International Team Solves Quantum Physics Problem with Wavefunction Matching, Predicts Nuclear Properties

An international team of researchers has developed a new method, called wavefunction matching, to solve complex quantum physics problems. The team, including Prof. Ulf-G. Meißner from the University of Bonn and Dean Lee from Michigan State University, used this method to calculate the masses and radii of all atomic nuclei up to mass number 50, with results aligning with measurements. The wavefunction matching method could be used in both classical and quantum computing, potentially improving predictions of properties of topological materials, which are important for quantum computing. The research was funded by various international institutions, including the U.S. Department of Energy.

Quantum Many-Body Problems: A New Approach

Quantum physics and quantum chemistry are fields that often grapple with the complexities of strongly interacting systems. These systems are typically investigated using stochastic methods such as Monte Carlo simulations. However, these methods encounter limitations when sign oscillations occur. An international team of researchers has now developed a new method, known as wavefunction matching, to overcome this challenge. This method has been successfully used to calculate the masses and radii of all nuclei up to mass number 50, with results aligning with measurements.

The Quantum Mechanics of Atomic Nuclei

All matter on Earth is composed of atoms, which in turn contain smaller particles: protons, neutrons, and electrons. These particles adhere to the rules of quantum mechanics, which forms the basis of quantum many-body theory. This theory describes systems with many particles, such as atomic nuclei. Nuclear physicists often use the ab initio approach to study atomic nuclei. This approach describes complex systems by starting from a description of their elementary components and their interactions. In the case of nuclear physics, the elementary components are protons and neutrons. Ab initio calculations can help answer key questions about the binding energies and properties of atomic nuclei and the link between nuclear structure and the underlying interactions between protons and neutrons.

The Challenge of Quantum Monte Carlo Simulations

Despite their potential, ab initio methods often struggle with reliable calculations for systems with complex interactions. One such method is quantum Monte Carlo simulations, where quantities are calculated using random or stochastic processes. While these simulations can be efficient and powerful, they are hampered by the sign problem. This problem arises in processes with positive and negative weights, which cancel each other out, leading to inaccurate final predictions.

Wavefunction Matching: A Solution to the Sign Problem

The new approach of wavefunction matching aims to solve the calculation problems associated with ab initio methods. This method maps the complicated problem to a simple model system that does not have sign oscillations, and then treats the differences in perturbation theory. The wavefunction matching method removes the short-distance part of the high-fidelity interaction and replaces it with the short-distance part of an easily calculable interaction. This transformation is done in a way that preserves all the important properties of the original realistic interaction. The researchers can now perform calculations with the easily computable interaction and apply a standard procedure for handling small corrections – called perturbation theory.

The Potential of Wavefunction Matching

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. The results closely matched real-world data on nuclear properties such as size, structure, and binding energy. Calculations that were once impossible due to the sign problem can now be performed with wavefunction matching. While the research team focused exclusively on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches. This method can be used in both classical computing and quantum computing, for example, to better predict the properties of so-called topological materials, which are important for quantum computing.