What Is the Shor Algorithm Quantum Phase Estimation (QPE) Calculator?
Shor algorithm is a quantum polynomial-time algorithm for finding the prime factors of an integer N.
How Does the Shor Algorithm Quantum Phase Estimation (QPE) Calculator Work?
Converts factorization into order-finding, then evaluates eigenvalue phases using QFT.
Shor Algorithm Quantum Phase Estimation (QPE) Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
L = lceil log_2 N
ceil, quad t = 2L + 1 + leftlceil log_2left(2 + rac{1}{2epsilon}
ight)
ight
ceil, quad n_{ ext{qubits}} = t + L
Register sizing for modular exponentiation and Quantum Fourier Transform phase estimation.
How to Use the Shor Algorithm Quantum Phase Estimation (QPE) Calculator
- Enter the integer N to factor and desired probability target of successful single-shot phase identification.
Step-by-Step Example Calculation
Factoring 11-Bit Number (N = 2048)
Input Values:
compositeNumberN:2048
successProbabilityTarget:0.95
Worked Steps: Requires L = 11 work qubits, t = 27 phase qubits, and 38 total logical qubits.
Understanding Your Result
Displays the minimum logical qubit budget needed for the upper and lower quantum registers.
Factors That Affect the Result
- Phase precision requires at least 2L bits to ensure continued fraction expansion uniquely resolves the period.
When Should You Use This Calculator?
- Cryptographic vulnerability assessment and quantum hardware requirement modeling.
Assumptions & Limitations
- Applies to logical error-corrected qubits; physical qubit counts are typically 1000x higher.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard sizing criteria from Nielsen & Chuang Quantum Computation.