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

TL;DR

This paper presents a deterministic quantum algorithm for preparing specific eigenstates of spin-$s$ chains with fixed total spin, utilizing Gray code-based gates for efficient state construction.

Contribution

The authors introduce a novel Gray code-based method for preparing $U(1)$-eigenstates of spin-$s$ chains, applicable to arbitrary spin values and chain lengths.

Findings

Efficient state preparation of spin-$s$ eigenstates demonstrated.

Algorithm applicable to integrable XXX Hamiltonians.

Exact eigenstates can be prepared deterministically.

Abstract

We formulate a deterministic algorithm for preparing a general $U(1)$-eigenstate of a spin-$s$ chain of length $n$. These states consist of linear combinations of computational basis states $|\vec{m}\rangle$ of $n$ qudits, each with $(2s+1)$ levels and $s= 1/2, 1, 3/2, \ldots$, whose ditstrings $\vec{m}$ 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-$s$ XXX Hamiltonians.