A Divide-and-Conquer Approach to Dicke State Preparation

We present a divide-and-conquer approach to deterministically prepare Dicke states
$|D^{n}_{k}\rangle$
(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. 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
et al.
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.