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  1. By contrast, Shor's algorithm can crack RSA in polynomial time.[1]
  2. Shor thus had to solve three "implementation" problems.[1]
  3. To achieve this, Shor used repeated squaring for his modular exponentiation transformation.[1]
  4. The results, which were published in Nature, represented the first experimental realization of Shor’s algorithm.[2]
  5. The researchers use laser pulses to perform “logic gates,” or components of Shor’s algorithm, on four of the five atoms.[2]
  6. That interaction lets us perform logic gates, which allow us to realize the primitives of the Shor factoring algorithm.[2]
  7. They directed the quantum system to factor the number 15 — the smallest number that can meaningfully demonstrate Shor’s algorithm.[2]
  8. You may guess that Shor’s algorithm aims to find the period r which we discussed in the first sections.[3]
  9. In the original paper of Shor performed QFT at this stage.[3]
  10. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer.[4]
  11. GEECM, a factorization algorithm said to be "often much faster than Shor's".[4]
  12. This assumption was challenged in 1995 when Peter Shor proposed a polynomial-time quantum algorithm for the factoring problem.[5]
  13. Shor’s algorithm is arguably the most dramatic example of how the paradigm of quantum computing changed our perception of which problems should be considered tractable.[5]
  14. Likewise, Shor’s algorithm exploits interference to measure periodicity of arithmetic objects.[5]
  15. Peter Shor wasn’t some malicious anarcho-hacktivist but a mathematician working for AT&T's Bell Labs looking to solve a difficult mathematical problem like every other mathematician in the field.[6]
  16. Without getting bogged down in the finite details, Shor’s Algorithm is a three-part answer to the problem of prime factorization for any integer, so it works no matter how large the integer involved.[6]
  17. When Shor devised his algorithm, quantum computing didn’t exist in any meaningful way.[6]
  18. Empirical formulas on expected success probability introduced in the paper give rise to the more profound analysis of classic part behaviour of the Shor’s algorithm.[7]
  19. In this section, we will talk about Shor’s algorithm, which is a quantum algorithm for factoring an integer \(N\) that runs in polynomial time with respect to the number of digits of \(N\).[8]
  20. We can think of Shor’s algorithm as being a classical algorithm that contains within it a certain subroutine.[8]
  21. 4.3 Quantum Fourier transform We now have almost all the steps we need to describe Shor’s algorithm.[8]
  22. To get the period out, Shor uses something called the quantum Fourier transform, or QFT.[9]
  23. And that’s exactly what’s going on in Shor’s algorithm.[9]
  24. This article will introduce Shor’s Algorithm in the Quantum Algorithms series.[10]
  25. Shor’s algorithm was invented by Peter Shor for integer factorization in 1994.[10]
  26. The code below shows a Shor’s algorithm implementation.[10]
  27. Shor’s period-finding algorithm (step 2 above) relies heavily on the ability of a quantum computer to be in many states simultaneously (a superposition of states).[11]
  28. Shor, P. W. (1997).[11]
  29. Shor’s Quantum Factoring Algorithm.[11]
  30. implement a scalable version of Shor's factorization algorithm.[12]
  31. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer.[12]
  32. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev.[12]
  33. Shor’s algorithm for factoring integers (1) is one example in which a quantum computer (QC) outperforms the most efficient known classical algorithms.[12]
  34. We have a complete period-finding algorithm for Shor’s algorithm.[13]
  35. Shor's algorithm provides a fast way to factor large numbers using a quantum computer, a problem called factoring.[14]
  36. Shor's algorithm can be thought of as a hybrid algorithm.[14]
  37. (See Shor's original paper for details, or one of the Basic quantum computing texts in For more information).[14]
  38. Therefore, the core of Shor’s algorithm is to transform the problem of large number decomposition into the problem of finding period (as shown in the following).[15]
  39. Quantum computers3, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm4,5,6.[16]
  40. Shor’s algorithm has two parts, a classical part and a quantum part.[17]
  41. Shor’s algorithm has been tested with various types of today’s quantum computers and has successfully factored the numbers 15 and 21.[17]
  42. Further, Shor’s algorithm was created in 1994 and there are encryption methods now in use that cannot be broken by Shor’s algorithm.[17]
  43. That isn’t to say that other algorithms couldn’t break them, but by the time we have very large quantum computers, Shor’s algorithm will not be useful in breaking the encryption in use at that time.[17]
  44. They could use Shor’s Algorithm to significantly reduce the number of steps to factor big numbers, thus more easily revealing the private key associated with a given public key.[18]
  45. A quantum computer made of five trapped ions has been used by physicists in Austria and the US to implement Shor’s factoring algorithm.[19]
  46. In 1994, Peter Shor realized that a quantum computer could be much more efficient at factoring large numbers than a conventional computer.[19]
  47. Shor’s factoring algorithm begins by using mathematics to transform the problem of factoring a large number into the problem of finding the period of a function that describes a sequence of numbers.[19]
  48. In Shor’s original scheme, a quantum computer with 12 quantum bits (qubits) is needed to factor the number 15.[19]
  49. In 1994 Peter Shor showed that for sufficiently large N, a quantum computer could perform the factoring with much less computational effort.[20]
  50. What’s Shor’s Algorithm?[21]
  51. What’s this Shor’s algorithm thing I keep on hearing about?[21]
  52. I admit there have been valiant attempts at explaining Shor without much math...[22]
  53. To understand Shor's quantum factoring algorithm, we'll work on first understanding several smaller things.[22]
  54. We're going to factor this number using Shor's algorithm.[22]
  55. Shor's algorithm is difficult to understand because it mixes together ideas from quantum physics, signal processing, number theory, and computer science.[22]
  56. In mathematical terms, Shor's solves the hidden subgroup problem for finite Abelian groups.[23]
  57. In layman's terms, Shor's algorithm could expose encrypted information, such as passwords, credit cards, or other confidential items, transmitted over the Internet.[23]
  58. In 1994 American applied mathematician Peter Shor, working at Bell Labs in Murray Hill, New Jersey, formulated Shor's algorithm, a quantum algorithm for integer factorization.[24]
  59. In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits.[24]
  60. Since IBM's implementation, several other groups have implemented Shor's algorithm using photonic qubits, emphasizing that entanglement was observed.[24]
  61. Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer", SIAM J. Comput.[24]
  62. None of the above techniques implement Shor's algorithm.[25]
  63. (there is) danger in ‘compiled’ demonstrations of Shor's algorithm.[25]
  64. This section describes Shor's algorithm from a functional point of view which means that it doesn't deal with the implementation for a specific hardware architecture.[26]
  65. We report a proof-of-principle demonstration of Shor’s algorithm with photons generated by an on-demand semiconductor quantum dot single-photon source for the first time.[27]
  66. A fully compiled version of Shor’s algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four-photon cluster state.[27]
  67. Demonstration of Shor’s algorithm requires lots of qubits and gates that is beyond the current quantum technologies.[27]
  68. Fortunately, Shor’s algorithm utilizing a quantum computer provides an effective way to execute it in a polynomial complexity.[27]

소스

  1. ↑ 1.0 1.1 1.2 Shor's factoring algorithm
  2. ↑ 2.0 2.1 2.2 2.3 The beginning of the end for encryption schemes?
  3. ↑ 3.0 3.1 Quantum Factorization
  4. ↑ 4.0 4.1 Shor's algorithm
  5. ↑ 5.0 5.1 5.2 IBM Quantum Experience
  6. ↑ 6.0 6.1 6.2 How Peter Shor’s Algorithm Dooms RSA Encryption to Failure
  7. ↑ Improved Estimation of Success Probability of the Shor’s Algorithm
  8. ↑ 8.0 8.1 8.2 Shor’s algorithm
  9. ↑ 9.0 9.1 Shtetl-Optimized » Blog Archive » Shor, I’ll do it
  10. ↑ 10.0 10.1 10.2 Topcoder Shor's Algorithm in Quantum Computing
  11. ↑ 11.0 11.1 11.2 Shor’s Algorithm – Breaking RSA Encryption
  12. ↑ 12.0 12.1 12.2 12.3 Realization of a scalable Shor algorithm
  13. ↑ QC — Period finding in Shor’s Algorithm
  14. ↑ 14.0 14.1 14.2 Applications in the Q# standard libraries - Microsoft Quantum
  15. ↑ Using Shor’s Algorithm to Achieve Factor Decomposition — Huawei HiQ 0.0.1 documentation
  16. ↑ Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
  17. ↑ 17.0 17.1 17.2 17.3 Shor’s Algorithm
  18. ↑ Quantum Threat to Blockchains: Shor’s and Grover’s Algorithms
  19. ↑ 19.0 19.1 19.2 19.3 Shor's algorithm is implemented using five trapped ions – Physics World
  20. ↑ Shor's factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers
  21. ↑ 21.0 21.1 What’s Shor’s Algorithm? (Quantum Computing Weekly News for Dec 11 2018)
  22. ↑ 22.0 22.1 22.2 22.3 Shor's Quantum Factoring Algorithm
  23. ↑ 23.0 23.1 toddwildey/shors-python: Implementation of Shor's algorithm in Python 3.X using state vectors
  24. ↑ 24.0 24.1 24.2 24.3 Formulation of Shor's Algorithm for Quantum Computers : History of Information
  25. ↑ 25.0 25.1 Largest integer factored by Shor's algorithm?
  26. ↑ Shor's Algorithm for Quantum Factorization
  27. ↑ 27.0 27.1 27.2 27.3 Proof-of-principle demonstration of compiled Shor’s algorithm using a quantum dot single-photon source

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