Understand Shor's Algorithm & Quantum Fourier Transform

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In summary, Shor's algorithm is a quantum algorithm for factoring large numbers into their prime factors. It is important because it is the most efficient known algorithm for this task and can have significant implications for cryptography and data security. It works by using a combination of classical and quantum operations to find the period of a function, which is then used to factor large numbers. The Quantum Fourier Transform (QFT) is a quantum version of the classical Fourier Transform and is an essential component of Shor's algorithm. It is used to efficiently find the period of a function, which is then used to factor large numbers. The main applications of Shor's algorithm and the QFT are in cryptography, number theory, and potentially quantum computing and communication.
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michael879
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hey, from what I've read here: http://www.quantiki.org/wiki/index.php/Shor%27s_Algorithm [Broken], I understand most of the algorithm. The one thing that I don't get is what the quantum Fourier transform does to the input register. Can someone either explain how this works or what exactly it does?
 
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thanks, that was pretty helpful. However there is almost no math or quantum mechanics in that article. All I understood was his metaphor for the QFT, not really the DFT.
 

1. What is Shor's algorithm and why is it important?

Shor's algorithm is a quantum algorithm for factoring large numbers into their prime factors. It is important because it is the most efficient known algorithm for this task, and can have significant implications for cryptography and data security.

2. How does Shor's algorithm work?

Shor's algorithm uses a combination of classical and quantum operations to find the period of a function, which is then used to factor large numbers. It relies on the principles of quantum superposition and entanglement to efficiently solve this problem.

3. What is the Quantum Fourier Transform (QFT)?

The Quantum Fourier Transform is a quantum version of the classical Fourier Transform, which is a mathematical operation used to transform a function from its original domain to a new domain. In the context of Shor's algorithm, the QFT is used to efficiently find the period of a function.

4. How does the QFT relate to Shor's algorithm?

The QFT is an essential component of Shor's algorithm, as it is used to efficiently find the period of a function. The period is then used to factor large numbers, making the QFT a crucial part of the overall algorithm.

5. What are the applications of Shor's algorithm and the QFT?

The main application of Shor's algorithm and the QFT is in the field of cryptography, where it can potentially be used to break certain types of encryption. It also has implications for number theory and could potentially have uses in quantum computing and quantum communication.

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