Quantum Fourier transform

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SUMMARY

The Quantum Fourier Transform (QFT) is utilized in period finding algorithms, specifically for functions like f(x) ≡ a^x mod N. The input register consists of 2n qubits, while the output register is limited to n qubits. Ancilla bits are employed in the overall period finding circuit but do not contribute to the QFT's input size. The QFT effectively processes n input bits and n ancilla bits, discarding the ancilla bits as measured garbage, resulting in n outputs.

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jimmycricket
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When using the Quantum Fourier transform to find the period of the function f(x)\equiv a^x\mod N why is it that the input register is 2n qubits in size and the output register is n qubits?
 
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The overall period finding circuit probably uses ancilla bits, but turns them into measured garbage along the way. The Quantum Fourier Transform doesn't need ancilla bits, or measurement, so it's not the cause for adding them.

Personally, I wouldn't count ancilla bits against the input size. The circuit takes n input bits and n ancilla bits, burns the neg-entropy in the ancilla bits, and produces n outputs.
 

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