Local random quantum circuits: ensemble CP maps and swap algebras

Paolo Zanardi

doi:10.1063/1.4891604

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arXiv · 1303.2832

Local random quantum circuits: ensemble CP maps and swap algebras

Paolo Zanardi

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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.

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Paolo Zanardi. 2014-08-12. Local random quantum circuits: ensemble CP maps and swap algebras. https://doi.org/10.1063/1.4891604

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