Simple Ways of Preparing Qudit Dicke States

Noah B. Kerzner; Federico Galeazzi; Rafael I. Nepomechie

doi:10.2478/qic-2025-0036

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(d) spin-s Dicke states and SU(2) 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.

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Simple Ways of Preparing Qudit Dicke States

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