While solving quantum-physical problems in multi-body systems, for example, estimating material properties, traditional computers quickly reach the limits of their potential. Although digital quantum simulators could be of help, to date, they are largely limited to small systems that have fewer particles and short simulation times.
Currently, Dr Philipp Hauke, a physicist at Heidelberg University, and collaborators from Dresden and Innsbruck (Austria) have shown that simulations such as these can be more “robust” and thus considerably more stable compared to what was assumed earlier. The outcomes of the study have been reported in Science Advances.
In quantum physics, a huge number of interacting particles are described by multi-body theory. In the state of thermodynamic equilibrium, the many-body system can be characterized by only limited values like pressure or temperature, which are mostly homogeneous for the whole system.
However, what happens over time following a major perturbation, for instance, when short laser pulses unexpectedly deposit energy in a material sample? Precise calculation of what is called the nonequilibrium dynamics of interacting multi-body systems is a high-profile problem in quantum physics.
Performing calculations using traditional computers needs resources that increase exponentially with the increase in the number of constituent quantum particles.
So computationally exact methods fail with just a few dozen particles. That is far less than the number needed to predict material properties, for example. In such cases, scientists rely on approximation methods that are often uncontrolled, particularly when it comes to dynamic properties.
Dr Hauke, Researcher, Kirchhoff Institute for Physics and Institute for Theoretical Physics of Heidelberg University
One probable temporary solution is offered by digital quantum simulation. The nonequilibrium dynamics are analyzed using simulators that themselves are controlled by quantum-mechanical laws.
In order to depict the time evolution in a quantum computer, it has to be discretized into individual operations. However, this strategy, also called Trotterization, inevitably produces an error intrinsic to the simulation itself. It is possible to mitigate this Trotter error by discretizations that are fine and sufficient.
However, it is necessary to choose very small discretization steps to reliably portray a longer time evolution. To date, studies have maintained that over long time periods and with an increase in the number of particles, the error rapidly grows—which, for all practical reasons, largely restricts digital quantum simulation to short times and small systems.
The researchers used analytical arguments and numerical demonstrations to show that quantum simulation is considerably more “robust” and thus more stable than assumed earlier, as long as only values that are relevant in practice—for example, averages across the whole system—are taken into account and not the complete state of each individual particle.
In the case of such values, there is an acute threshold between a region that has controllable errors and a simulation that cannot deliver a usable result anymore. Under this threshold, the Trotter error has only lesser influence—indeed, for all time periods that can be simulated practically and mostly independent of the number of constituent particles.
Meanwhile, the study demonstrated that digital quantum simulation has the potential to deliver surprisingly accurate results using usually large Trotter steps. “A simulation that can predict the behaviour of many quantum particles over a longer time therefore becomes more and more likely. This further opens the door for practical applications, ranging from materials science and quantum chemistry to issues in fundamental physics,” stated Dr Hauke, who heads the “Quantum optics and quantum many-body theory” research group.
The study was carried out in collaboration with Dr Markus Heyl of the Max Planck Institute for the Physics of Complex Systems in Dresden and Prof. Dr Peter Zoller of the University of Innsbruck. At Heidelberg University, it was conducted as part of the Collaborative Research Centre “Isolated Quantum Systems and Universality in Extreme Conditions” (SFB 1225).