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I've started getting into quantum computing in the last few days. As part of the learning, I've figured it would be fun to implement some circuits on IBMQ Experience as I learn. So now I'm stuck with implementing a 2-qubit QFT. My first try was this:

Where in red is my implementation of a controlled-phase rotation by pi. I did it based on some paper I found which explains how to construct a universal controlled gate. On 00 input it gave a 1/4 1/4 1/4 1/4 probability as expected. Then for sanity check, I figured I might try a 'DC' input (hence the Hadamard gates at the start) so the output would be 100% 00 but it failed. After some reading on the internet, I came by this question. The answer there is basically that the 'controlled' phase shift need only use a simple phase rotation on the MSB qubit. His explanation seemed sound and it did work for the 'DC' case. So, my final question is - why my implementation is wrong? I've tried doing the math and it seems ok: when q[2] is 0, q[1] isn't rotated, and when q[2] is 1 q[1] is rotated by pi (+ a global -pi/2 phase).

Can I get some explanation, please? I think I'm missing something.

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    $\begingroup$ algassert.com/… $\endgroup$
    – Craig Gidney
    Jun 3, 2019 at 21:30
  • $\begingroup$ Hey craig, I haven't understood what were you trying to show me with that circuit. Do you care to explain? Thanks. $\endgroup$
    – Dan Yaron
    Jun 4, 2019 at 17:34

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I think my circuit is wrong is as there is indeed a conditional phase shift on q[1], but as I said it also adds to him a 'global' phase which I didn't care for. This 'global' phase isn't actually global for the whole 2-qubits system, as it doesn't affect q[2].

A reminder for me of the necessity to look at the system as a whole when talking about qubits, as opposed to classical bit by bit examination.

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