Quantum geometry describes quantum states in systems with changing system parameters, such as an electron spinning in a magnetic field whose direction is slowly changing. The state of the electron evolves, and this change is quantified by what is known as the quantum geometric distance.

With the help of this abstract geometric description, it is possible, for example, to explain superconductivity—defined as the resistance-free conduction of current—in exotic quantum materials. Another example can be found in quantum metrology: by applying quantum geometry, fundamental limits on measurement accuracy can be determined.