In the coming years, increasingly larger and more powerful quantum systems are expected to tackle problems that are difficult or impossible to solve using conventional computers. However, the more powerful quantum simulations become, the more difficult it is to independently verify their results. Where classical simulation is still feasible, results can be cross-checked against it directly; beyond that regime, other methods are needed.
Researchers 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, have now demonstrated how a quantum simulator can be experimentally characterized and how the uncertainties that arise in the process can be translated into quantitative error limits for its results. The approach was demonstrated by a team led by Manoj Joshi and Christian Roos using an ion-trap quantum simulator containing up to 51 ions.
Not only the result, but also its accuracy
Quantum simulators are physical systems that can be used to replicate the behavior of other quantum systems. Their potential lies in the ability to study complex many-particle systems, the calculation of which quickly reaches its limits with classical computers. "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."
The researchers have now developed an approach that uses experimental data to learn how the quantum simulator actually behaves. "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 Tristan Kraft. "The quantum simulator thus provides not just a single value, but a result with error margins that quantify its accuracy."
The new method was first tested on a system of ten ions, whose dynamics can still be calculated using a conventional computer. The resulting models and error bounds were compared with independent measurements. The researchers then applied the method to a chain of 51 ions and demonstrated that the approach can also be applied to significantly larger systems.
Error limits also for 2D quantum simulation
The researchers will now apply this approach to two-dimensional quantum systems. "This is particularly important because classical calculations for such systems become significantly more difficult as the number of particles increases," explains quantum computing pioneer Peter Zoller. "This also makes independent verification of the results increasingly complex, making the question of experimentally determined error limits all the more important."
The researchers are working to adapt the approach to the latest generation of two-dimensional quantum simulators. These systems offer greater precision and allow for the study of larger numbers of particles. In the long term, this approach could also open up a way to quantitatively measure quantum advantages. "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. In the future, quantum simulation could be measured not only by the size of a system or the speed at which a calculation is performed, but also by which problems can be solved with verifiable accuracy.
The new approach was published in the journal Physical Review X and the researchers received funding from the Austrian Science Fund (FWF), the German Ministry of Research, Technology and Space, the European Union, and BMW among others.
Publication: Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning. Tristan Kraft, Manoj K. Joshi, William Lam, Tobias Olsacher, Florian Kranzl, Johannes Franke, Lata Kh Joshi, Rainer Blatt, Augusto Smerzi, Daniel Stilck França, Benoît Vermersch, Barbara Kraus, Christian F. Roos und Peter Zoller. Phys. Rev. X 16, 031037. DOI: 10.1103/s96t-n8tx
