Quantum Simulation of Open Systems via Stochastic Variational Monte Carlo.

The behaviour of quantum systems invariably involves interaction with their environment, leading to dissipation and decoherence that complicate theoretical modelling. Researchers are continually developing methods to accurately simulate these ‘open quantum dynamics’, crucial for understanding phenomena ranging from the efficiency of quantum technologies to the behaviour of materials. A new approach, detailed in a recent publication, circumvents the computational challenges traditionally associated with modelling these systems by combining time-dependent variational Monte Carlo (tVMC) with trajectory techniques. This allows for the efficient simulation of complex, dissipative systems in multiple dimensions. Christian Apostoli, Jacopo D’Alberto, Marco G. Genoni, Gianluca Bertaina, and Davide E. Galli, from the University of Milan and the National Metrological Research Institute, present their work, entitled “Unraveling Open Quantum Dynamics with Time-Dependent Variational Monte Carlo”, demonstrating its efficacy through simulations of the locally dissipative long-range Ising model, a system relevant to experiments utilising trapped ions and Rydberg atoms.

Researchers have developed a new computational method for simulating open quantum systems, addressing longstanding challenges in tracking the evolution of the density matrix and overcoming limitations inherent in traditional approaches. Open quantum systems, unlike isolated ones, interact with their environment, leading to decoherence and dissipation which are notoriously difficult to model accurately. The team combines time-dependent variational Monte Carlo (tVMC), a stochastic method for approximating solutions to the time-dependent Schrödinger equation, with trajectory techniques. This transforms the Lindblad master equation, the standard equation describing the evolution of open quantum systems, into a set of stochastic Schrödinger equations governed by a variational ansatz. A variational ansatz is an educated guess for the form of the solution, which is then optimised to minimise the energy of the system. This allows for efficient simulation of complex systems with many interacting particles.

The innovation circumvents the exponential scaling of computational cost typically encountered when simulating open quantum systems. Traditional methods struggle because the computational resources required grow exponentially with the number of particles, quickly becoming intractable. The authors employ Stratonovich numerical solvers, a type of algorithm designed to accurately handle the stochastic equations governing the variational parameters. This ensures the stability and precision of the simulations, particularly when dealing with multiple sources of noise and complex interactions. Furthermore, the method exhibits compatibility with a wide range of variational ansatzes, including those utilising the expressive power of neural networks. This offers unparalleled flexibility in modelling diverse quantum systems and exploring a broader range of physical phenomena.

To validate the approach, researchers simulate quenches – sudden changes in system parameters – within the locally dissipative long-range Ising model in a transverse field. This model, relevant to experiments involving trapped ions and Rydberg atoms, allows for a rigorous test of the method’s capabilities. The simulations accurately capture both the magnetization, the average spin orientation of the particles, and spin squeezing, a measure of quantum correlations beyond those found in classical systems. This confirms the method’s ability to model realistic physical phenomena and predict system behaviour under dynamic conditions.

The computational efficiency and scalability of the framework are particularly noteworthy. Researchers can run simulations on high-performance computing platforms, enabling investigations of larger and more complex systems than previously possible. This advancement promises significant implications for both fundamental science and technological advancements, including the development of more robust quantum technologies and a deeper understanding of materials with exotic properties. The team highlights the ease with which this methodology integrates into existing tVMC implementations, lowering the barrier to adoption for researchers already familiar with this powerful technique and fostering collaboration within the scientific community.