aiqbench analysis
This paper presents a deterministic algorithm for generating specific multi-qudit states within a definite-weight subspace using Gray code-based rotations. The method enables the preparation of exact eigenstates for SU(3)-invariant Heisenberg Hamiltonians and various Dicke states, offering a structured approach to complex quantum state engineering.
Preparing multi-qudit states in a definite-weight subspace
arXiv:2606.24659v3 Announce Type: replace 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.
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.
arXiv:2606.24659 [quant-ph]
(or arXiv:2606.24659v3 [quant-ph] for this version)
J. Phys. A: Math. Theor. 59, 415302 (2026)
https://doi.org/10.1088/1751-8121/aeaf22 DOI(s) linking to related resources
From: Rafael I. Nepomechie [view email] [v1] Tue, 23 Jun 2026 14:51:31 UTC (22 KB) [v2] Sat, 27 Jun 2026 21:34:54 UTC (23 KB) [v3] Wed, 14 Oct 2026 13:19:45 UTC (108 KB)
Full text under the publisher's open licence · 149 words
Related coverage
Debugging Logprob Mismatches in LLM Reinforcement Learning
AMD · Sep 23, 2026
Links #5: 2026/07
LessWrong · Jul 31, 2026
Frontier post-training recipe review with Finbarr Timbers
Interconnects · Jun 16, 2026
Agentic coding without the cloud: evaluating open-weight large language models on longitudinal data preparation tasks
arXiv · Jul 25, 2026