Constant-Depth Unitary Preparation of Dicke States

TL;DR

This paper introduces the first constant-depth, unitary protocols for preparing Dicke states in quantum systems, surpassing previous depth limitations by leveraging global interactions and advanced circuit classes.

Contribution

It presents novel constant-depth quantum circuits for exact Dicke state preparation using global interactions, advancing quantum state engineering beyond standard models.

Findings

First constant-depth protocols for exact Dicke states

Use of unbounded CZ gates within QAC$^0$ circuit class

Achieves arbitrary-weight Dicke states with polynomial ancillae

Abstract

Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.