A constructive algorithm for the commutative Quantum Lovász Local Lemma
Seminar Room 1, Newton Institute
AbstractCo-authors: Martin Schwarz (University of Vienna), Frank Verstraete (University of Vienna)
The recently proven Quantum Lovász Local Lemma generalises the well-known Lovász 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 quantum kQSAT satisfiability problem are necessarily satisfiable, or that many-body systems with "not too many" interactions are never frustrated.
However, the QLLL only asserts existence; it says nothing about how to find the quantum state that satisfies the constraints. Inspired by Moser's breakthrough classical results, we present a constructive version of the QLLL in the setting of commuting constraints, proving that a simple quantum algorithm converges efficiently to the sought quantum state. As well as proving a constructive commutative QLLL, this provides a non-trivial poly-time example of a new type of "dissipative quantum algorithm".