NVIDIA’s GPUs Are Helping Researchers Attain New Skill Levels in Quantum Dynamics Simulations

Insider Brief

• Researchers at the Free University of Berlin are using NVIDIA GPUs to accelerate simulations of quantum dynamics, a key tool for advancing quantum technologies.
• The new method simplifies quantum systems by breaking down complex calculations, using GPUs to handle tasks that would take much longer on traditional CPUs.
• With these simulations, researchers can model larger quantum systems more efficiently, which is critical for future advancements in quantum computing and materials science.

Graphic Processing Units — once regarded primarily as a way to power video games — is now leveling up investigations into quantum information science.

A team of researchers at the Free University of Berlin introduced a powerful new method for simulating quantum dynamics by using GPUs, according to a NVIDIA Developer blog post.

Their approach, published in Nature Physics and supported by a NVIDIA Academic Grant, uses GPUs to tackle the complex challenges in simulating quantum systems, essential for the development of quantum computing and materials science. According to the research team, led by Jens Eisert and Steven Thomson, this method is a key step toward more accurate simulations that are computationally feasible at larger scales.

Quantum dynamics describe the behavior of systems that follow the laws of quantum mechanics. Simulating these systems is essential for understanding and predicting the behavior of materials, solar cells, batteries, and even novel qubit designs for quantum computing. However, simulating quantum systems in practice is notoriously difficult due to the complexity of their underlying mathematics, according to the post. Traditional simulation methods rely on solving differential equations, such as the Schrödinger Equation, which govern how quantum systems evolve over time.

The challenge lies in the fact that many-body quantum systems exist in vast mathematical spaces known as Hilbert spaces. The size of these spaces increases exponentially with the number of particles in the system, making exact solutions computationally intractable for large systems using conventional methods. Typically, researchers rely on approximations to make these simulations feasible, but striking the right balance between computational efficiency and accuracy remains difficult.

Eisert and Thomson’s work focuses on a technique called flow equations to simulate quantum dynamics. Instead of evolving a quantum state step by step, flow equations work by diagonalizing the Hamiltonian matrix that describes the system. This is done by applying many small transformations to the Hamiltonian, reducing the problem to a series of simpler calculations that can be handled efficiently by GPUs, according to the post.

In other words, the researchers turned the problem into a series of easier calculations. Then the GPUs, which can perform thousands of calculations at once, handled these tasks efficiently, allowing the researchers to simulate quantum systems that were previously too complex to model.

One of the primary advantages of the flow equation method is that it is not constrained by the degree of entanglement in the system — or, how strongly different parts of a quantum system are interconnected or correlated with each other. The higher the degree of entanglement, the more complex the interactions within the system. This is a limitation faced by many other simulation techniques. This makes it well-suited for simulating large quantum systems that have been difficult to handle with existing methods. Additionally, the method can be extended to simulate multidimensional systems, which are crucial for real-world quantum applications. For example, two-dimensional quantum lattices can be represented as one-dimensional chains, making the problem easier to solve computationally.

However, the method is not without its challenges. Flow equations can struggle to converge when the initial Hamiltonian, which you could think of as a map or formula for how the system behaves based on its energy, has multiple states with nearly identical energies, which is common in some of the more complex quantum systems researchers are interested in studying. To address this, Eisert and Thomson introduced the idea of scrambling transforms. These transforms “scramble” the initial Hamiltonian to remove energy degeneracies that would otherwise slow down or prevent the diagonalization process. This modification significantly improves the robustness of their approach.

The use of GPUs is central to the success of this new method. GPUs, originally developed for rendering graphics in video games, have become indispensable for scientific computing due to their ability to perform many calculations in parallel. For example, a single NVIDIA GPU contains tens of thousands of cores that can handle matrix multiplications and tensor operations, the backbone of quantum dynamics simulations, much more efficiently than traditional central processing units (CPUs).

The speedup provided by GPUs is dramatic. In their tests, the researchers showed that simulating a system of 24 particles, which would take over two hours on a CPU, could be completed in under 15 minutes on a GPU. Larger systems and more powerful GPUs, such as data-center grade models, could offer even greater speedups. These computational gains make it possible to explore larger and more complex quantum systems than previously feasible.

While the flow equation method is still in its early stages, it shows promise for advancing the study of quantum dynamics. The method’s ability to handle large, highly entangled systems could open up new avenues of research in quantum materials, condensed matter physics, and quantum computing. Eisert and Thomson are already planning to extend their work to simulate even larger and more complex systems, including those with multiple spatial dimensions.

Future efforts will likely involve multi-node GPU systems, allowing for even more efficient simulations of two- and three-dimensional quantum systems. These advancements in simulation techniques, combined with the power of GPUs, are expected to provide valuable insights into the behavior of quantum systems and further the development of practical quantum technologies.