TalentQ Seminar | Low-density parity-check codes as stable phases of quantum matter – Andrew Lucas

Speaker: Andrew Lucas

Title: Low-density parity-check codes as stable phases of quantum matter

Abstract: Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error correcting code, when does it define a stable gapped quantum phase of matter, whose ground state degeneracy is robust against perturbations in the thermodynamic limit? An affirmative answer to this question could allow us to leverage techniques from quantum error correction to learn new things about quantum statistical mechanics. We have proved that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits a property that we call «check soundness». Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric code phases are robust to spatially nonlocal few-body perturbations.  I will conclude with potential applications for our ideas in condensed matter physics.

Registration: https://events.teams.microsoft.com/event/9464c6bd-6894-42be-8276-11b8b5b731a1@8f0d452c-b7a4-4964-b810-8c397374477b/