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# Questions tagged [factorization]

Questions regarding quantum algorithms that factorize numbers, finding smaller integer factors or prime factors such as in Shor algorithm.

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### Why circuit in Shor algorithm differs for different factorized numbers?

I recently started studying quantum algorithms, and I have a question about Shor algorithm. I have been reading Qiskit documentation and other books and articles, I felt like it was changing the ...
• 13
52 views

### Benefits of using quantum encrypted keys

Considering, in a perfect world everyone has the capability to create a quantum key. What would the benefits of using quantum encrypted keys instead of using classically encrypted keys? Besides the ...
• 31
184 views

### Practical implementation of Shor and other factoring algorithms

I explore the realm of open-source quantum computers, particularly those available in the current or near-term future. My goal is to implement the largest possible integer factorizations. I would ...
62 views

### Bound on success Probability for Regev's factoring algorithm

Theorem 4.1 in Regev's paper talks about a theorem due to Pomerance as follows: Theorem 4.1: Suppose G is a finite abelian group with minimal number of generators $r$. Then, when choosing elements ...
• 657
1k views

### (April Fools 2024) Where can we find out more details about the recent factoring of RSA-2048?

[Note that this was originally asked on April 1, 2024, also known as April Fool's day in many Western nations] I'm hearing some rumors that a combination of neutral atoms (Lukin's group?), in ...
• 12.5k
289 views

### Is QFT qubit recycling compatible with Zeckendorf's Fibonacci representation of integers?

Background Phase estimation circuits prepare $n$ qubits $Q_0, \dots, Q_{n-1}$ in the $|+\rangle$ state, then apply $U^{2^q}$ controlled by $Q_q$ for each $q$, then apply a quantum Fourier transform, ...
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