# Quantum Computing Basics Papers

Here are some papers on the basics of quantum computing:

**Basics of Quantum Computation****Author**: Vlatko Vedral, et al.**Date**: August 4, 2011**Snippet**: Discusses the basic principles of quantum computation, including the construction of basic gates and networks.

**Quantum Computations: Fundamentals And Algorithms****Author**: Steven Duplij, et al.**Date**: December 10, 2007**Snippet**: Reviews basic concepts of quantum theory of information and principles of quantum calculations.

**Quantum information and quantum computing: an overview and some mathematical aspects****Author**: Maurice Robert Kibler**Date**: November 22, 2018**Snippet**: Provides main ideas behind quantum computing and quantum information, focusing on quantum bits or qubits.

**Quantum computing: principles and applications****Author**: Guanru Feng, et al.**Date**: October 17, 2023**Snippet**: Discusses the current progress in the number of qubits, coherence times, and gate fidelities.

**Quantum computing via measurements only****Author**: Robert Raussendorf, et al.**Date**: May 23, 2007**Snippet**: Talks about the scalability of quantum systems to a large number of qubits for practical applications.

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The paper "Basics of Quantum Computation" discusses Shor's algorithm in the section titled "4. Outline of Quantum Factorization". It describes the algorithm as probabilistic and explains how to determine the factors of a given number $N$ using quantum computation. The algorithm's efficiency is also discussed, noting that modular exponentiation dominates the time complexity.

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### Gentle Summary for Beginners:

Shor's algorithm is a quantum computing method for finding the factors of a large number $N$. In simpler terms, it helps you break down a big number into smaller numbers that multiply together to give you the original number. This is a crucial problem in computer science and cryptography.

Here's how it works:

**Choose a Number**: Pick a random number $a$ that is smaller than $N$ and has no common factors with $N$.**Find the Period**: Use quantum computing to find the "period" $r$ of the function $a^r \mod N$. The period is the smallest $r$ such that $a^r$ equals 1 when divided by $N$.**Calculate Factors**: Once you have $r$, you can easily find the factors of $N$.**Check and Repeat**: Sometimes, the algorithm might give a wrong answer. You can quickly check this by multiplying the factors. If they don't give you $N$, you run the algorithm again.

The beauty of Shor's algorithm is that it can do this much faster than any known method using classical computers. This makes it a game-changer for tasks like breaking encryption codes, which rely on the difficulty of factorization.

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