Connection Between Classical and Quantum Descriptions of Spin Waves Using Quantum Circuits

TL;DR

This paper introduces a quantum circuit that models spin wave dynamics in quantum systems, bridging classical and quantum descriptions, and verified through simulations and quantum hardware.

Contribution

It presents a novel quantum circuit approach to simulate spin waves, revealing the connection between classical and quantum models and aiding quantum processor characterization.

Findings

Circuit accurately reproduces spin wave dispersion relation.

Simulation and hardware results confirm theoretical predictions.

Potential for quantum error characterization.

Abstract

A quantum computing circuit is presented that approximates a single spin wave quantum on a linear chain of spin 1/2 particles described by a Heisenberg Hamiltonian. The circuit is a product state where each qubit represents a spin. The spin wave motion is represented by opening the cone angle using Y rotations and then adding progressive Z rotations along the chain to represent wave propagation. We show analytically that this product state yields the correct dispersion relation in the limit of an unbounded chain. This surprising observation is confirmed using both a simulator and various quantum processors. The quantum circuit calculation leads to insight into the connection between classical and quantum descriptions of spin waves, and may also be useful for characterizing the error in quantum processors.