Local random quantum circuits: Ensemble completely positive maps and swap algebras
Abstract
We define different classes of local random quantum circuits (L-RQC) and show that (a) statistical properties of L-RQC are encoded into an associated family of completely positive maps and (b) average purity dynamics can be described by the action of these maps on operator algebras of permutations (swap algebras). An exactly solvable one-dimensional case is analyzed to illustrate the power of the swap algebra formalism. More in general, we prove short time area-law bounds on average purity for uncorrelated L-RQC and infinite time results for both the uncorrelated and correlated cases.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 01, 2014
- Source ID
- 10.1063/1.4891604
Entities
People
- Paolo Zanardi
Organizations
- Army Research Office
- National University of Singapore
- University of Southern California