2021년 2월 17일 (수) 07:52에 Pythagoras0님의 편집

2021-02-17T07:52:01Z

Pythagoras0: /* 위키데이터 */

2021-02-12T17:42:35Z

위키데이터

Pythagoras0: /* 메타데이터 */ 새 문단

2020-12-26T12:08:26Z

메타데이터: 새 문단

Pythagoras0: /* 노트 */ 새 문단

2020-12-22T01:50:22Z

노트: 새 문단

새 문서

== 노트 ==

===위키데이터===
* ID : [https://www.wikidata.org/wiki/Q940334 Q940334]
===말뭉치===
# By contrast, Shor's algorithm can crack RSA in polynomial time.<ref name="ref_10c6f526">[https://www.quantiki.org/wiki/shors-factoring-algorithm Shor's factoring algorithm]</ref>
# Shor thus had to solve three "implementation" problems.<ref name="ref_10c6f526" />
# To achieve this, Shor used repeated squaring for his modular exponentiation transformation.<ref name="ref_10c6f526" />
# The results, which were published in Nature, represented the first experimental realization of Shor’s algorithm.<ref name="ref_9e2c9849">[https://news.mit.edu/2016/quantum-computer-end-encryption-schemes-0303 The beginning of the end for encryption schemes?]</ref>
# The researchers use laser pulses to perform “logic gates,” or components of Shor’s algorithm, on four of the five atoms.<ref name="ref_9e2c9849" />
# That interaction lets us perform logic gates, which allow us to realize the primitives of the Shor factoring algorithm.<ref name="ref_9e2c9849" />
# They directed the quantum system to factor the number 15 — the smallest number that can meaningfully demonstrate Shor’s algorithm.<ref name="ref_9e2c9849" />
# You may guess that Shor’s algorithm aims to find the period r which we discussed in the first sections.<ref name="ref_6b563676">[https://towardsdatascience.com/quantum-factorization-b3f44be9d738 Quantum Factorization]</ref>
# In the original paper of Shor performed QFT at this stage.<ref name="ref_6b563676" />
# 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.<ref name="ref_2811e8f5">[https://en.wikipedia.org/wiki/Shor%27s_algorithm Shor's algorithm]</ref>
# GEECM, a factorization algorithm said to be "often much faster than Shor's".<ref name="ref_2811e8f5" />
# This assumption was challenged in 1995 when Peter Shor proposed a polynomial-time quantum algorithm for the factoring problem.<ref name="ref_1edb2558">[https://quantum-computing.ibm.com/docs/iqx/guide/shors-algorithm IBM Quantum Experience]</ref>
# 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.<ref name="ref_1edb2558" />
# Likewise, Shor’s algorithm exploits interference to measure periodicity of arithmetic objects.<ref name="ref_1edb2558" />
# 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.<ref name="ref_87cdad00">[https://interestingengineering.com/how-peter-shors-algorithm-dooms-rsa-encryption-to-failure How Peter Shor’s Algorithm Dooms RSA Encryption to Failure]</ref>
# 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.<ref name="ref_87cdad00" />
# When Shor devised his algorithm, quantum computing didn’t exist in any meaningful way.<ref name="ref_87cdad00" />
# 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.<ref name="ref_7fcd7bdf">[https://link.springer.com/chapter/10.1007/978-3-642-13861-4_5 Improved Estimation of Success Probability of the Shor’s Algorithm]</ref>
# 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 \(N\).<ref name="ref_39e605ca">[https://riliu.math.ncsu.edu/437/notes3se4.html Shor’s algorithm]</ref>
# We can think of Shor’s algorithm as being a classical algorithm that contains within it a certain subroutine.<ref name="ref_39e605ca" />
# 4.3 Quantum Fourier transform We now have almost all the steps we need to describe Shor’s algorithm.<ref name="ref_39e605ca" />
# To get the period out, Shor uses something called the quantum Fourier transform, or QFT.<ref name="ref_959d4a1a">[https://www.scottaaronson.com/blog/?p=208 Shtetl-Optimized » Blog Archive » Shor, I’ll do it]</ref>
# And that’s exactly what’s going on in Shor’s algorithm.<ref name="ref_959d4a1a" />
# This article will introduce Shor’s Algorithm in the Quantum Algorithms series.<ref name="ref_6eca0a18">[https://www.topcoder.com/shors-algorithm-in-quantum-computing/ Topcoder Shor's Algorithm in Quantum Computing]</ref>
# Shor’s algorithm was invented by Peter Shor for integer factorization in 1994.<ref name="ref_6eca0a18" />
# The code below shows a Shor’s algorithm implementation.<ref name="ref_6eca0a18" />
# 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).<ref name="ref_bb6d8da2">[https://blogs.ams.org/mathgradblog/2014/04/30/shors-algorithm-breaking-rsa-encryption/ Shor’s Algorithm – Breaking RSA Encryption]</ref>
# Shor, P. W. (1997).<ref name="ref_bb6d8da2" />
# Shor’s Quantum Factoring Algorithm.<ref name="ref_bb6d8da2" />
# implement a scalable version of Shor's factorization algorithm.<ref name="ref_392a212a">[https://science.sciencemag.org/content/351/6277/1068 Realization of a scalable Shor algorithm]</ref>
# 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.<ref name="ref_392a212a" />
# Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev.<ref name="ref_392a212a" />
# Shor’s algorithm for factoring integers (1) is one example in which a quantum computer (QC) outperforms the most efficient known classical algorithms.<ref name="ref_392a212a" />
# We have a complete period-finding algorithm for Shor’s algorithm.<ref name="ref_17614a64">[https://jonathan-hui.medium.com/qc-period-finding-in-shors-algorithm-7eb0c22e8202 QC — Period finding in Shor’s Algorithm]</ref>
# Shor's algorithm provides a fast way to factor large numbers using a quantum computer, a problem called factoring.<ref name="ref_3fb725b6">[https://docs.microsoft.com/en-us/quantum/user-guide/libraries/standard/applications Applications in the Q# standard libraries - Microsoft Quantum]</ref>
# Shor's algorithm can be thought of as a hybrid algorithm.<ref name="ref_3fb725b6" />
# (See Shor's original paper for details, or one of the Basic quantum computing texts in For more information).<ref name="ref_3fb725b6" />
# 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).<ref name="ref_d5357c0f">[https://hiqsimulator.readthedocs.io/en/latest/examples/examples.ShorAlgorithm.html Using Shor’s Algorithm to Achieve Factor Decomposition — Huawei HiQ 0.0.1 documentation]</ref>
# Quantum computers3, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm4,5,6.<ref name="ref_131d38bb">[https://www.nature.com/articles/414883a Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance]</ref>
# Shor’s algorithm has two parts, a classical part and a quantum part.<ref name="ref_36ece962">[https://www.carriermanagement.com/features/2020/05/06/206352.htm Shor’s Algorithm]</ref>
# Shor’s algorithm has been tested with various types of today’s quantum computers and has successfully factored the numbers 15 and 21.<ref name="ref_36ece962" />
# Further, Shor’s algorithm was created in 1994 and there are encryption methods now in use that cannot be broken by Shor’s algorithm.<ref name="ref_36ece962" />
# 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.<ref name="ref_36ece962" />
# 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.<ref name="ref_29dfd7d3">[https://codeburst.io/quantum-threat-to-blockchains-shors-and-grover-s-algorithms-9b01941bed01 Quantum Threat to Blockchains: Shor’s and Grover’s Algorithms]</ref>
# A quantum computer made of five trapped ions has been used by physicists in Austria and the US to implement Shor’s factoring algorithm.<ref name="ref_93800a26">[https://physicsworld.com/a/shors-algorithm-is-implemented-using-five-trapped-ions/ Shor's algorithm is implemented using five trapped ions – Physics World]</ref>
# In 1994, Peter Shor realized that a quantum computer could be much more efficient at factoring large numbers than a conventional computer.<ref name="ref_93800a26" />
# 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.<ref name="ref_93800a26" />
# In Shor’s original scheme, a quantum computer with 12 quantum bits (qubits) is needed to factor the number 15.<ref name="ref_93800a26" />
# In 1994 Peter Shor showed that for sufficiently large N, a quantum computer could perform the factoring with much less computational effort.<ref name="ref_2cdc5c47">[https://ui.adsabs.harvard.edu/abs/2005AmJPh..73..521G/abstract Shor's factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers]</ref>
# What’s Shor’s Algorithm?<ref name="ref_d030a5aa">[https://hackernoon.com/whats-shor-s-algorithm-quantum-computing-weekly-news-for-dec-11-2018-721a4934a46f What’s Shor’s Algorithm? (Quantum Computing Weekly News for Dec 11 2018)]</ref>
# What’s this Shor’s algorithm thing I keep on hearing about?<ref name="ref_d030a5aa" />
# I admit there have been valiant attempts at explaining Shor without much math...<ref name="ref_7acdc279">[https://algassert.com/post/1718 Shor's Quantum Factoring Algorithm]</ref>
# To understand Shor's quantum factoring algorithm, we'll work on first understanding several smaller things.<ref name="ref_7acdc279" />
# We're going to factor this number using Shor's algorithm.<ref name="ref_7acdc279" />
# Shor's algorithm is difficult to understand because it mixes together ideas from quantum physics, signal processing, number theory, and computer science.<ref name="ref_7acdc279" />
# In mathematical terms, Shor's solves the hidden subgroup problem for finite Abelian groups.<ref name="ref_ee597c31">[https://github.com/toddwildey/shors-python toddwildey/shors-python: Implementation of Shor's algorithm in Python 3.X using state vectors]</ref>
# In layman's terms, Shor's algorithm could expose encrypted information, such as passwords, credit cards, or other confidential items, transmitted over the Internet.<ref name="ref_ee597c31" />
# 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.<ref name="ref_e8ec5340">[https://www.historyofinformation.com/detail.php?id=3877 Formulation of Shor's Algorithm for Quantum Computers : History of Information]</ref>
# 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.<ref name="ref_e8ec5340" />
# Since IBM's implementation, several other groups have implemented Shor's algorithm using photonic qubits, emphasizing that entanglement was observed.<ref name="ref_e8ec5340" />
# Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer", SIAM J. Comput.<ref name="ref_e8ec5340" />
# None of the above techniques implement Shor's algorithm.<ref name="ref_c6871346">[https://crypto.stackexchange.com/questions/59795/largest-integer-factored-by-shors-algorithm Largest integer factored by Shor's algorithm?]</ref>
# (there is) danger in ‘compiled’ demonstrations of Shor's algorithm.<ref name="ref_c6871346" />
# 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.<ref name="ref_d33e3b61">[http://tph.tuwien.ac.at/~oemer/doc/quprog/node18.html Shor's Algorithm for Quantum Factorization]</ref>
# 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.<ref name="ref_f683455a">[https://www.osapublishing.org/abstract.cfm?uri=oe-28-13-18917 Proof-of-principle demonstration of compiled Shor’s algorithm using a quantum dot single-photon source]</ref>
# 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.<ref name="ref_f683455a" />
# Demonstration of Shor’s algorithm requires lots of qubits and gates that is beyond the current quantum technologies.<ref name="ref_f683455a" />
# Fortunately, Shor’s algorithm utilizing a quantum computer provides an effective way to execute it in a polynomial complexity.<ref name="ref_f683455a" />
===소스===
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 * ID :  [https://www.wikidata.org/wiki/Q940334 Q940334]

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 == 노트 ==
 ===말뭉치===
 # By contrast, Shor's algorithm can crack RSA in polynomial time.<ref name="ref_10c6f526">[https://www.quantiki.org/wiki/shors-factoring-algorithm Shor's factoring algorithm]</ref>

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		+	* ID : [https://www.wikidata.org/wiki/Q940334 Q940334]

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