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Add Shor's Algorithm implementation #13989

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@thotaDeepika thotaDeepika commented Dec 6, 2025
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Describe your change:

  • ✔ Add an algorithms

Checklist:

  • I have read CONTRIBUTING.md
  • This pull request is all my own work
  • I know that pull requests will not be merged if they fail the automated tests
  • This PR only changes one algorithm file
  • All new Python files are placed inside an existing directory
  • All filenames are in all lowercase characters with no spaces or dashes
  • All functions and variable names follow Python naming conventions
  • All function parameters and return values are annotated with Python type hints
  • All functions have doctests that pass the automated testing
  • All new algorithms include at least one URL that points to Wikipedia

Fixes #12318

This PR implements Shor's Algorithm for integer factorization as a classical
simulation, demonstrating how the algorithm breaks RSA cryptography without
requiring Qiskit or Cirq.

@algorithms-keeper algorithms-keeper bot added the require descriptive names This PR needs descriptive function and/or variable names label Dec 6, 2025
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Click here to look at the relevant links ⬇️

🔗 Relevant Links

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Python:

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from fractions import Fraction


def gcd(a: int, b: int) -> int:
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Please provide descriptive name for the parameter: a

Please provide descriptive name for the parameter: b

return a


def is_prime(n: int) -> bool:
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Please provide descriptive name for the parameter: n

return all(n % i != 0 for i in range(3, int(math.sqrt(n)) + 1, 2))


def is_perfect_power(n: int) -> tuple[int, int] | None:
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Please provide descriptive name for the parameter: n

return result


def find_order(a: int, n: int) -> int | None:
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Please provide descriptive name for the parameter: a

Please provide descriptive name for the parameter: n

return None


def quantum_period_finding_simulation(a: int, n: int) -> int | None:
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Please provide descriptive name for the parameter: a

Please provide descriptive name for the parameter: n

return convergents


def shors_algorithm(n: int, max_attempts: int = 10) -> tuple[int, int] | None:
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Please provide descriptive name for the parameter: n

return None


def demonstrate_rsa_vulnerability(p: int, q: int) -> dict:
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Please provide descriptive name for the parameter: p

Please provide descriptive name for the parameter: q

return result


def factor_with_explanation(n: int) -> None:
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Please provide descriptive name for the parameter: n

@algorithms-keeper algorithms-keeper bot added awaiting reviews This PR is ready to be reviewed tests are failing Do not merge until tests pass and removed tests are failing Do not merge until tests pass labels Dec 6, 2025
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