A Divide-and-Conquer Approach to Dicke State Preparation

Abstract

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.

Keywords

• Circuit
• Dicke state
• fidelity
• IBM Q
• noisy intermediate scale quantum (NISQ)
• QISKIT