A Divide-and-Conquer Approach to Dicke State Preparation

TL;DR

This paper introduces a divide-and-conquer method for preparing Dicke states on quantum computers, demonstrating improved fidelity on IBM devices through circuit design and error mitigation techniques.

Contribution

The paper presents a novel divide-and-conquer approach for deterministic Dicke state preparation, optimized for IBM's hardware constraints, with experimental validation showing enhanced fidelity.

Findings

Higher state fidelity achieved compared to previous methods

Effective use of measurement error mitigation

Successful implementation on IBM's heavy-hex architecture

Abstract

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.