Quantum circuits to measure scalar spin chirality

TL;DR

This paper introduces a quantum measurement scheme using the Hadamard test to estimate scalar spin chirality, a key observable in classical and quantum magnetism, and demonstrates its application to specific quantum states.

Contribution

It proposes a novel indirect measurement method for scalar spin chirality applicable to general quantum states, unifying classical and quantum magnetic descriptions.

Findings

Single-shot determination of scalar chirality for eigenstates

Application to one-magnon states and ground states of complex models

Use of quantum phase estimation with a qutrit for measurement

Abstract

The scalar spin chirality is a three-body physical observable that plays an outstanding role both in classical magnetism, characterizing non-coplanar spin textures, and in quantum magnetism, as an order parameter for chiral spin liquids. In quantum information, the scalar spin chirality is a witness of genuine tripartite entanglement. Here we propose an indirect measurement scheme, based on the Hadamard test, to estimate the scalar spin chirality for general quantum states. We apply our method to study chirality in two types of quantum states: generic one-magnon states of a ferromagnet, and the ground state of a model with competing symmetric and antisymmetric exchange. We show a single-shot determination of the scalar chirality is possible for chirality eigenstates, via quantum phase estimation with a single auxiliary qutrit. Our approach provides a unified theory of chirality in classical and quantum magnetism.