Implicit differentiation of variational quantum algorithms

Understand

Several quantities important in condensed matter physics, quantum information, and quantum chemistry, as well as quantities required in meta-optimization of machine learning algorithms, can be expressed as gradients of implicitly defined functions of the parameters characterizing the system.

• Here, we show how to leverage implicit differentiation for gradient computation through variational quantum algorithms and explore applications in condensed matter physics, quantum machine learning, and quantum information.
• A function defined implicitly as the solution of a quantum algorithm, e.g., a variationally obtained ground- or steady-state, can be automatically differentiated using implicit differentiation while being agnostic to how the solution is computed.
• We apply this notion to the evaluation of physical quantities in condensed matter physics such as generalized susceptibilities studied through a variational quantum algorithm.