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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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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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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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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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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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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Possible results from Shor's algorithm in practice

After reading through Shor's algorithm, I have a few questions about the probability of factoring semiprime number out. Here is some background of the question. To factor a semiprime number $N$ such ...
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Would this quantum algorithm implementation work?

I am trying to implement the order finding algorithm on Cirq finding the minimal positive $r$ for coprime $x$ and $N$ satisfying the equation $x^r \ = \ 1$(mod$ \ N$). In my case, I have set $x \ = \ ...
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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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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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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"...