Simple ways of preparing qudit Dicke states

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.

arXiv comment25 pages, 9 figures, implementations of circuits in cirq are available on GitHub; v2: references added

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Cited by in corpus (1)

• Spin-$s$ $U(1)$-eigenstate preparation