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arXiv · 2606.24659

Preparing multi-qudit states in a definite-weight subspace

Nabi Zare Harofteh·Rafael I. Nepomechie
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Abstract

We formulate a deterministic algorithm for preparing arbitrary multi-qudit states in a definite-weight subspace. By ordering the corresponding computational basis states according to a Gray code for multiset permutations, the state-preparation task is reduced to performing a sequence of controlled 2-qudit Gray rotations. We use this algorithm to prepare exact eigenstates of the SU(3)-invariant Heisenberg Hamiltonian, whose Bethe ansatz is nested. In particular, we describe the preparation of the Bethe states, which are SU(3) highest-weight states, as well as their lower-weight descendants. We also consider the preparation of SU(d) Dicke states and their q-deformations.

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Nabi Zare Harofteh, Rafael I. Nepomechie. 2026-06-23. Preparing multi-qudit states in a definite-weight subspace. https://arxiv.org/abs/2606.24659

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