Quantum Simulations That Are Ten Thousand Times Faster

Researchers at the University of Warwick and University of Oxford have developed a new way to simulate quantum systems of many particles, that allows for the investigation of the dynamic properties of quantum systems fully coupled to slowly moving ions.

Effectively, they have made the simulation of the quantum electrons so fast that it could run extremely long without restrictions and the effect of their motion on the movement of the slow ions would be visible.

Journal Science Advances – Fast nonadiabatic dynamics of many-body quantum systems

It is based on a long-known alternative formulation of quantum mechanics (Bohm dynamics) which the scientists have now empowered to allow the study of the dynamics of large quantum systems.

The new methods demonstrated an increase of speed by more than a factor of 10,000 (four orders of magnitude) yet is still consistent with previous calculations for static properties of quantum systems.

The new approach was then applied to a simulation of warm dense matter, a state between solids and hot plasmas, that is known for its inherent coupling of all particle types and the need for a quantum description. In such systems, both the electrons and the ions can have excitations in the form of waves and both waves will influence each other. Here, the new approach can show its strength and determined the influence of the quantum electrons on the waves of the classical ions while the static properties were proven to agree with previous data.

Many-body quantum systems are the core of many scientific problem ranging from the complex biochemistry in our bodies to the behaviour of matter inside of large planets or even technological challenges like high-temperature superconductivity or fusion energy which demonstrates the possible range of applications of the new approach.


Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. However, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. On the basis of the Bohmian trajectory formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without using the adiabatic Born-Oppenheimer approximation.

Let us consider a many-particle electron-ion system at finite temperature. In calculating the dynamics of both the electrons and ions, we must account for the fact that the ions evolve multiple orders of magnitude more slowly than the electrons, as a result of their much higher masses. If we are interested in the long-time ionic dynamics (for example, the ion mode structure), then we face a choice of how to deal with this time scale issue. We can either model the system on the time scale of the electrons—nonadiabatically—and incur a substantial computational cost (a cost that is prohibitive in most simulation schemes), or model the system on the time scale of the ions—adiabatically—by treating the electrons as a static, instantaneously adjusting background. The latter approach is far cheaper computationally but does not allow for a viable description of the interplay of ion and electron dynamics.

The method enables us to use the former (nonadiabatic) approach, retaining the dynamic coupling between electrons and ions by reducing the simulation’s computational demands. We achieve this by treating the system dynamics with linearized Bohmian trajectories. Having numerical properties similar to those of molecular dynamics for classical particles. The approach permits calculations previously out of reach: Systems containing thousands of particles can be modeled for long (ionic) time periods, so that dynamic ion modes can be calculated without discounting electron dynamics.

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