J. Yi - Complexity and order in approximate quantum error-correcting codes
- Starts: 12:00 pm on Friday, April 4, 2025
- Ends: 1:00 pm on Friday, April 4, 2025
Quantum codes achieving approximate quantum error correction (AQEC) are useful and often fundamentally important, yet their systematic understanding remains incomplete. In this talk, I will present our recent work establishing rigorous connections between quantum circuit complexity and AQEC properties, revealing a "complexity phase diagram" for general quantum codes. To achieve this, we introduce a code parameter called "subsystem variance," closely related to the optimal AQEC precision. Our key finding is that if the subsystem variance lies below a critical threshold, any state within the code subspace must satisfy certain lower bounds on circuit complexity, thereby identifying nontrivial "phases" of quantum codes. I will also discuss implications of our AQEC results for topological phases and critical systems, where the same threshold relates to characteristics associated with nontrivial quantum order. [Ref: arXiv:2310.04710, in press at Nature Physics]
- Location:
- SCI 352
- Speaker
- Jinmin Yi
- Institution
- Perimeter Institute