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