While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum states on a lattice in real space. In particular, the present algorithm is able to prepare general pure and mixed many-particle states of any number of particles. It relies on a procedure for converting from a second-quantized state to its first-quantized counterpart. The algorithm is efficient in that it operates in time that is polynomial in all the essential descriptors of the system, such the number of particles, the resolution of the lattice, and the inverse of the maximum final error. This scaling holds under the assumption that the wavefunction to be prepared is bounded or its indefinite integral known and that the Fock operator of the system is efficiently simulatable.
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