# 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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### Has there been any truly ground breaking advance in quantum algorithms since Grover and Shor?

(Sorry for a somewhat amateurish question) I studied quantum computing from 2004 to 2007, but I've lost track of the field since then. At the time there was a lot of hype and talk of QC potentially ...
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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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### 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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### Simplified explanation of Shor/QFT transformation as thumbtack

As a non-mathematician/software programmer I'm trying to grasp how QFT (Quantum Fourier Transformation) works. Following this YouTube video: https://www.youtube.com/watch?v=wUwZZaI5u0c And this ...
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### How many logical qubits are needed to run Shor's algorithm efficiently on large integers ($n > 2^{1024}$)?

First, I know there are differences in logical qubits and physical qubits. It takes more physical qubits for each logical qubit due to quantum error. Wikipedia states that it takes quantum gates of ...
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### How do quantum computers prevent “quantum noise”?

On the Wikipedia page for Shor's algorithm, it is stated that Shor's algorithm is not currently feasible to use to factor RSA-sized numbers, because a quantum computer has not been built with enough ...
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### Why is quantum Fourier transform required in Shor's algorithm?

I’m currently studying the Shor’s algorithm and am confused about the matter of complexity. From what I have read, the Shor’s algorithm reduces the factorization problem to the order-finding problem ...
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### 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 ...
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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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### Shor's algorithm weaknesses & uniqueness of close rational

I'm working through a problem set, and am stuck on the following problem: a) What can go wrong in Shor’s algorithm if Q (the dimension of the Quantum Fourier Transform) is not taken to be ...
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### Does the quantum Fourier transform have many applications beyond period finding?

(This is a somewhat soft question.) The quantum Fourier transform is formally quite similar to the fast Fourier transform, but exponentially faster. The QFT is famously at the core of Shor's ...
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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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### What are the thermodynamic limits of Shor's algorithm

The asymptotic time complexity of Grover's algorithm is the square root of the time of a brute force algorithm. However, according to Perlner and Liu, the thermodynamic behavior (theoretical minimum ...
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### What happens with first phase factor in QFT?

I'm using Mermin's Quantum Computer Science book to understand Shor's algorithm, but I can't figure out why one of the phase factors drops out of the probability for measuring a certain y. This is ...
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### How many qubits does it take to break a 10 characters password?

Let's assume we developed a hashcat-like programs for quantum computer. How many qubits we need to find the correct hash (WPA, MD5,...) from a 10 characters password make from upper, lower & ...
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### Lesser qubit computer doing the parts of Shor's against e.g., RSA-2048 sized prime

After posting this question to Physics, it became pretty clear I should have posted here. So: How might a (e.g.) 72-bit crypto-relevant quantum computer attack RSA-2048? Bonus: how might that be ...
In phase estimation, we start by using an eigenvector $\newcommand{\ket}{\lvert#1\rangle}\ket u$ to find the corresponding eigenvalue lambda. So far so good. In the order finding algorithm, we also ...