Stabilizing multiple topological fermions on a quantum computer

TL;DR

This paper demonstrates on IBM quantum computers how to stabilize multiple topological fermions beyond the limitations of single-particle modes using specially designed interactions and advanced quantum algorithms.

Contribution

It introduces a method to stabilize multiple fermions in topological systems on quantum hardware, surpassing traditional single-particle constraints with complex Hamiltonians and tensor network techniques.

Findings

Successfully realized complex topological Hamiltonians on quantum hardware

Demonstrated stabilization of multiple fermions beyond available modes

Reconstructed topological band structures using iterative quantum phase estimation

Abstract

In classical and single-particle settings, non-trivial band topology always gives rise to robust boundary modes. For quantum many-body systems, however, multiple topological fermions are not always able to coexist, since Pauli exclusion prevents additional fermions from occupying the limited number of available topological modes. In this work, we show, through IBM quantum computers, how one can robustly stabilize more fermions than the number of topological modes through specially designed 2-fermion interactions. Our demonstration hinges on the realization of BDI- and D-class topological Hamiltonians of unprecedented complexity on transmon-based quantum hardware, and crucially relied on tensor network-aided circuit recompilation approaches beyond conventional trotterization. We also achieved the full reconstruction of multiple-fermion topological band structures through iterative quantum phase estimation (IQPE). All in all, our work showcases how advances in quantum algorithm implementation enables NISQ-era quantum computers to be exploited for topological stabilization beyond the context of single-particle topological invariants.