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The expression "O(n²)" in this quote is referring to the time complexity of the quantum Fourier transform algorithm. It means that the number of operations required to perform the transform grows proportionally to the square of the number of qubits (n).

Here's a breakdown:

• Big O Notation: "O" is a mathematical notation used in computer science to describe how the time or space resources required by an algorithm grow as the input size increases.
• n²: This means the number of operations scales quadratically with the number of qubits. If you double the number of qubits, the number of operations needed will increase by a factor of four.

In simpler terms: The quantum Fourier transform is relatively efficient, especially compared to classical algorithms for the Fourier transform. However, its efficiency does decrease slightly as the number of qubits increases, but not as drastically as some other algorithms that might require O(n³) or even higher complexities.