Nature of project: theory, software
Available to students on full-time physics degree schemes only.
The project aims to understand the ideas behind Fisher information, the Cramer-Rao inequality and the generalization to quantum probabilities.
Here we wish to understand the relationship with entropy.
We also want to apply the theory to the recent notion of a quantum natural gradient.
A successful project will develop beyond the above in one/some of the following directions:
A full description of the technical details behind the theory.
When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.
Additional scope or challenge if taken as a Year-4 project: Applying the ideas to understand recent work on quantum gradient descent algorithms.
Please speak to John Gough if you consider doing this project.
Initial literature for students:
Fisher information is not part of the curriculum and will need to be researched. neither, of course is its quantum analogue. Understanding these concepts will be important.
Describing the eigensolver problem and the natural gradient method, and how they relate to quantum Fisher information will be the challenging part of the project: this will be based on references 2 and 3.
|milestone||to be completed by|
|basic theory and references||end of October|
|formulation of problem - outlook||end of November|
|applications of Fisher information and its quantum analogue||Christmas|