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There has been an extensive development in the use of multi-partiteentanglement as a resource for various quantum information processing tasks. Inthis paper we focus on preparing arbitrary spin eigenstates whose subsetcontain important entangled resources like Dicke states as well as some othersub-radiant states that are difficult to prepare. Leveraging on the symmetry ofthese states we consider uniform pairwise exchange coupling between every pairof qubits. Starting from a product state of a given spin eigenstate with asingle qubit state, another spin eigenstate can be prepared using simple timeevolutions. This expansion paves a deterministic approach to prepare arbitraryDicke states in linear steps. We discuss an improvement in this cost buildingup on a previous work for W states deterministic preparation in logarithmiccircuit depth. The modified algorithm requires several iterations of pumpingspin angular momentum into the system and is akin to the amplitudeamplification in Grover search. As a use case to demonstrate the proposedscheme, we choose a system of non-interacting static spin qubits connected to aferromagnetic reservoir. The flying qubits emerging from the reservoir locallyinteract with static qubits successively, mediating an in-direct exchangeinteraction between all the pairs.

Quantum state preparation of spin eigenstates including the Dicke states  with generalized all-coupled interaction in a spintronic quantum computing  architecture