  We propose how to compute the complexity of operators generated by
Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The
Hamiltonians in QFT/QM and quantum circuit have a few essential differences,
for which we introduce new principles and methods for complexity. We show that
the complexity geometry corresponding to one-dimensional quadratic Hamiltonians
is equivalent to AdS$_3$ spacetime. Here, the requirement that the complexity
is nonnegative corresponds to the fact that the Hamiltonian is lower bounded
and the speed of a particle is not superluminal. Our proposal proves the
complexity of the operator generated by a free Hamiltonian is zero, as
expected. By studying a non-relativistic particle in compact Riemannian
manifolds we find the complexity is given by the global geometric property of
the space. In particular, we show that in low energy limit the critical
spacetime dimension to ensure the "nonnegative" complexity is the 3+1
dimension.
