Operator entanglement in local quantum circuits

Bruno Bertini (Author), Pavel Kos (Author), Tomaž Prosen (Author)

Abstract

We provide exact results for the dynamics of local-operator entanglement in quantum circuits with two-dimensional wires featuring ultralocal solitons, i.e. single-site operators which, up to a phase, are simply shifted by the time evolution. We classify all circuits, allowing for ultralocal solitons and show that only dual-unitary circuits can feature moving ultralocal solitons. Then, we rigorously prove that if a circuit has an ultralocal soliton moving to the left (right), the entanglement of local operators initially supported on even (odd) sites saturates to a constant value and its dynamics can be computed exactly. Importantly, this does not bound the growth of complexity in chiral circuits, where solitons move only in one direction, say to the left. Indeed, in this case we observe numerically that operators on the odd sublattice have unbounded entanglement. Finally, we present a closed-form expression for the local-operator entanglement entropies in circuits with ultralocal solitons moving in both directions. Our results hold irrespectively of integrability.

Keywords

kvantna prepletenost;kubiti;večdelčni sistemi;entanglement;qubits;quantum many-body systems;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	530.145
COBISS:	14722819
ISSN:	2542-4653
Views:	499
Downloads:	255
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	kvantna prepletenost;kubiti;večdelčni sistemi;
Pages:	23 str.
Volume:	ǂVol. ǂ8
Issue:	ǂart. no. ǂ068
Chronology:	Apr. 2020
DOI:	10.21468/SciPostPhys.8.4.068
ID:	11670867