Digital Simulation of Non-Hermitian Knotted Bands on Quantum Hardware

TL;DR

This paper demonstrates a method to simulate and analyze complex non-Hermitian knotted band structures on quantum hardware, enabling the study of intricate topological phenomena without extensive optimization.

Contribution

Introduces a non-variational protocol for characterizing non-Hermitian knotted bands on quantum processors, extracting topological invariants efficiently.

Findings

Successfully reconstructed knots like Hopf chain and Solomon's knot.

Developed measurement strategy for braid words and knot invariants.

Enabled exploration of exotic topologies on near-term quantum devices.

Abstract

Knots and links represent a fundamental motif of non-local connectivity that permeates the physical sciences from string theory to protein folds. While spectral braiding has been explored in two-band non-Hermitian models across various platforms, its direct simulation and characterization on programmable quantum hardware, particularly beyond two strands, remains a formidable challenge due to the limitations of variational optimization in these systems. Here, we introduce a family of non-Hermitian multi-band twister models and implement a non-variational protocol to characterize their complex braided band structures on a programmable superconducting quantum processor. By mapping the winding of eigenstates to the spectral topology, we devise an efficient measurement strategy that extracts braid information, including braid words and knot invariants like the Alexander and Jones polynomials, without requiring full spectral tomography or repeated optimization. We experimentally demonstrate the reconstruction of complicated knots and links such as the Hopf chain and Solomon's knot. Our approach provides a general framework for investigating exotic non-Hermitian topology on near-term quantum devices, opening a route to simulate more sophisticated topological structures in knot theory.