  When the electric conductance of a nano-sized metal is measured at low
temperatures, it often exhibits complex but reproducible patterns as a function
of external magnetic fields, called quantum fingerprints in electric
conductance. Such complex patterns are due to quantum-mechanical interference
of conduction electrons; when thermal disturbance is feeble and coherence of
the electrons extends all over the sample, the quantum interference pattern
reflects microscopic structures, such as crystalline defects and the shape of
the sample, giving rise to complicated interference. Although the interference
pattern carries such microscopic information, it looks so random that it has
not been analysed. Here we show that machine learning allows us to decipher
quantum fingerprints; fingerprint patterns in magneto-conductance are shown to
be transcribed into spatial images of electron wave function intensities (WIs)
in a sample by using generative machine learning. The output WIs reveal quantum
interference states of conduction electrons, as well as sample shapes. The
present result augments the human ability to identify quantum states, and it
should allow microscopy of quantum nanostructures in materials by making use of
quantum fingerprints.
