A Divide-and-Conquer Approach to Dicke State Preparation
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
[B\"artschi 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.
Shamminuj Aktar Andreas Bärtschi Abdel-Hameed A. Badawy Stephan Eidenbenz