How much memory is required for simulating a quantum computer?

Difference between Classical Computer and Quantum Computer

The fundamental representation of information differs significantly between classical computer bits and quantum computer qubits. This is because qubits can exist in intermediate states between 0 and 1, so even for just a single qubit, a considerable number of classical bits are needed to accurately represent that information.

How to estimate

So, how much memory is needed for a quantum computer? Let’s make a rough estimate:

• Let’s assume that the real and imaginary parts of one quantum bit (qubit) are each represented using 64 bits.
• There are 2^n probability amplitudes for n qubits.

2 × 64 × 2^{n}

If we were to represent 30, 40, 50 qubits using classical bits, then:

\begin{align*}
2 × 64 × 2^{30} / 2^{30} / 2^{8}= 16[GB]\\
2 × 64 × 2^{40} / 2^{30} / 2^{8} =16[TB]\\
2 × 64 × 2^{50} / 2^{30} / 2^{8} =16[PB]\\
\end{align*}

It means that simulating 50 bits of Quantum Computers is quite difficult because a massive amount of memory is required.

Reference

[1] 量子コンピューティング 基本アルゴリズムから量子機械学習まで