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# Questions tagged [shors-algorithm]

Shor's algorithm, named after American mathematician Peter Shor, is a quantum algorithm for integer factorization, formulated in 1994. Informally, it solves the following problem: given an integer N, find its prime factors.

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### Suggestions for hybrid factoring algorithm on DWave and Qiskit

I was wondering if the multi-prime factoring problem can be solved in a hybrid approach using DWave (to factor) and Shor's algorithm (in Qiskit)? Please let me know your thoughts. Thanks!
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### How to measure entanglement in an algorithm?

Entanglement in Algorithms Most algorithms in quantum computing find their strength in making use of entanglement. I am interested in evaluating the amount of entanglement generated within an ...
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### Is it possible to run a general implementation Shor's algorithm on a real IBM quantum computer at least for N = 15?

I need to make a general implementation of Shor's algorithm that factors, at least, N = 15. I have been able to perform an implementation that works in simulators, with ProjectQ, but when running it ...
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### Is there a simple, formulaic way to construct a modular exponentiation circuit?

I'm a newcomer to quantum computing and circuit construction, and I've been struggling to understand how to make a modular exponentiation circuit. From what I know, there are several papers on the ...
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### Can anybody explain or suggest a good reference on how to make a modular exponentiation circuit for N=15 with any coprime base?

I have read many papers related to it but in every paper, they just show the circuit of order finding algorithm for N=15, but did not explain what is the procedure to make it. It will be great if ...
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### Why should we use inverse QFT instead of QFT in Shor's algorithm?

Why should we use inverse QFT instead of QFT in Shor's algorithm? When I tried to simulate Shor's algorithm for small numbers, I got an answer even when I used just QFT instead of inverse QFT.
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### Are there any other published quantum factoring algorithms that are simpler or more efficient than Shor’s?

How many qubits and what is the minimum number of gate operations needed to factor an n-bit integer? Are there any other published algorithms that are simpler or more efficient?
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### Reason for evaluating $a^x \bmod N$ from $x = 0$ to $N^2$

As per the Shor's algorithm, we need to evaluate $a^x \bmod N$ from $x = 0$ to $N^2$. What is the reason for this? Why can't we just evaluate for $N$, $2N$ or something like that?
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### Why do we use the quantum superposition for a period instead of factors in Shor's algorithm?

I understand in Shor's algorithm we use quantum computers to find the period of a function which can then be used to find N, and we increase the probability of observing the state with the correct ...
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### Does Shor's algorithm end the search for factoring algorithms in the quantum world of computation?

In other words, will factoring research remain solely in the classical world or are there interesting research on-going in the quantum world related to factoring?
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### Entanglement in Shor's algorithm

One deals with the notion of superposition when studying Shor's algorithm, but how about entanglement? Where exactly does it appear in this particular circuit? I assume it is not yet present in the ...
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### What integers have been factored with Shor's algorithm?

Shor's algorithm is expected to enable us to factor integers far larger than could be feasibly done on modern classical computers. At current, only smaller integers have been factored. For example, ...
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### Confusion about random sampling of integers in Shor's algorithm

My understanding of Shor's algorithm is that you have to carry out the following steps if you are trying to factor $N$: Chose a random number less than $N$. Let's call it $a$. Calculate the period ...
### Shor's algorithm caveats when $a^{r/2} =-1 \mod N$
For an integer, $N$, to be factorised, with $a$ (uniformly) chosen at random between $1$ and $N$, with $r$ the order of $a\mod N$ (that is, the smallest $r$ with $a^r\equiv 1\mod N$): Why is that in ...