There has been an extensive development in the use of multi-partite entanglement as a resource for various quantum information processing tasks. In this paper, we focus on preparing arbitrary spin eigenstates whose subset contains important entangled resources like Dicke states. Leveraging on the symmetry of these states, we consider uniform pairwise exchange coupling between every pair of qubits. Starting from a product state of a given spin eigenstate with a single-qubit state, another spin eigenstate can be prepared using simple time evolutions. This expansion paves a deterministic approach to prepare arbitrary Dicke states in linear steps. We discuss an improvement in this cost, building up on a previous work on deterministic preparation of W states in logarithmic circuit depth (Sharma and Tulapurkar in Phys Rev A 101:062330, 2020). The modified algorithm requires several iterations of pumping spin angular momentum into the system and is akin to the amplitude amplification in Grover’s search. To demonstrate the proposed scheme, we choose a system of non-interacting static spin qubits connected to a ferromagnetic reservoir. The flying qubits emerging from the reservoir locally interact with static qubits successively, mediating an in-direct exchange interaction between all the pairs.

在使用多部分缠结作为各种量子信息处理任务的资源方面已经有了广泛的发展。在本文中，我们着重于准备任意自旋本征态，其子集包含重要的纠缠资源（如狄克态）。利用这些状态的对称性，我们考虑每对量子位之间的均匀成对交换交换耦合。从具有单量子位状态的给定自旋本征态的乘积状态开始，可以使用简单的时间演化来准备另一个自旋本征态。这种扩展铺平了确定性方法，以线性步骤准备任意迪克状态。我们基于对数电路深度中W状态的确定性准备的先前工作（Sharma和Tulapurkar在Phys Rev A 101：062330，2020年）基础上讨论了此成本的改进。改进的算法需要多次旋转自旋角动量到系统中，并且类似于Grover搜索中的幅度放大。为了演示所提出的方案，我们选择了一个与铁磁储层连接的非相互作用静态自旋量子位的系统。从储层中出来的飞行量子位先后在局部与静态量子位相互作用，从而在所有对之间间接地交换相互作用。