Adiabatic Quantum Simulation of the Topological Su--Schrieffer--Heeger--Hubbard Model

TL;DR

This paper presents a quantum simulation framework on gate-based quantum computers to explore topological features of the SSHH model, including state preparation, evolution, and measurement protocols.

Contribution

It introduces explicit quantum circuits and a measurement method for analyzing topological properties of the SSHH model, demonstrating robustness against weak interactions.

Findings

Topological characteristics remain robust against weak Hubbard interactions.

Quantum circuits scale polynomially with system size.

Topological breakdown occurs when chiral-symmetry-breaking interactions exceed a threshold.

Abstract

We develop an adiabatic quantum simulation framework on gate-based quantum computers to probe topological signatures of the one-dimensional fermionic Su--Schrieffer--Heeger--Hubbard (SSHH) model. We present explicit quantum-circuit constructions for initial-state preparation and time evolution, together with a practical measurement protocol and classical post-processing procedure for extracting the many-body Berry phase and the spatial profile of the sublattice polarization. Using classical simulations of the proposed circuits, we demonstrate -- for the first time within a genuine many-body framework -- that the topological characteristics of the SSH model remain robust against weak Hubbard interactions but eventually break down as the chiral-symmetry-breaking component of the interaction exceeds a threshold. The required qubit number, gate complexity, measurement shots, and classical pre- and post-processing costs all scale polynomially with system size. Our results provide a proof-of-concept framework for probing topological properties of interacting many-body systems via adiabatic quantum simulation on future large-scale quantum computers.