We can now simulate the quantum dynamics with tensor networks

The results contained in “Converting long-range entanglement into mixture: Tensor-network
approach to local equilibration” published on the 07/03/2024 in PRL bring us closer to simulating quantum-many-body systems out of equilibrium. Life is an out-of-equilibrium process, it starts with our birth, we grow, we interact with our society that changes us and that we change and ultimately, we die. Everyone can understand this. Unfortunately the quantum life of a single spin, immersed in the large world of a quantum many-body system is much more complicated. In principle our physical laws allow the spin to go back to where it has started from at any time. In practice, from the interaction with the quantum many-body system it slowly irreversibly ages, like us and ultimately relaxes into the equilibrium equivalent of our death. This fact has defeated our understanding, due to the exponential increase in computational resources necessary to describe the dynamics of the spin with the number of spins in the many body systems and the duration of their mutual interactions.

A new algorithm developed by researchers from the Spanish Research Council (CSIC) and the Max Planck Institute for Quantum Optics has paved the way for shading light on the life of single quantum constituent, by showing how to predict the local properties of a quantum system in 1D over extended times after it is quenched out of equilibrium.

This paves the way to addressing important open theoretical questions, such as the origin of the arrow of time, in quantum mechanics but also to better design technological applications based on quantum processes. For instance, the algorithm could be used to assist in designing processes that help protect specific properties of quantum systems, such e.g. their coherence over a long time.

The algorithm leverages the inherent relaxation process of quantum systems, gradually simplifying the complex quantum states generated during the system’s evolution into simpler environments. These simplified environments, while not fully capturing the quantum behavior, emulate the effect of the real quantum system on the desired spin while providing a manageable description of its environment in real time.

In summary, the innovative approach represents a critical step forward in our understanding and description of quantum phenomena.

The full article is available at the Physical Review Letter website and is open-access,

“Converting Long-Range Entanglement into Mixture: Tensor-Network Approach to Local Equilibration”
Miguel Frías-Pérez, Luca Tagliacozzo, and Mari Carmen Bañuls
Phys. Rev. Lett. 132, 100402 – Published 7 March 2024

Marie Carmen Bañuls has led the MPQ group participating in this collaboration while Luca Tagliacozzo has been working from Quinfog