CMSA Quantum Matter in Mathematics and Physics: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries

Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.

References:
1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O'Connor, Guanyu Zhu
3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhus.

--------
Subscribe to Harvard CMSA Quantum Matter and other seminar videos
(more to be uploaded):
https://www.youtube.com/playlist?list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup

Subscribe to Harvard CMSA seminar mailing list:
https://forms.gle/1ewa7KeP6BxBuBeRA