Quantum Monte Carlo from polynomial roots

We introduce a Quantum Monte Carlo method for calculating the thermal averages of arbitrary powers of quantum many-body Hamiltonians. Within our technique, configuration weights can be calculated via polynomial root finding. The convergence of the Markov chain to equilibrium is guaranteed for every conceivable case because the QMC updates are provably ergodic and satisfy detailed balance. We demonstrate the ease with which a wide variety of arbitrarily complicated quantum many-body Hamiltonian moments can be computed.