Precursors

Abstract

The best source of confirmation of the $\mathcal{{C}}= V$ hypothesis is to perturb the evolution of the black hole, and see if the correspondence between GR and quantum circuits continues to hold. For example we may allow some time-dependent perturbations to the CFT Hamiltonian and calculate the effect on the black hole geometry. At the same time we may study the effects of time-dependent perturbations on the complexity of a quantum circuit. By comparing the two we can confirm the complexity-volume correspondence. In this context so-called precursor operators are a useful tool.