Running Quantum Computers in Discovery Mode

We propose using quantum computers in conjunction with classical machine learning to discover instances of interesting quantum many-body dynamics. Concretely, an ``interest function'' is defined for a given circuit (family) instance that can be evaluated on a quantum computer. The circuit is then adapted by a classical learning agent to maximize interest. We illustrate this approach using two examples and show numerically that, within a sufficiently general circuit family, two simple interest functions based on (i) classifiability of evolved states and (ii) spectral properties of the unitary circuit, are maximized by discrete time crystals (DTCs) and dual-unitary circuits, respectively. For (i), we also simulate the adaptive optimization and show that it indeed finds DTCs with high probability. Our study suggests that learning agents with access to quantum-computing resources can discover new phenomena in many-body quantum dynamics, and establishes the design of good interest functions as a future research paradigm for quantum many-body physics.