The building blocks of universal quantum computers are usually two-level systems (qubits). However, several physical implementations also contain quantum oscillators (infinite-level, or continuous-variable (CV), systems). These oscillators can be used to manipulate the qubits, but they can also play a more central part in storing and processing quantum information.
The so-called stellar-holomorphic representation is an efficient, albeit less common, way of representing states of quantum oscillators by analytic functions in the complex plane. The roots of this function are directly related to the state's non-Gaussianity, which is a resource in quantum information processing.
Quantum information processing and quantum simulations can benefit from finding efficient methods of controllably manipulating these roots using elementary physical operations. The goal of this project is to contribute to this research direction. This will involve a fair amount of analytical work, but likely also some numerical simulations.
Tentative milestones for the project are:
1. Study different representations of CV states, in particular the Fock basis, phase space quasiprobability distributions, and stellar representation.
2. Study how discrete and continuous variable systems interact in quantum information processing architectures.
3. Study how quantum information processing and simulation can be understood in terms of the time dynamics of the stellar representation.
4. Investigate how various elementary physical processes can be combined into a toolbox for manipulating zeros of the stellar function.
There is room for the project to develop in different directions depending on the student's interests and the development of the research front.