CQE PI Feature – Jean-Jacques Slotine 

Featured in QSEC August newsletter 2025

Jean-Jacques Slotine is a Professor of Mechanical Engineering and of Brain and Cognitive Sciences. He works on dynamical systems theory and machine learning, with applications to robotics, adaptive nonlinear control, computational neuroscience, and convergence and generalization in deep networks.

Although his Interest in all things quantum started with quantum computing in the early 2000’s, when he co-authored the first paper on analog quantum error correction, he has returned to research in the field only recently. Specifically, his work with WInfried Lohmiller (first presented at Helgoland 2025) shows that the Schroedinger equation can be solved exactly based only on classical least action. The fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic Dirac and Maxwell equations, and suggest a smooth transition between physics across scales.

Most quantum mechanics problems have classical versions which involve multiple least action solutions. These extremal action paths may stem  from spatial inequality constraints (as in the double slit experiment), from singularities in the Hamiltonian (as in a Coulomb potential), from a closed configuration manifold (as for a spinning particle), or just from the initial action distribution.

One can show that the exact Schroedinger wave function  of the original quantum problem can be constructed by combining this classical multi-valued action with the density of the classical position dynamics, where a key point is that along each extremal action path the density can be easily computed from the action. The construction is general and does not involve any quasi-classical approximation.

These computations based on action are very different from the usual techniques for solving the Schroedinger or Dirac equations. For instance, a wave solution for general nonlinear potentials is obtained from an eikonal p.d.e. Current research explores deriving quantum gravity waves based on the known action solution of the Schwarzschild metric. The results also provide a simpler computational alternative to Feynman path integrals, as they use only a minimal set of classical paths and avoid zig-zag paths and time-slicing altogether

Further exploration of this action-based perspective may also simplify the study of systems modeled as composites of quantum and classical dynamics. The differentiability of the classical paths may make machine learning techniques readily applicable, e.g. in computational quantum chemistry. The close analogy of stationary action paths and classical density with light rays and intensity in classical optics might open the way to translate the results into optical or electromagnetic methods for quantum simulation and quantum computing. Finally, the ability to derive quantum quantities from a discrete set of classical action paths may have implications on some of the assumptions in quantum information processing.