CMT Forum: Andrew Lucas

29 May 2024
Seminars and colloquia
Simpkins Lee

Andrew Lucas (Boulder)

Seminar series
CMT Forum
Knowledge of physics?
Yes, knowledge of physics required
For more information contact

Two tales about quantum statistical mechanics in LDPC codes

Low-density parity check (LDPC) codes are a powerful way to robustly protect classical, or quantum, information.  Although the Ising model is already the simplest kind of LDPC code, mathematicians have discovered more useful LDPC codes, in which n physical bits store O(n) logical bits, and protect them against O(n) errors.   I will summarize what LDPC codes are and then explain how we have used the structure of LDPC codes to prove two intriguing results in quantum statistical mechanics.  First, I will show that quantum LDPC codes are counterexamples to the intuition that passive quantum error correction only exists in systems with a finite temperature phase transition to topological order.  LDPC codes can have trivial free energy, like the 1d Ising model, yet also be superior quantum memories than high-dimensional toric codes.  This suggests that qLDPC codes could enable new experimental techniques for quantum error correction based only on few-body measurements and feedback.  Secondly, I will present extensive many-body Hamiltonians based on LDPC codes that have a many-body mobility edge:  all eigenstates below a critical energy density are localized in an exponentially small fraction of the "energetically-accessible" state space.  Localization does not require strong disorder, but is guaranteed by the “infinite spatial dimensions” of the code.