The disclosed method and computer-readable medium allow efficient simulation of both stabilizer and non-stabilizer states in general quantum circuits on a classical computer by maintaining global phases and orthogonalizing linear combinations of stabilizer states during simulation. This is accomplished by representing arbitrary quantum states as superpositions of stabilizer states, which may be implemented using one or more stabilizer frames. Each stabilizer frame includes a stabilizer matrix, one or more phase vectors corresponding to the stabilizer states, and an amplitude vector corresponding to the global phases of each stabilizer state. Orthogonality is maintained throughout the simulation for efficient computation and measurement. Some embodiments utilize a multiframe representation of the quantum state to reduce the number of stabilizer states required to represent the quantum state, which multiframe representation may also be used to implement parallel simulation.