Simulation of sparse qubit systems

We simulate the effect of unitary transformations on multi-qubit systems. The memory requirements arising from a exponentially growing state space are managed by assuming that the density matrix stays sparse during the simulation. We replace the customary matrix exponentiation with optimized computations in structure-constant Lie algebras. This allows us to better account for efficiency and sparsity while increasing the number of qubits. We present computer experiments with several tens of qubits and explore applications to the simulation of quantum algorithms.