a realistic situation. Theorists have also considered relaxing the requirement, in tomography, to output an approximation of the full density matrix -- and have proposed learning models in which, the learner need only predict the state's acceptance probability on measurements. We show that many of these ``reduced" learning models are information-theoretically related. Finally, we switch gears: instead of applying the lessons of learning theory to quantum mechanics, we do the reverse. We develop a quantum algorithm for what is considered the ``quantum" version of Bayes' rule -- the Petz recovery channel. As a byproduct, we also obtain an algorithm for implementing pretty-good measurements. Ours is the first systematic prescription to implement these ubiquitous theoretical tools in quantum error correction and quantum algorithms on a quantum computer.
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 | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Quek, Yihui |
|---|---|
| Degree supervisor | Mabuchi, Hideo |
| Degree supervisor | Weissman, Tsachy |
| Thesis advisor | Mabuchi, Hideo |
| Thesis advisor | Weissman, Tsachy |
| Thesis advisor | Wilde, Mark M |
| Degree committee member | Wilde, Mark M |
| Associated with | Stanford University, Department of Applied Physics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Yihui Quek. |
|---|---|
| Note | Submitted to the Department of Applied Physics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/hh334vn9663 |
Access conditions
- Copyright
- © 2021 by Yihui Quek
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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