A quantum computer has been used to tie mathematical knots inside the energy bands of a solid material.
Researchers used a quantum processor to simulate complex topological shapes like the Hopf chain and Solomon’s knot. These are not physical strings, but abstract knots formed by the way energy levels twist around each other. This is the first time these intricate mathematical structures have been physically mapped using quantum bits. It shows that we can use quantum hardware to explore the most complex corners of geometry. This could eventually lead to new materials with braided properties that are immune to heat or interference.
Digital Simulation of Non-Hermitian Knotted Bands on Quantum Hardware
arXiv · 2604.26914
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-Hermitia