Simulating spin dynamics with quantum computers

TL;DR

This paper demonstrates how IBM quantum computers can simulate quantum spin dynamics for small systems, revealing insights into conservation laws and symmetries, and discusses the challenges of scaling to larger systems.

Contribution

The study introduces methods for simulating spin dynamics on quantum computers, including exact evolution for small systems and approximate methods for larger ones, highlighting current limitations and educational value.

Findings

Exact evolution computed for systems with fewer than three spins.

Quantum circuit simulator effectively models systems with around 10 spins.

Larger systems require advanced algorithms and error correction.

Abstract

IBM quantum computers are used to simulate the dynamics of small systems of interacting quantum spins. For time-independent systems with fewer than three spins, we compute the exact time evolution at arbitrary times and measure spin expectation values and energy. It is demonstrated that even in such small systems, one can observe the connection between conservation laws and symmetries in the model. Larger systems require approximating the time-evolution operator, and we investigate the case of $N=3$ spins explicitly. While it is shown to be unfeasible to use such devices to probe such larger systems without more advanced algorithms or reliable error correction, we demonstrate that the quantum circuit simulator is an easy-to-use method for studying spin dynamics in systems with $N\sim\mathcal{O}(10)$) spins. The computations presented provide an interesting experimental component to the standard treatment of quantum spin in an undergraduate quantum mechanics course.