Play around with simulations of quantum circuits!
QuantumMechanic [currently down] simulates and displays quantum circuits using QuTiP, and outputs the behaviour of the resulting n-qubit circuit as a 2n-by-2n unitary matrix. (Naturally, this means you’re not allowed to use very many qubits!)
Built as my final project in 6.845: Quantum Complexity Theory.
See the code on GitHub.