Dynamics of Majorana Fermions on a Quantum Computer

TL;DR

This paper demonstrates how constant-depth quantum circuits can simulate Majorana fermion dynamics and probe their signatures in a transverse-field Ising chain on noisy quantum devices.

Contribution

It introduces a constant-depth circuit algorithm for real-time Majorana fermion dynamics and shows how impurities can reveal Majorana modes on current quantum hardware.

Findings

Identified two dynamical regimes based on spin interaction strength.

Showed impurities act as probes for Majorana modes.

Validated the approach on noisy intermediate-scale quantum devices.

Abstract

The study of quasiparticle dynamics is central to understanding non-equilibrium phenomena in quantum many-body systems. Direct simulation of such dynamics on quantum hardware has been limited by circuit depth and noise constraints. In this work, we use a recently developed constant-depth circuit algorithm to examine the real-time evolution of site-resolved magnetization in a transverse-field Ising chain on noisy intermediate-scale quantum devices. By representing each spin as a pair of Majorana fermions, we identify two distinct dynamical regimes governed by the relative strength of spin interaction. Furthermore, we show how local impurities can serve as probes of Majorana modes, acting as dynamical barriers in the weak coupling regime. These results demonstrate that constant-depth quantum circuits provide a viable route for studying quasiparticle propagation and for probing Majorana signatures on currently available quantum processors.