Spin‐sU(1)‐Eigenstate Preparation

ABSTRACT We formulate a deterministic algorithm for preparing a general ‐eigenstate of a spin‐ chain of length . These states consist of linear combinations of computational basis states of qudits, each with levels and , whose ditstrings have a fixed digit sum. Exploiting a Gray code for bounded integer compositions, whose consecutive ditstrings obey the Gray property, the quantum state is prepared by applying corresponding “Gray gates.” We use this algorithm to prepare exact eigenstates of integrable spin‐ XXX Hamiltonians. We also consider the preparation of AKLT states and spin‐ Dicke states.