Bounds on LDPC codes

Quantum circuit components will always be unreliable. To protect quantum information from becoming corrupted, we require quantum error correcting codes. The drawback is that quantum error correcting codes necessitate a trade-off the better the code protects information, the more resources it requires to be sustained. Our current resource estimates to construct useful quantum circuits seem insurmountable.It was recently shown that if a certain class of error correcting codes, called quantum LDPC codes, were to exist, then they could potentially lower resource requirements significantly. However, it is unknown whether these codes exist and the hunt for these codes has become an active area of research.By borrowing ideas from the theory of classical error correcting codes, we hope to explore the limits of quantum LDPC codes. These methods are abstract yet powerful tools that exploit the mathematical structure of LDPC codes to bound their performance. By establishing what is (im)possible with quantum LDPC codes, we help move towards answering an important open problem towards the realization of quantum computation.

Faculty Supervisor:

David Poulin

Student:

Anirudh Krishna

Partner:

Discipline:

Physics / Astronomy

Sector:

University:

Program:

Globalink