Quantum computers process information in quantum bits (qubits) using quantum gates. At a first glance, it seems unrealistic or impossible that the brain can meet the challenges to provide either of them. Nevertheless, we will sketch a rough roadmap to show that the brain may have the incredible ability to perform quantum computing. First, we will suggest the existence of an unknown non-neuronal computing network in the brain. Then, we will further argue that this network must be based on quantum computing. Finally, we look at how the brain could realize it.