  We present and compare new types of algorithms for lattice QCD with staggered
fermions in the limit of infinite gauge coupling. These algorithms are
formulated on a discrete spatial lattice but with continuous Euclidean time.
They make use of the exact Hamiltonian, with the inverse temperature beta as
the only input parameter. This formulation turns out to be analogous to that of
a quantum spin system. The sign problem is completely absent, at zero and
non-zero baryon density. We compare the performance of a continuous-time worm
algorithm and of a Stochastic Series Expansion algorithm (SSE), which operates
on equivalence classes of time-ordered interactions. Finally, we apply the SSE
algorithm to a first exploratory study of two-flavor strong coupling lattice
QCD, which is manageable in the Hamiltonian formulation because the sign
problem can be controlled.
