Shor's algorithm

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Community · Shor's algorithm

Summary

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer.

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inventor of the algorithm
Peter Shor developed this algorithm in 1994 while working at Bell Labs, demonstrating the potential for quantum computers to solve problems intractable for classical machines.
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mathematical core of Shor's algorithm
This transformation is the quantum analogue of the discrete Fourier transform and is the essential mechanism used to find the period of a function in Shor's algorithm.
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cryptographic system vulnerable to Shor's algorithm
The security of RSA relies on the difficulty of integer factorization, which Shor's algorithm renders computationally trivial on a sufficiently powerful quantum computer.
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computational problem solved by Shor's algorithm
Shor's algorithm provides a polynomial-time solution for this problem, which is the basis for the security of RSA encryption.
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general category of the source
Shor's algorithm is a specific instance of a quantum algorithm designed to solve a problem faster than any known classical algorithm.
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computational step within the algorithm
This operation is the most computationally expensive part of Shor's algorithm and must be implemented efficiently using quantum circuits.
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implementation model for the algorithm
Shor's algorithm is typically described and implemented as a sequence of quantum logic gates acting on qubits within a quantum circuit.
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defining quantum algorithm
This algorithm demonstrates the potential of quantum computers to factor large integers exponentially faster than classical algorithms, threatening current cryptographic standards.
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field developed in response to Shor's algorithm
This field focuses on developing cryptographic systems that are secure against attacks by quantum computers running algorithms like Shor's.
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complexity class containing Shor's algorithm
Shor's algorithm is a primary example of an algorithm that resides in BQP (Bounded-error Quantum Polynomial time) but is not known to be in P.
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theoretical framework for evaluating the algorithm
This field provides the tools to compare the efficiency of Shor's algorithm against classical factoring algorithms like the General Number Field Sieve.
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serves as the primary counterpart in quantum algorithm history
While Shor's algorithm provides exponential speedup for specific number-theoretic problems, Grover's algorithm provides a more general, albeit quadratic, speedup.
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