In quantum computing, the basic unit of information is a qubit. Simulation of a general quantum program takes exponential time in the number of qubits, which makes simulation infeasible beyond 50 qubits on current supercomputers. So, for the understanding of larger programs, we turn to static techniques. In this paper, we present an abstract interpretation of quantum programs and we use it to automatically verify assertions in polynomial time. Our key insight is to let an abstract state be a tuple of projections. For such domains, we present abstraction and concretization functions that form a Galois connection and we use them to define abstract operations. Our experiments on a laptop have verified assertions about the Bernstein-Vazirani, GHZ, and Grover benchmarks with 300 qubits.