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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Can I access device specifications of IBMQ paying devices?

I need to perform some tests for my thesis in real quantum computers, however, I only have access to IBM's free quantum devices (the maximum number of qubits I can use is 15, in ...
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Is there a general order finding quantum algorithm for a given a and N?

I'm trying to construct a general circuit for Shor's algorithm in Qiskit. I understood the later parts of the circuit (inverse QFT and QPE), but can't really understand the order finding. For example, ...
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Braket and Q# Simulators

I have implemented Shor's algorithm in Qiskit, and everything works as expected within the IBM Q experience for both the IBM qasm_simulator and real hardware. However, after I've implemented Shors in ...
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How does this represent modular multiplication

How does this circuit map $|x\rangle$ to $|7x \space mod15\rangle$? Looking into Shor's and I thought that phase kickback causes the modular exponentiation part to be mapped onto the measurement ...
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Shor's implementation problem on qiskit

If q4-7 are all supposed to be eigenstates of the operation, why is it just that q7 is in $|1\rangle$? Shouldn't all qubits 4 to ...
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What is stopping FACTORING from being BQP-complete?

Classical complexity theory makes much of the study of so-called intermediate problems - that is, problems that are in $\mathsf{NP}$ but are nonetheless not knownto be in $\mathsf{P}$ and further not ...
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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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Question Regarding Quantum Period-Finding Fourier Transform Approximation

I am following the 5.4.1 Period-Finding Algorithm in Nielsen and Chuang as shown below: My confusion lies with the second expression of point 3 in the procedure. Why is the second expression an ...
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How to build an example of Shor's algorithm for the discrete log?

I have been trying to build myself an example of Shor's computations for the discrete log. I started out with this objective and I realized I should understand the factorization first, which I did ...
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How to show that amount of qubits needed to crack the RSA-2048 protocol using Shor's algorithm?

I've read that under current technology we would need around 20 million qubits to crack the RSA-2048 protocol. How would one prove this?
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Is there an example of Shor's algorithm for the discrete log problem with concrete numbers anywhere?

I understand the problem well enough and I'm trying to understand the algorithm, Shor's version. It's not easy to read the abstract descriptions available everywhere --- Shor's paper, Nielsen's book ...
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Shor's algorithm: what to do after reading the QFT's result twice?

I asked about how to identify the period looking at a Fourier transform plot. The answer seems to be to run the fourier transform multiple times getting multiple values associated to high ...
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What are the interesting spikes in this after-QFT graph (page 241) of Programming Quantum Computers?

I'm reading Programming Quantum Computers trying to understand Shor's algorithm. I learned there that we prepare a state $|x^i \bmod N\rangle$, then apply the QFT to this state. The QFT changes the ...
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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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Simplifying Qiskit circuit with c_if()

I'm trying to simplify the inner for loop of this implementation of the Mosca-Ekert semi-classical variant of Shor's algorithm. The inner for loop should have only linear length, but this ...
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Shor's algorithm: initialization of second register

I am trying to understand Shor's algorithm. I am not quite sure why the initialization, indicated as $|1\rangle$ in the below image at the bottom left is chosen as it is? I understand the modular ...
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Constructing arbitrary functions for the Abelian HSP

My question might be similar to Hidden subgroup problem. However, I'm not exactly sure though. In addition, that question doesn't have an answer. I'm trying to create some simple instances of the ...
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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 is a maximal number factored by Shor's algorithm so far?

With reference to similar question here I would like to know what is the maximal number which has been factored with Shor's algorithm so far on actual quantum hardware. The reason I am asking similar ...
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Abelian Hidden Subgroup Problem for arbitrary cyclic p-Groups

I had asked a question similar to this one here regarding how to handle the HSP for groups whose cyclic decomposition contains factors whose order is not a power of two. I also had some prior ...
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How to write a classical version of Shor's algorithm

For learning purposes, I would like to write a classical version of Shor's algorithm. From what I have read, what makes this algorithm fast is the quantum FFT, which is used to find the period of the ...
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In Shor's algorithm, how can we guarantee that each controlled-U will kickback to the same eigenvalue?

I'm studying the Shor algorithm as part of my thesis and have a question about the "measured" phases after the QPE. So, I take the controlled-U operations on the second register and in cause ...
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Problem with Shor's factoring algorithm [closed]

I'm trying to figure out the Shor's factoring algorithm. References i've been using wikipedia page, the book Quantum Computer Science by David Mermin and the orignal paper(1996) By Peter Shor. I ...
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Quantum Phase Estimation Circuit and Modular Exponentiaton

In Nielsen and Chuang, it is stated that the effect of phase estimation circuit is mapping state $|j\rangle |u\rangle$ to $|j\rangle U^j |u\rangle$. Here is my solution: Consider the first $CU^{2^0}...
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Eigenvectors and eigenvalues of the gate $U_a:|s\rangle\mapsto|sa \bmod N\rangle$

I'm studying Shor algorithm. This is a demostration about the eigenvectors and eigenvalues of $U_a$ gate: Can somebody explain me from the third step to the last?
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Why can I use the Sum of Eigenvectors for Phase Estimation in Shor

In phase estimation, we start by using an eigenvector $\newcommand{\ket}[1]{\lvert#1\rangle}\ket u$ to find the corresponding eigenvalue lambda. So far so good. In the order finding algorithm, we also ...
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Shor's Discrete Logarithm Algorithm with a QFT with a small prime base

Suppose you replace both QFTs in Shor's discrete logarithm algorithm with simpler QFTs with small prime base w. Does this algorithm extract the discrete logarithm modulo w? It seems it does, provided ...
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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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Calculating power of a quantum computer — RSA

As discussed in this question, the expected security of 1024-bit RSA is 80-bits: NIST SP 800-57 §5.6.1 p.62–64 specifies a correspondence between RSA modulus size $n$ and expected security strength ...
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How to implement Cx mod N unitary

The following links provides circuts for $a\in\{2,7,8,11,13\}$ and $N=15$: https://qiskit.org/textbook/ch-algorithms/shor.html#3.-Qiskit-Implementation https://arxiv.org/abs/1202.6614v3. I am ...
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Energy cost of quantum computation

A quantum computer can be modeled as a single unitary transition of a (large) effective quantum state to another. In order to get errors under control, quantum error correction is assumed. A logical ...
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Questions on May & Schlieper's “Quantum Period Finding is Compression Robust”

https://arxiv.org/abs/1905.10074 https://crypto.stanford.edu/~dabo/pubs/abstracts/quantum.html Below are a few questions about May and Schlieper's paper "Quantum Period Finding is Compression Robust"...
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Building the period-finding circuit for Shor's Algorithm & the classical complexity of finding the period

I've been trying to learn about Shor's algorithm by writing out implementations of the circuit for modular exponentiation, ${ a }^{ x }\; ({ mod }\; N)$, to find the period $r$ for small numbers such ...
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Any other quantum algorithms than Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm?

I have been working on implementing Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm on my home-made 2 qubits device. I am wondering if there are any other ...
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Quantum computers don't try all the possible solutions, so how does the QFT really work?

Scott Aaronson is fond of saying "Quantum computers do not solve hard search problems instantaneously by simply trying all the possible solutions at once." That is, they are not non-deterministic ...
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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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What is Quantum Phase Estimation in Shor's Algorithm?

While I'm studying Algorithm, I couldn't understand what Quantum Phase Estimation is. And I heard there is relation between Phase-Kickback and Quantum Phase Estimation. I wonder what it is. Also, I'm ...
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Shor algorithm - how to obtain a period from diagram?

I'm studying shor's algorithm. I implemented in Qiskit and apriori I know that a period is 3 in my example. However, unless I know about period, how to obtain this period only according to seeing ...
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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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When increase the shot, why the result is different?

when I measure the shot = 1024 when I measure the shot = 8192 I want to derive result value 011(=3) However, I know if measure the more shots, increase the accuracy. why this result derive??? why ...
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What do empty white circles mean in a quantum circuit?

I'm studying Shor's algorithm. but I see from the beginning this empty circle. what this circle means??
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Implementing QFT for Shor's Algorithm?

I'm studying Shor's algorithm. This diagram shows a calculation of $4^x\mod21$. I don't understand how this expresses $4^x \mod21$. Could you explain this? For example, by showing another calculation ...
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Implementing QFT for Shor's Algorithm

I’m trying to get a Quantum Fourier Transform working with the rest of a compiled version of Shor’s algorithm, attempting to factor $N=21$. In the following image, there’s an initialization phase (...
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Quantum computing w.r.t. the many-worlds theory [duplicate]

Quantum algorithms are inherently probabilistic. Let's say I run Shor's factoring algorithm on some number. There's a chance that the output I observe is incorrect. Does the many-worlds theory suggest ...
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How to implement modular exponentiation efficiently in Shor's algorithm?

I'm a noob in quantum computing and I'm trying to get Shor's algorithm working on Q# (the language is unrelated). However, I'm stuck on computing $f(x)$s in the quantum circuit. Let $N\sim \log_2(n)$ ...
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Why is the size of the top register for Shor's algorithm chosen as it is?

Let $N$ be the number we're trying to factor. In Shor's algorithm, the top register then has $2 \lceil\log_2(N)\rceil+1$ qubits, while the bottom register (the ancilla qubits) has $\lceil\log_2(N)\...
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How to make a Shor's algorithm for an arbitrary number of qubits with Qiskit on a IBM machine?

So suppose you want to do a Shor algorithm on an arbitrary number of qubits using an arbitrary $a$ (the base number in the periodic function $a^x \mod c$) and $c$ ( the factored number). Making the ...
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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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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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Why is this implementation of the order finding algorithm not working?

I asked a question about this earlier, but I am still coming across problems in my algorithm implementation. I am trying to implement the order finding algorithm on Cirq finding the minimal positive $...