Complexity Growth Rate in Lovelock Gravity.

Using the complexity=action framework, we compute the late time growth of complexity for charged black holes in Lovelock gravity. Our calculation is facilitated by the fact that the null boundaries of the Wheeler-DeWitt patch do not contribute at late times and essential contributions coming from the joints are now understood. The late time growth rate reduces to a difference of internal energies associated with the inner and outer horizons, and in the limit where the mass is much larger than the charge, we reproduce the celebrated result of 2M/π with corrections proportional to the highest Lovelock coupling in even (boundary) dimensions. We find in some cases a minimum mass below which complexity remains effectively constant, even if the black hole contains a nondegenerate horizon.

Toward a Definition of Complexity for Quantum Field Theory States.

We investigate notions of complexity of states in continuous many-body quantum systems. We focus on Gaussian states which include ground states of free quantum field theories and their approximations encountered in the context of the continuous version of the multiscale entanglement renormalization ansatz. Our proposal for quantifying state complexity is based on the Fubini-Study metric. It leads to counting the number of applications of each gate (infinitesimal generator) in the transformation, subject to a state-dependent metric. We minimize the defined complexity with respect to momentum-preserving quadratic generators which form su(1,1) algebras. On the manifold of Gaussian states generated by these operations, the Fubini-Study metric factorizes into hyperbolic planes with minimal complexity circuits reducing to known geodesics. Despite working with quantum field theories far outside the regime where Einstein gravity duals exist, we find striking similarities between our results and those of holographic complexity proposals.