Dissipative State Engineering of Complex Entanglement with Markovian Dynamics

TL;DR

This paper demonstrates how to engineer Markovian dissipative processes to reliably generate complex multipartite entangled states, like cluster states, in spin systems, with robustness against system size.

Contribution

It introduces a method to design Lindblad operators that produce a unique cluster state as the steady state in spin systems with Ising interactions.

Findings

Cluster state is the unique steady state under engineered dissipation.

Fidelity and spectral gap are robust against increasing system size.

Dissipation dominates over local interactions for successful state preparation.

Abstract

Highly multipartite entangled states play an important role in various quantum computing tasks. We investigate the dissipative generation of a complex entanglement structure as in a cluster state through engineered Markovian dynamics in the spin systems coupled via Ising interactions. Using the Lindblad master equation, we design a projection based dissipative channel that drives the system toward a unique pure steady state corresponding to the desired cluster state. This is done by removing the contribution of the orthogonal states. By explicitly constructing the Liouvillian superoperator in the full $2^N$-dimensional Hilbert space, we compute the steady-state density matrix, the Liouvillian spectral gap, entanglement witness and the fidelity with respect to the ideal cluster state. The results demonstrate that the cluster state emerges as the steady state when the engineered Liouvillian dissipation dominates over the local Ising interaction between spins. Moreover, we find that the fidelity and Liouvillian spectral gap is relatively insensitive to the system size once the saturation dissipation has been achieved that scales linearly with the qubit number. This analysis illustrates a physically realizable path towards steady-state entanglement generation in the spin systems using engineered dissipation.