A constructive commutative quantum Lovasz Local Lemma, and beyond

Understand

The recently proven Quantum Lovasz Local Lemma generalises the well-known Lovasz Local Lemma.

• It states that, if a collection of subspace constraints are "weakly dependent", there necessarily exists a state satisfying all constraints.
• It implies e.g.
• that certain instances of the kQSAT quantum satisfiability problem are necessarily satisfiable, or that many-body systems with "not too many" interactions are always frustration-free.