Quasi-local stabilization of multipartite quantum pure states

Presenting Author: Salini Karuvade, Dartmouth College
Contributing Author(s): Peter D. Johnson, Francesco Ticozzi, Lorenza Viola

Dissipative quantum control techniques under realistic resource constraints are attracting increasing attention across quantum information processing. A multipartite pure state is quasi-locally stabilizable (QLS) by continuous-time Markovian dynamics if it can be prepared using Hamiltonian as well as Lindblad noise operators that obey a fixed locality constraint. We provide a necessary and sufficient condition for a target pure state to be QLS with respect to a fixed locality constraint. We show that the QLS property of the pure state is determined by the existence of a Hamiltonian that is QL relative to the specific constraint and leaves the pure state invariant while having no other eigenstates in a certain subspace of the Hilbert space which is determined by the dissipative action. In particular, we focus on quantum states that are the unique ground states of QL (in general frustrated) Hamiltonians and show that they need not be stabilizable using QL resources alone. We illustrate this by using the paradigmatic W-state on N qubits, under a fixed nearest-neighbor locality constraint. We also discuss control strategies for approximately stabilizing unique ground states of QL Hamiltonians in one dimension, in cases where exact QL stabilization is not feasible.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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