 Note that there is currently no proof that a quantum algorithm can solve an NP-complete problem in polynomial time, so the efficiency of quantum computers relative to classical computers could turn out to be illusory. If there is indeed a speed-up, it would seem to be due to the phenomenon of entanglement. The amount of information required to describe a general entangled state of \(n\) qubits grows exponentially with \(n\). The state space (Hilbert space) has \(2^n\) dimensions, and a general entangled state is a superposition of \(2^n\) \(n\)-qubit states. In classical mechanics there are no entangled states: a general \(n\)-bit composite system can be described with just \(n\) times the amount of information required to describe a single bit system. So the classical simulation of a quantum process would involve an exponential increase in the classical informational resource required to represent the quantum state, as the number of qubits that become entangled in the evolution grows linearly, and there would be a corresponding exponential slowdown in calculating the evolution, compared to the actual quantum computation performed by the system. 