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Paper 1

A Divide-and-Conquer Approach to Dicke State Preparation

Shamminuj Aktar, Andreas Bärtschi, Abdel-Hameed A. Badawy, Stephan Eidenbenz

Year

2021

Journal

arXiv preprint

DOI

arXiv:2112.12435

arXiv

2112.12435

We present a divide-and-conquer approach to deterministically prepare Dicke states $\lvert D_k^n\rangle$ (i.e., equal-weight superpositions of all $n$-qubit states with Hamming Weight $k$) on quantum computers. In an experimental evaluation for up to $n=6$ qubits on IBM Quantum Sydney and Montreal devices, we achieve significantly higher state fidelity compared to previous results [Mukherjee and others, TQE'2020], [Cruz and others, QuTe'2019]. The fidelity gains are achieved through several techniques: Our circuits first "divide" the Hamming weight between blocks of $n/2$ qubits, and then "conquer" those blocks with improved versions of Dicke state unitaries [Bärtschi and others, FCT'2019]. Due to the sparse connectivity on IBM's heavy-hex-architectures, these circuits are implemented for linear nearest neighbor topologies. Further gains in (estimating) the state fidelity are due to our use of measurement error mitigation and hardware progress.

Paper 2

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