Exploring Lattice Gauge Theory with Google’s Quantum Computers

Google’s quantum processors enable groundbreaking research into particle interactions, confinement, and gauge theory, setting the stage for innovations in physics and beyond.

Research: Confinement in a Z2 lattice gauge theory on a quantum computer

Science is always looking for more computing power and more efficient tools capable of answering its questions. Quantum computers are the new frontier in data processing, as they use the quantum properties of matter, such as the superposition of states and entanglement, to perform very complex operations.

A research team coordinated by the Department of Physics of the University of Trento had the opportunity to test some hypotheses on confinement in ℤ2​ lattice gauge theory on the quantum computers of Google's Quantum Artificial Intelligence Lab in California. Their work was published in Nature Physics.

Gauge theories describe the fundamental forces in the standard model of particle physics and play an important role in condensed matter physics. The constituents of gauge theories, such as charged matter and electric gauge fields, are governed by local gauge constraints, which lead to key phenomena that are not yet fully understood. The team's work focused on demonstrating confinement dynamics, where charges are bound together by gauge fields, and how modifying these constraints can influence system behavior. In this context, quantum simulators may offer solutions that cannot be reached using conventional computers.

"At the end of 2019 – explains Philipp Hauke, professor of theoretical physics of fundamental interactions at UniTrento and corresponding author of the research – Google launched a call for projects exploring the potential of quantum computers. The University of Trento was among the eight winners worldwide, the only institution in the entire European Union."

The group led by Professor Hauke chose to work on a question concerning elementary particles, particularly lattice gauge theory, according to which continuous spacetime is typically discretized into a hypercubic lattice of points. The question concerned the ways in which electrons, positrons, and, in perspective, quarks and gluons interact to form particles and matter.

The research team wrote an algorithm that was sent to Google's powerful computers, which performed the computations remotely. These quantum supercomputers, located in Santa Barbara, use the quantum properties of matter to describe quantum objects in a very natural way, something that the classic "bits," based on the binary opposition between 0 and 1, cannot do. These processors, specifically Sycamore-class chips, employed advanced error mitigation techniques to maintain the integrity of gauge constraints and handle up to 21 qubits in simulations.

"To give you an idea of the potential of these computers – continues Hauke – we can say that classical instruments, without further approximations, are able to correctly solve the dynamics of systems with a maximum of 40 particles. Quantum computers have the potential to process an exponentially greater number. To achieve this goal, however, it is necessary to work at the interface between fundamental physics and engineering. And that is where our research is located."

The experiments demonstrated confinement, where increasing the interaction strength between gauge fields and charges restricted the motion of particles. In another experiment, modifying the gauge constraints from ℤ2 symmetry showed how the system's dynamics could be frozen entirely. These results validate quantum computing as a viable tool for exploring such phenomena.

What about the future of this research? Hauke replies: "At the moment, our research is interesting for theoretical and experimental physics. In the future, however, it could have various applications, for example in the industrial sector for the study of new materials, or in the pharmaceutical sector for chemical compounds." Additionally, the work paves the way for studying more complex non-Abelian gauge theories and refining error mitigation strategies, which could significantly advance the field of quantum simulation.

The results of the research have been published in Nature Physics. The article "Confinement in ℤ2 lattice gauge theory on a quantum computer" is available at: https://www.nature.com/articles/s41567-024-02723-6.

The authors of the study are Julius Mildenberger (Pitaevskii Bec Center, CNR-INO and Department of Physics of the University of Trento, Trento Institute for Fundamental Physics and Applications), Wojciech Mruczkiewicz (Google Quantum Ai), Jad C. Halimeh (Pitaevskii Bec Center, CNR-INO and Department of Physics of the University of Trento, Ludwig-Maximilians-Universität München and Munich Center for Quantum Science and Technology), Zhang Jiang (Google Quantum Ai) and Philipp Hauke (Pitaevskii Bec Center, CNR-INO and Department of Physics of the University of Trento, Trento Institute for Fundamental Physics and Applications).