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5 votes

Why doesn't Shor's algorithm output a solution for some numbers?

What you should have seen in texts is the statement that you have to pick $a$ at random from the numbers that are coprime to $N$. There are then certain claims about the order, $r$ that you get: with ...
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8 votes

Why doesn't Shor's algorithm output a solution for some numbers?

If $f(x) = a^x \pmod{N}$ passes through $-1$, that value of $a$ won't work. For example, $a=2$ fails for $N=33$ because $2^5 = 32 \equiv -1 \pmod{33}$. This should have been mentioned in whatever ...
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1 vote

I have question about cost of 'modular multiplication unitary' in Shor's algorithm

The point is that you can perform this calculation efficiently on a classical computer. So you can implement the same algorithm on a quantum computer. Just think: if you had to do this calculation by ...
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0 votes

Continued fractions with Shor's algorithm: which convergent?

This is actually a good question that most texts don't bother to explain. I don't see a reason why we should pick the largest possible convergent, that is, $p_k/q_k$ such that $q_k < N$ but $q_{k+1}...
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0 votes

Implementation of Unitary in Shor's Algorithm in PennyLane

Yes, it seems to me you apply it in a right way, except some points I listed after. The circuit making $U$ you found is simply a way to check how Shor's algorithm works, and is simply built from the ...
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1 vote

Is it possible to turn modular multiplication into in-place operation?

I thought this question was going to be about whether you can perform the operation $|k\rangle \rightarrow |k\cdot C \pmod{N}\rangle$ for classical constants $C, N$ using only the $k$ register (i.e. ...
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0 votes
Accepted

Is it possible to turn modular multiplication into in-place operation?

Okay so the paper epelaaez mentionned answers to the question. The answer it gives is : no, the modular multiplication is not useless. It is even very close to what is needed. Having the operation $...
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4 votes

How accurate must QM be for applications of quantum computing?

Because quantum mechanics is linear, and all operations have eigenvalues on the complex unit circle, relative precision is the key metric. A uniform superposition over 1000 qubits has amplitudes ...
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1 vote

How to run Quantum Instance into ibmq_qasm_simulator

You can run it on IBM circuit runner.Just execute the following code with your circuit. ...
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