# Tag Info

Accepted

### 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 ...

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
Accepted

### 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 $2$):                               ...

### 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 ...
Accepted

### 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 ...
1 vote
Accepted

### 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 ...
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 ...