A state (i.e., ket) of a set of qubits may be simulated via a classical computer. Ordering characteristics of the ket (i.e., the “current” permutation associated with the state) may be determined. An operator (which may be associated with a certain operation to perform on the ket) may be defined and simulated. Ordering characteristics of the operator (i.e., the “current” permutation associated with operator) may be determined. If the current permutations of the state and operator match, then the operation may be performed to generate a new ket. Alternatively, the operator may be permuted to match the permutation of the current state. Or the state may be permuted to match the current operator permutation. The operation may then be performed, and the state and permutation remembered for the next operation. The process may be repeated for each operation in the series.