In a study published today in Science, researchers report the creation of the first molecule exhibiting a half-Möbius electronic topology — a form of quantum matter that had not even been conjectured before.

The molecule was built atom by atom, and to understand its behavior, the team from IBM, Oxford, the University of Manchester, ETH Zurich, École Polytechnique Fédérale de Lausanne, and the University of Regensburg used quantum-centric supercomputing, a new paradigm of quantum and classical systems working together.

This work notably represents the convergence of two visions of physicist Richard Feynman. In 1959, Feynman stood before an audience at Caltech and declared: “There’s plenty of room at the bottom.” By that, he meant matter could be engineered atom by atom; if we could place individual atoms where we wanted them, it might become possible to build entirely new forms of matter.

Two decades later, Feynman said, “Nature isn’t classical… if you want to make a simulation of nature, you’d better make it quantum mechanical.” Quantum systems are most naturally described, and therefore most naturally simulated, by quantum devices.

Engineering a new molecular topology

Topology is the mathematical study of the properties of innate structures, and how things are connected. Typically, a ring of atoms connected in a molecule is “topologically trivial,” meaning that if you trace their atomic orbitals — the cloud-like structure representing the location of electrons — around the ring, you return to where you started after one loop.

Now you can imagine a molecule where the electron cloud forms a ring with a half-twist, like the famous Möbius strip — if you ride around the topside of the ring, you need to go around the ring twice to return where you started. That additional twist fundamentally changes the symmetry and properties of the system compared to topologically trivial systems with no twist.

With the newly engineered half-Möbius molecule, the team created something even more intricate: The electron cloud completes a full twist after four complete loops, with its electronic phase twisting by 90 degrees per revolution. This half-Möbius topology defines an entirely new electronic class, distinct from so-far known molecular topologies.

And more strikingly, the system can be reversibly switched between a right-handed half-Möbius, a left-handed half-Möbius, and the topologically trivial configuration. Topology here is not a passive property; it is engineered, controlled, and manipulated.

The molecule itself (C₁₃Cl₂) was assembled at IBM Research Europe – Zurich using scanning probe microscopy on a thin insulating layer of gold, at temperatures just above absolute zero. Three important pieces of IBM Research’s scientific legacy made this discovery possible: the scanning tunneling microscope (STM), atom manipulation, and the atomic force microscope (AFM).

Employing IBM-developed techniques

Gerd Binnig and Heinrich Rohrer invented the STM in 1981 at IBM Research Europe – Zurich. This innovation made it possible to study the surface of structures atom by atom and brought Binnig and Rohrer the Nobel Prize in Physics in 1986. Here, STM was used to map molecular orbitals.

In 1989, IBM fellow Donald Eigler used the STM to devise the first technique for reliably manipulating individual atoms, an achievement that earned him the 2010 Kavli Prize in Nanoscience. The team today used atom manipulation to create the molecule and to switch it between topologies.

And in 2016, Binnig, along with former IBM Research scientist Christoph Gerber and Stanford physicist Calvin Quate, won the Kavli Prize in Nanoscience for inventing AFM. AFM uses a tip on a cantilever and can read molecular structures with high precision, based on sensing tiny forces between the tip and the sample. In this instance, AFM was used to resolve the geometry of the half-Möbius molecule.

Decades after the invention of the STM and the first demonstrations of controlled atom manipulation, the ability to design matter at the single-atom level has matured into the capacity to engineer new quantum matter.

Creating such complex molecular systems is fascinating, but it is only the first step. Understanding their behavior presents an equally formidable challenge. These molecules exhibit intricate electronic structures and strong quantum correlations that cannot be fully interpreted using conventional theoretical tools alone.

Understanding what we built

Traditional post-Hartree-Fock simulation methods like Quantum Monte Carlo, CASSCF, CASPT2, CCSD, CCSD(T) and Selective CI have long extended the reach of classical computation, each representing remarkable progress within the classical paradigm. However, the half-Möbius system exhibits strong electronic correlations and pronounced multireference character, meaning it’s extra challenging to study the relevant electronic or quantum mechanical properties of the molecule with classical simulation methods. The relevant configuration space grows exponentially with system size.

So, here, the team adopted a fundamentally different computational approach.

Using SqDRIFT, a sample-based quantum diagonalization algorithm run on a quantum-centric supercomputer, the team explored an active space far beyond what brute-force classical diagonalization could directly access. Convergence of their results was proven by performing SqDRIFT calculations on up to 100 qubits of an IBM Heron processor. The goal was not to demonstrate hardware performance in isolation, but to decode the electronic structure of a newly synthesized quantum material.

Rather than compressing or approximating the exponential structure of the Hilbert space, quantum algorithms represent it directly in physical qubits. The quantum simulations helped reveal the origin of the topology switching, an effect called the helical pseudo-Jahn-Teller effect, essentially a tweak to the molecule’s electronic structure caused by its twisted geometry which provided a microscopic explanation for the experimentally observed electronic fingerprints. The quantum simulations also confirmed the prediction of a twisted molecular orbital for electron attachment, a hallmark of the half-Möbius topology.

In this case, quantum computing was not a proof-of-principle on a toy example — it was a scientific instrument used to interpret real experimental data.

Entering the quantum advantage era in chemistry

This work marks a meaningful step in using quantum computing for quantum chemistry. The team applied quantum hardware to study an experimentally realized system whose complexity challenged conventional approaches.

At this stage, SqDRIFT does not aim to replace classical methods; it complements them. Alongside the aforementioned simulation methods, we can now add a new member to the post-Hartree-Fock toolbox, one based on an entirely different computational paradigm. And thanks to its better scaling behavior, will soon surpass some of the abilities of its counterparts. Furthermore, with the advent of next-generation quantum computers, IBM sees a realistic path toward quantum advantage on studying molecules with large active spaces.

Two visions, one convergence

The importance of this milestone stems not only from the molecule engineered, nor from the novel quantum algorithm alone, but from their convergence.

Exotic molecules are crafted by atom manipulation, and quantum processors are used to model their behavior through algorithms grounded in the same physical laws. Fabrication and simulation reinforce one another: experiments create and explore new quantum matter, while quantum computation offers predictive and interpretative power.

Ultimately, this combination of experiment and quantum computing explores that room Feynman spoke of and deepens our understanding of quantum physics — the fundamental laws that govern our world. In that sense, the approach embodies Feynman’s visions, bringing them to life. We now have the tools to engineer molecules atom-by-atom, which requires study at the quantum level. And, if nature is quantum, then simulating it with quantum systems is not merely possible, it’s the natural path to take.