Simple ways of preparing qudit Dicke states

TL;DR

This paper introduces simple, explicit methods for preparing higher-dimensional qudit Dicke states on quantum computers, utilizing deterministic matrix product state representations and probabilistic quantum phase estimation techniques.

Contribution

It presents new, straightforward quantum circuits for preparing $SU(2)$ spin-$s$ and $SU(d)$ Dicke states, improving upon previous methods in simplicity and clarity.

Findings

Deterministic preparation using matrix product states

Probabilistic preparation via quantum phase estimation

Circuits are simpler than previous approaches

Abstract

Dicke states are permutation-invariant superpositions of qubit computational basis states, which play a prominent role in quantum information science. We consider here two higher-dimensional generalizations of these states: $SU(2)$ spin-$s$ Dicke states and $SU(d)$ Dicke states. We present various ways of preparing both types of qudit Dicke states on a qudit quantum computer, using two main approaches: a deterministic approach, based on exact canonical matrix product state representations; and a probabilistic approach, based on quantum phase estimation. The quantum circuits are explicit and straightforward, and are arguably simpler than those previously reported.