The state vector (all the probability amplitudes) of 50 qubits is stored in the memory of a classical computer as double-precision complex numbers of 16 bytes each. Which is closest to the memory required?

Answer: C. About 18 PB

There are 2 to the power of 50, about 1.13×10¹⁵, amplitudes, so the memory required is about 1.8×10¹⁶ bytes, or about 18 PB. Each additional qubit doubles the memory: 30 qubits need only about 17 GB, but 40 qubits need about 18 TB, and with 50 qubits even the largest supercomputers have difficulty holding the state vector as is. On the other hand, a single measurement of a quantum computer yields only 50 bits. Quantum algorithms therefore have to use interference to arrange the amplitudes so that the desired answer is obtained with high probability.

• A. This is 50 × 16 bytes, assuming one amplitude per qubit. 2 to the power of 50 amplitudes are needed.
• B. This is 2 to the power of 40 × 16 bytes, the value for 40 qubits.
• C. Correct. 2 to the power of 50 × 16 bytes ≈ 1.8×10¹⁶ bytes.