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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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Cite

BibTeXRIS
BibTeX
@misc{harofteh2026preparing,
  title = {{Preparing multi-qudit states in a definite-weight subspace}},
  author = {Nabi Zare Harofteh and Rafael I. Nepomechie},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.24659},
  eprint = {2606.24659},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.24659},
}
RIS
TY  - UNPB
TI  - Preparing multi-qudit states in a definite-weight subspace
AU  - Nabi Zare Harofteh
AU  - Rafael I. Nepomechie
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2606.24659
UR  - https://arxiv.org/abs/2606.24659
AB  - 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.
ER  -