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3 votes
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Qiskit: How to implement this function?

The easiest way to do this is to use the classical function compiler to build a boolean function and synthesize a quantum circuit object from that function. For example, using your boolean logic ...
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Oracle for amplitude addition

You can do this using linear combination of unitaries (LCU) technique. It is described in the paper you mentioned (section 7.3). More specifically, see example 7.12
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5 votes
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Depth circuit optimization for 6-qubits GHZ state

If you have nearest neighbor ("grid") connectivity, you can prepare an $n$-qubit GHZ with depth $O(\log(n))$ (with the best savings when $n$ is a power of $2$):                               ...
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3 votes

Depth circuit optimization for 6-qubits GHZ state

How about that: It has depth of 4 instead of 6
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2 votes

What is the average amount of gates needed to implement a random Clifford gate?

It's $O(n^2)$ operations from various constructive decompositions (such as in "Hadamard-free circuits expose the structure of the Clifford group "). You can prove from information theoretic ...
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3 votes
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Construct a two-qubit quantum gate with given action using the gates ${CNOT, H, T}$

The $T$ gate applies a phase of $e^{\pi i / 4}$ to $|1\rangle$, i.e., it has the following effect: $T(\alpha|0\rangle + \beta|1\rangle) = \alpha|0\rangle + e^{\pi i / 4}\beta|1\rangle$. We want this ...
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1 vote
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Qiskit: QAOAnsatz circuit with custom Hamiltonian

Assume that $U$ is given as a quantum circuit: U = QuantumCircuit(num_qubits) Then to get the state vector $\left| b \right>$ we can use ...
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There exists an efficient gate that swaps values of different superposition kets?

If you know $\alpha_1$ and $\beta_1$, this is easy. Let $x=\alpha_1\oplus\beta_1$ (bit-wise addition modulo 2). Let $X_x$ apply bit flips on the sites where the bits of $x$ are 1, and identity on the ...
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