Local random quantum circuits: Ensemble completely positive maps and swap algebras

Journal Article · Fri Aug 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4891604· OSTI ID:22306089

Zanardi, Paolo ^[1]

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1. Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA and Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore)

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.

• OSTI ID: 22306089
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
EXACT SOLUTIONS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
RANDOMNESS
STATISTICS