Researchers Develop Experimental Error Bounds for Large Quantum Systems

A team led by Tristan Kraft of the Technical University of Munich and Peter Zoller of the University of Innsbruck and the Institute for Quantum Optics and Quantum Information at the Austrian Academy of Sciences, together with Barbara Kraus of the Technical University of Munich, has developed a method to assign numerical error limits to quantum simulations. Manoj Joshi and Christian Roos led experimental validation using an ion-trap quantum simulator with up to 51 ions.

How uncertainty is quantified in real devices

Quantum simulators are physical systems built to emulate other quantum systems—particularly many-particle configurations whose behavior overwhelms classical computation. “But no real experiment is perfect,” says Tristan Kraft. “Interactions may turn out differently than expected, the system is influenced by its environment, and measurements are also subject to uncertainties.” Rather than assuming ideal operation, the researchers rely on experimental data to reconstruct how the simulator actually functions.

“From this data, we determine the relevant interactions as well as key influences from fluctuations and noise. We then calculate how the uncertainties in this model affect the simulation results,” explains Kraft. “The quantum simulator thus provides not just a single value, but a result with error margins that quantify its accuracy.”

From ten to fifty-one ions

The method was first validated on a ten-ion system—small enough for full classical verification. Researchers compared the experimentally derived model and its predicted error bounds against independent measurements to confirm fidelity. They then scaled the technique to a linear chain of 51 ions, confirming applicability to significantly larger quantum systems.

Next: two-dimensional quantum architectures

Work is now underway to adapt the approach for two-dimensional quantum simulators. “This is particularly important because classical calculations for such systems become significantly more difficult as the number of particles increases,” explains Peter Zoller. “This also makes independent verification of the results increasingly complex, making the question of experimentally determined error limits all the more important.”

What verifiable accuracy means for quantum advantage

The researchers are integrating the method into next-generation two-dimensional quantum simulators, which offer higher precision and support larger particle counts. In the longer term, the framework could enable quantitative assessment of quantum advantage—not only by speed or scale, but by comparing how reliably quantum and classical systems solve identical problems.

“After all, when a classical computer and a quantum simulator tackle the same problem, it’s not just a matter of which one delivers a result faster. What’s also crucial is which one can solve the problem with a smaller, verifiable margin of error,” says Peter Zoller. That shift could redefine evaluation criteria: performance may hinge not solely on system size or calculation time, but on whether a solution carries independently quantifiable accuracy.

Reference: “Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning” by Tristan Kraft, Manoj K. Joshi, William T. Lam, Tobias Olsacher, Florian Kranzl, Johannes Franke, Lata Kh Joshi, Rainer Blatt, Augusto Smerzi, Daniel Stilck França, Benoît Vermersch, Barbara Kraus, Christian F. Roos and Peter Zoller, 13 August 2026, Physical Review X. DOI: 10.1103/s96t-n8tx

Funding from the Austrian Science Fund (FWF), the German Ministry of Research, Technology and Space, the European Union, and BMW among others.