Shadow Hamiltonian Simulation

Understand

Simulating quantum dynamics is one of the most important applications of quantum computers.

• Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.
• Here, we present a different and novel approach to quantum simulation that uses a compressed quantum state that we call the ``shadow state''.
• The amplitudes of this shadow state are proportional to the time-dependent expectations of a specific set of operators of interest, and it evolves according to its own Schr\"odinger equation.