Finnish researchers at Aalto University have simulated a topological quasicrystal across 268 million lattice sites — a structure so dense it stalls every conventional supercomputer in service today.

The work, published on May 13, 2026 in Physical Review Letters as an Editor's Suggestion, comes from Assistant Professor Jose Lado's group in Aalto's Department of Applied Physics. Doctoral researcher Tiago Antão led the paper; QDOC doctoral researcher Yitao Sun and Academy Research Fellow Adolfo Fumega round out the team of four.

Quasicrystals don't repeat. Predicting how electrons move inside them demands more than a quadrillion numbers, a scale today's largest HPC systems cannot reach. Aalto's fix borrows the math quantum computers already use.

"Quantum computers work in exponentially large computational spaces, so we used a special family of algorithms to encode those spaces, known as tensor networks, to compute a quasicrystal with over 268 million sites," Antão says. "Our algorithm shows how colossal problems in quantum materials can be directly solved with the exponential speed-up that comes from encoding the problem as a quantum many-body system."

What's a topological quasicrystal, and why bother?

Topological quasicrystals host quantum excitations that protect electrical conductivity from noise. That's the single biggest reason the materials interest quantum-hardware designers hunting for fault-tolerant qubits.

Stacking and twisting two-dimensional layers — graphene chief among them — into moiré and super-moiré patterns can flip an ordinary sheet into a topological host. Geometries that work, though, are rare, and the parameter space is brutal. Even at modest sizes, the right configuration can take ages of computation to find.

How does the algorithm actually pull it off?

Rather than calculating the full material wavefunction, the team reformulated the problem as one of real-space topology. Tensor networks — the same class of algorithms used in strongly correlated condensed-matter physics — were retargeted at the irregular, non-periodic geometry of a quasicrystal, capturing its topological excitations as "Chern mosaics." The simulation ran on classical hardware, not quantum, but the encoding mimics the math a real quantum processor would exploit.

Lado frames the bigger picture: "Crucially, these new quantum algorithms can enable the development of new quantum materials to build new paradigms of quantum computers, creating a productive two-way feedback loop between quantum materials and quantum computers," he says.

The team says the technique yields super-moiré quasicrystals several orders of magnitude beyond what conventional methods handle — exactly the regime, Lado argues, for designing topological qubits from van der Waals materials.

Who's paying for the work?

• Project: ERC Consolidator grant ULTRATWISTROICS, focused on topological qubits built from van der Waals materials.
• Center: Center of Excellence in Quantum Materials, or QMAT.
• Hardware hook: AaltoQ20, the university's new quantum platform, plus Finland's national quantum-computing infrastructure.
• Citation: Physical Review Letters, 2026, vol. 136 (15), DOI 10.1103/hhdf-xpwg.

What's the commercial hook beyond physics?

Two threads. First, a route to topological qubits that shrug off noise — a long-standing bottleneck in scaling quantum hardware. Second, dissipationless electronics, devices that move current without shedding energy as heat. That second thread matters outside the lab: AI data centers face growing heat and energy demands, and circuits with zero resistive loss would cool what today takes a small power plant to dissipate.

What's next on the roadmap?

Lado says the move to real quantum hardware is in sight, just not in hand yet.

"Our method can be adapted to run on real quantum computers, once they reach necessary scale and fidelity," Lado says. "In particular, the new AaltoQ20 and the Finnish Quantum Computing Infrastructure can play a significant role for future demonstrations."

The Aalto group is now lining up experimental runs on AaltoQ20. Watch the platform's fidelity numbers — once they stabilize, 268-million-site super-moiré quasicrystals move from simulation to measurement, and the next bottleneck in topological-qubit design opens up.