Galli graduated summa cum laude, in physics, from the University of Modena, Italy, in 1982. She then attended the International School for Advanced Studies in Trieste, Italy, receiving a master’s degree in 1984 and a doctorate in 1986, both in physics. Postdoctoral fellowships followed for Galli at the University of Illinois, Urbana-Champaign, and at the IBM Research Division in Zurich, Switzerland. Galli continued her career at the Swiss Federal Institute of Technology in Lausanne, Switzerland, and at Lawrence Livermore National Laboratory, where she led the Quantum Simulations Group.