5 votes
Accepted

Is it possible to modify the QFT circuit to use only 1-qubit gates?

This is called qubit recycling (when combined with introducing the qubits-to-QFT one by one). All you have to do is take the normal circuit, measure each qubit immediately after it gets Hadamard'ed, ...
Craig Gidney's user avatar
  • 35.3k
3 votes

Qiskit Runtime forbids reset gate?

Indeed, the problem is that initialize introduces a reset (see docs). ...
luciano's user avatar
  • 5,743
3 votes

How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

Surprisingly, the way to make a uniform superposition of all permutations is by using a sorting network. You make random shuffle states by sorting! Weird, right? This was figured out in "Improved ...
Craig Gidney's user avatar
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2 votes
Accepted

How to create the state $(n!)^{-\frac{1}{2}} \sum_{\pi \in S_n} | \pi, \pi (G) \rangle$ when $G$ is an undirected graph and $\pi$ a permutation

What you're missing is that if there is an efficient classical circuit to compute $\pi(G)$ from a binary representation of $\pi$, then it means that you are able to build the oracle: $$\mathcal{O}|\pi,...
Tristan Nemoz's user avatar
1 vote

U(2) vs. SU(2) for single-qubit gates; ignoring global phases

It is true that an element from U(2) can change the global phase of a state in an arbitrary way, the U(2) matrix $$\tag{1} \begin{pmatrix} e^{i\varphi} & 0 \\ 0 & e^{i\varphi} \end{...
Jos Bergervoet's user avatar
1 vote
Accepted

How does syndrome extraction in bit-flip codes using stabilizers work?

The state is not $-\vert ++\rangle\vert 100\rangle$ after the second set of gates. That would be true if you applied $Z$ gates but you are applying controlled $Z$ gates. Let's just look at the ...
rnva's user avatar
  • 692

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