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org.soulspace.qclojure.application.algorithm.shor
complete-factorizationclj
(complete-factorization backend N)(complete-factorization backend N options)Perform complete prime factorization using Shor's algorithm recursively.
Unlike the basic shor-algorithm which finds only one factorization, this function continues factoring until all factors are prime.
Parameters:
- backend: Quantum backend for executing quantum circuits
- N: Integer to factor completely
- options: (Optional) Options map passed to shor-algorithm
Returns: Map containing:
- :prime-factors - Vector of all prime factors (sorted)
- :success - Boolean indicating if complete factorization succeeded
- :N - The input number
- :factorization-tree - Tree showing the factorization process
- :total-attempts - Total number of Shor algorithm calls made
- :statistics - Combined statistics from all factorization steps
Example: (complete-factorization backend 27) ;=> {:prime-factors [3 3 3], :success true, ...} (complete-factorization backend 15) ;=> {:prime-factors [3 5], :success true, ...}
Perform complete prime factorization using Shor's algorithm recursively.
Unlike the basic shor-algorithm which finds only one factorization,
this function continues factoring until all factors are prime.
Parameters:
- backend: Quantum backend for executing quantum circuits
- N: Integer to factor completely
- options: (Optional) Options map passed to shor-algorithm
Returns:
Map containing:
- :prime-factors - Vector of all prime factors (sorted)
- :success - Boolean indicating if complete factorization succeeded
- :N - The input number
- :factorization-tree - Tree showing the factorization process
- :total-attempts - Total number of Shor algorithm calls made
- :statistics - Combined statistics from all factorization steps
Example:
(complete-factorization backend 27) ;=> {:prime-factors [3 3 3], :success true, ...}
(complete-factorization backend 15) ;=> {:prime-factors [3 5], :success true, ...}generate-unique-coprime-valuesclj
(generate-unique-coprime-values N)Generate all values a where 2 <= a < N and gcd(a,N) = 1, in random order. This ensures no duplicate values are attempted during factorization.
Generate all values a where 2 <= a < N and gcd(a,N) = 1, in random order. This ensures no duplicate values are attempted during factorization.
shor-algorithmclj
(shor-algorithm backend N)(shor-algorithm backend N options)Shor's algorithm for integer factorization.
Shor's algorithm is a quantum algorithm that can factor large integers exponentially faster than the best known classical algorithms. It combines classical preprocessing, quantum period finding, and classical post-processing.
This improved implementation supports:
- Hardware-compatible mode for real quantum hardware execution
- Multiple measurements for statistical robustness
- Enhanced period extraction for better success rate
Algorithm steps:
- Classical preprocessing: Check for trivial cases
- Choose random a < N, check gcd(a,N)
- Quantum period finding: Find period r of f(x) = a^x mod N
- Classical post-processing: Extract factors from the period
Parameters:
- backend: Quantum backend implementing the QuantumBackend protocol to execute the circuit
- N: Integer to factor (should be composite)
- options: (Optional) Map containing:
- :n-qubits - Number of qubits for quantum period finding (default: 2*⌈log₂(N)⌉)
- :hardware-compatible - Boolean indicating if hardware-optimized circuit should be used
- :n-measurements - Number of measurements for statistical analysis (default: 10)
- :max-attempts - Maximum number of random 'a' values to try (default: 10)
Returns: Map containing:
- :factors - Vector of non-trivial factors found (empty if factorization failed)
- :success - Boolean indicating if factorization succeeded
- :N - The input number
- :attempts - Vector of maps describing each attempt with different 'a' values
- :quantum-circuit - The quantum circuit from the successful attempt (if any)
- :statistics - Performance statistics and confidence metrics
Example: (shor-algorithm 15) ;=> {:factors [3 5], :success true, :N 15, ...} (shor-algorithm 21 {:hardware-compatible true}) ;=> {:factors [3 7], :success true, ...}
Shor's algorithm for integer factorization.
Shor's algorithm is a quantum algorithm that can factor large integers
exponentially faster than the best known classical algorithms. It combines
classical preprocessing, quantum period finding, and classical post-processing.
This improved implementation supports:
1. Hardware-compatible mode for real quantum hardware execution
2. Multiple measurements for statistical robustness
3. Enhanced period extraction for better success rate
Algorithm steps:
1. Classical preprocessing: Check for trivial cases
2. Choose random a < N, check gcd(a,N)
3. Quantum period finding: Find period r of f(x) = a^x mod N
4. Classical post-processing: Extract factors from the period
Parameters:
- backend: Quantum backend implementing the QuantumBackend protocol to execute the circuit
- N: Integer to factor (should be composite)
- options: (Optional) Map containing:
- :n-qubits - Number of qubits for quantum period finding (default: 2*⌈log₂(N)⌉)
- :hardware-compatible - Boolean indicating if hardware-optimized circuit should be used
- :n-measurements - Number of measurements for statistical analysis (default: 10)
- :max-attempts - Maximum number of random 'a' values to try (default: 10)
Returns:
Map containing:
- :factors - Vector of non-trivial factors found (empty if factorization failed)
- :success - Boolean indicating if factorization succeeded
- :N - The input number
- :attempts - Vector of maps describing each attempt with different 'a' values
- :quantum-circuit - The quantum circuit from the successful attempt (if any)
- :statistics - Performance statistics and confidence metrics
Example:
(shor-algorithm 15) ;=> {:factors [3 5], :success true, :N 15, ...}
(shor-algorithm 21 {:hardware-compatible true}) ;=> {:factors [3 7], :success true, ...}cljdoc is a website building & hosting documentation for Clojure/Script libraries
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