Variational Quantum Simulations Model Open Systems with Long-Range Interactions up to Sites

Competition between short and long-range interactions drives many fascinating phenomena in the natural world, yet simulating these complex systems remains a significant challenge for computational physicists. Dawid A. Hryniuk and Marzena H. Szymańska, both from University College London, now present a new method to accurately model these ‘open quantum systems’, which exchange energy and information with their surroundings. Their approach combines matrix product operators with time-dependent Monte Carlo simulations, offering a scalable way to study the behaviour of many interacting particles. The team demonstrates the power of this technique by simulating the dynamics of spin lattices with competing interactions, revealing the emergence of spatially-modulated magnetic order even when the system is far from equilibrium, and opening new avenues for understanding diverse systems like Rydberg atoms and trapped ions.

This research addresses the challenge of accurately simulating open quantum many-body systems at scale by developing a variational approach to study systems with long-range competing interactions. The method employs a systematically improvable ansatz, constructed from locally entangled states, to efficiently represent the many-body wavefunction, allowing for the inclusion of both dissipative and coherent dynamics. The team demonstrates the efficacy of this method by applying it to a model system, revealing previously inaccessible insights into its behaviour.

The research overcomes limitations by introducing an efficient and scalable approach to dissipative quantum lattices in one and two dimensions, combining matrix product operators and time-dependent variational Monte Carlo. Simulations reveal the emergence of spatially-modulated magnetic order far from equilibrium, a phenomenon previously difficult to observe with existing methods, and offer promising prospects for advancing understanding of the complex non-equilibrium properties of experimentally-relevant systems.

Open Quantum System Simulations with Tensor Networks

This research presents a new computational method for simulating complex many-body systems exhibiting both short- and long-range interactions. The team developed a technique combining tensor networks with variational Monte Carlo simulations, enabling the study of systems with up to hundreds of sites. This approach successfully models the emergence of spatially-modulated magnetic order in spin lattices with competing interactions, revealing dynamic behaviour far from equilibrium conditions.

Long-Range Interactions Simulated with Monte Carlo

The significance of this work lies in its ability to tackle the longstanding challenge of accurately and scalably simulating systems with long-range interactions. By demonstrating the effectiveness of their method on several model systems, the researchers provide a valuable tool for investigating a wide range of physical phenomena, including those found in Rydberg atoms, ultracold dipolar molecules, and trapped ions. Future research directions include exploring more efficient algorithms and applying the method to study more complex and realistic physical systems.