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

Tags

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.
  • Regression Analysis.

Technology Areas

  • Quantum Computing