Tensor Networks in Simulation of Quantum matter

Quantum systems are known for their unique properties that are unmatched in the classical world, making them promising candidates for developing new materials and technologies. First, however, we need to be able to study the properties of such quantum matter. Unfortunately, the quantum features that make these systems so interesting are also what prevents us from understanding them with our established classical tools, such as supercomputer simulations. Luckily, quantum mechanics also offers a solution to this problem: quantum simulators. These are special purpose quantum devices that are designed to mimic the physics of a quantum system of interest, just like a wind tunnel mimics the physics of air flow around an aircraft. Small-scale quantum simulators are now a well-established technology, and are starting to enter a regime where classical computers can no longer keep up. The present project is dedicated to bringing these devices to the next level by addressing key challenges that come with scaling quantum systems beyond the classical regime. On the one hand, there is an urgent need for tools that allow us to ensure these devices really do what they promise. On the other hand, we need to design new algorithms for using these quantum simulators to study physical systems of interest. Finally, learning from the quantum way of simulating physical systems can allow us to make more efficient use of classical as well as quantum resources and get the best of both worlds. A promising way to addressing all these challenges is through the use of so-called Tensor Networks. These are mathematical objects with a structure that is inspired by the properties of the underlying quantum systems, yet with a complexity that can be kept manageable for classical computers. This makes tensor networks ideal for supporting the development of quantum simulators. They can provide approximate classical solutions for a range of large-scale quantum problems, which can be used to benchmark and validate quantum simulators before using them for problems that cannot be solved classically. At the same time, tensor networks can inspire new ways of using our quantum devices in tandem with classical computers. Together, these advances will contribute to unlocking a wealth of new physics to be studied by quantum simulators.

Quantum systems are known for their unique properties that are unmatched in the classical world, making them promising candidates for developing new materials and technologies. First, however, we need to be able to study the properties of such quantum matter. Unfortunately, the quantum features that make these systems so interesting are also what prevent us from understanding them with our established classical tools, such as supercomputer simulations. Luckily, quantum mechanics also offers a solution to this problem: quantum simulators. These are special-purpose quantum devices that are designed to mimic the physics of a quantum system of interest, just like a wind tunnel mimics the physics of air flow around an aircraft. Small-scale quantum simulators are now a well-established technology, and are starting to enter a regime where classical computers can no longer keep up. The present project is dedicated to bringing these devices to the next level by addressing key challenges that come with scaling quantum systems beyond the classical regime. On the one hand, there is an urgent need for tools that allow us to ensure these devices really do what they promise. On the other hand, we need to design new algorithms for using these quantum simulators to study physical systems of interest. Finally, learning from the quantum way of simulating physical systems can allow us to make more efficient use of classical as well as quantum resources and get the best of both worlds. A key result of this project is the experimental study of quantum states of matter in chains of quantum magnets, which have no classical counterpart. The simplest case, where each of these quantum magnets, or spins, has two distinct possible states, is called a qubit and forms the basis of most of today's quantum computers. In nature, however, spins typically have more than two states, which can lead to surprisingly different behaviour. In his Nobel Prize-winning work, D. Haldane discovered that spin chains with an odd number of states show so-called topological features, not seen in any classical systems, while spin chains with an even number of states do not. By using a novel quantum computer based on multi-state spins, we directly realized and observed Haldane physics and studied the properties from the perspective of material science, as well as quantum information. These results pave the way for quantum simulation of matter as it appears naturally in the world.