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

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Abstract

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.

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Acknowledgements

We acknowledge the support of Department of Science and Technology (DST), Government of India through Project No. SR/NM/NS-1112/2016 and Science and Engineering Research Board (SERB) through Project No. EMR/2016/007131.

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  1. Amritesh Sharma

    Present address: Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, 15260, USA

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  1. Solid State Devices Group, Department of Electrical Engineering, Indian Institute of Technology - Bombay, Mumbai, 400076, India

    Amritesh Sharma & Ashwin A. Tulapurkar

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Sharma, A., Tulapurkar, A.A. Preparation of spin eigenstates including the Dicke states with generalized all-coupled interaction in a spintronic quantum computing architecture. Quantum Inf Process 20, 172 (2021). https://doi.org/10.1007/s11128-021-03063-7

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