How many logical qubits are needed to run Shor's algorithm …
Jan 12, 2019 · In terms of concrete resource estimates for Shor's algorithm, the paper by Haener et al might be a good entry point which implemented the arithmetic in terms of so-called Toffoli gates which have the advantage of being testable at scale on classical input vectors.
circuit construction - Shor's algorithm: initialization of second ...
Nov 18, 2020 · $\begingroup$ Typically, there are two approaches to demonstrating Shor's algorithm: (i) build up from phase estimation, using eigenvector inputs, then make the jump to an input that is a superposition of eigenvectors. I believe this method gives the most understanding , or (ii) just happen to pick some particular input state, work though the ...
What integers have been factored with Shor's algorithm?
May 20, 2018 · The prime factorization of 21 (7x3) seems to be the largest done to date with Shor's algorithm; it was done in 2012 as detailed in this paper. It should be noted, however, that much larger numbers, such as 56,153 in 2014, have been factored using a minimization algorithm, as detailed here. For a convenient reference, see Table 5 of this paper:
Implementation of Unitary in Shor's Algorithm in PennyLane
I've been working on implementing Shor's Algorithm in PennyLane, but am struggling to understand how the circuit for 'U' has been constructed according to Qiskit. In the Qiskit textbook, they seek to factor 15, which, for my own sake, is what I decided to do as well (but in PennyLane).
What is period finding useful for in Shor's algorithm?
Jun 4, 2023 · Shor's algorithm is designed to work faster on a quantum computer since quantum computers run multiple steps simultaneously due to their ability to store qubits in superposition. We use period-finding in specific so we can apply QPE (quantum phase estimation).
How exactly does modular exponentiation in Shor's algorithm work?
Feb 9, 2019 · $\begingroup$ @foaly Don't worry, it's a common point of confusion; Shor's algorithm (and most quantum algorithms) appear strange in that we evaluate a (say boolean) function and store the results in a second register, but then we perform some quantum action (e.g. a Fourier transform) only on the first register, without having to touch the ...
Shor's algorithm in Python with qiskit - How to implement the …
May 10, 2023 · I found this code for Shor's algorithm but it always was failing at the end of the modular_exponentiation routine because the keyvalue of '00000' was not found in the dictionary on the call to b_measure = result.get_counts()[format(i, '0{}b'.format(n+1))[-(n+1):]] Here is the original code in its entirety:
Implementing Shor's algorithm on IBM Quantum Composer
Jan 24, 2022 · Implementing Shor's algorithm on IBM Quantum Composer. Ask Question Asked 2 years, 11 months ago.
Probability of success proof for Shor's algorithm
Jun 14, 2022 · In the book "Quantum Computation and Information" by Nielsen and Chuang, Shor's algorithm is presented with a related probability of success theorem and proof found on page 634, Theorem A4.13. In the last paragraph of this proof, the authors write that:
Does Shor's algorithm imply the existence of the multiverse?
Mar 2, 2023 · Whereas a many worldser will bet confidently and without reservation on "of course Shor's algorithm has to work". In this sense, applying Bayes rule to "Shor's algorithm worked" must cause a small update away from collapse interpretations (by eliminating the ones with spontaneous collapse) and towards many-worlds interpretations.