Drawing on recent advances, I will discuss the circuit complexity of preparing ground states and thermal states of a variety of quantum many-body systems whose low energy physics is well described by a quantum field theory. I will then argue that the structure of the relevant circuits is such that they may be implementable on near term quantum devices. Finally, I will discuss how these ideas may be used to simulate aspects of black holes and quantum gravity.
*This talk is part of the Computational Complexity and High Energy Physics Workshop*
