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2

"SWAPN" isn't something that would be universally understood. But you say you want it for your Fourier Transform algorithm, so by that, I interpret that what you want is: SWAP2(1,N).SWAP2(2,N-1).SWAP2(3,N-2)...., i.e. the pairwise swap between opposite qubits. It depends on context as to what it is you actually want to write down. For implementing in some ...

3

Depends on what you mean by SWAPN, that is what qubits are swapped. Your SWAP3 gate in Dirac notation is $$|000\rangle\langle 000|+|001\rangle\langle100|+|010\rangle\langle010|+|011\rangle\langle110|+|100\rangle\langle001|+|101\rangle\langle101|+|110\rangle\langle011|+|111\rangle\langle111|$$ that is the first and third qubits are swapped; assuming SWAPN ...

1

The action of any controlled gate is to do nothing (i.e. apply the identity operation) if the control qubit is in $\vert 0\rangle$ and apply an operation $U$ on the target when the control is in $\vert 1\rangle$. All other qubits in the system are also left untouched (i.e. apply the identity operation). Use the subscripts $c$ and $t$ for the control qubit ...

1

This feature is now available using the snapshot function of Qiskit Aer. Snapshots can be added to the circuit and the values are then returned in the results object. This is an example of how you can create a circuit, add a snapshot to it and then get the result: from qiskit import * qc = QuantumCircuit(2) qc.h(0) qc.snapshot('1') # add a ...

4

how can you compare the result of your algorithm with an ideal evolution? You cannot and you do not need to. As you said, computing $e^{-iHt}$ is intractable for most of the interesting cases. If it was not, chemistry simulations would be easy, solving the Schrödinger equation too. The thing you can do though is to prove that your algorithm will, for a (...

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