One of the central challenges to building quantum computers is that its building blocks, the qubits, are easily disturbed by their surroundings. This highly nontrivial challenge can in principle be overcome by so-called quantum error correction, which requires correcting errors at the same time as no information about the original quantum state is revealed.
The main focus of quantum error correction has so far been on preserving the state of the qubits in isolation. However, to perform computations, one has to apply gates both in order to manipulate the qubits individually (single-qubit gates) and to have them interact (two-qubit gates). These gate operations take time, during which errors can also occur. To combat this problem, the concept of error-transparent gates is increasingly being studied, both theoretically and experimentally. This would allow to correct such errors after the gate operation has been completed.
The goal of this project is to contribute to this research direction with a focus on error-transparent gates for bosonic codes. This will involve a fair amount of analytical work, but likely also some numerical computations and/or use of machine learning techniques.
Tentative milestones for the project are:
1. Study the fundamentals of quantum error correction.
2. Study bosonic codes, i.e., the encoding of qubits in quantum oscillators.
3. Study and reproduce existing proposals and implementations of error-transparent gates.
4. Search for the simplest possible ways to implement a universal set of error-transparent gates on two qubits encoded in bosonic modes.
5. Perform numerical simulations of the full set of error-transparent gates for two encoded qubits subject to noise and quantitatively compare different approaches.
There is room for the project to develop in different directions depending on the student's interests and the development of the research front.
Recommended courses for theoretical curriculum in the master's programme: