The true power of quantum computing only becomes evident as we increase the number of qubits. Single-qubit gates possess some counter-intuitive features, such as the ability to be in more than one state at a given time. However, if all we had in a quantum computer were single-qubit gates, then a calculator and certainly a classical supercomputer would dwarf its computational power.
Quantum computing power arises, in part, because the dimension of the vector space of quantum state vectors grows exponentially with the number of qubits. This means that while a single qubit can be trivially modeled, simulating a fifty-qubit quantum computation would arguably push the limits of existing supercomputers. Increasing the size of the computation by only one additional qubit doubles the memory required to store the state and roughly doubles the computational time. This rapid doubling of computational power is why a quantum computer with a relatively small number of qubits can far surpass the most powerful supercomputers of today, tomorrow, and beyond for some computational tasks.
