Quantum Computers: Shor's Algorithm & Factoring 15

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In summary, in 2001, a 7-qubit quantum computer successfully ran Shor's algorithm and was able to factor the number 15. This demonstrated the accuracy and validity of Quantum Mechanics and its principles, such as superposition of states. While some may have doubts about the reliability of Quantum Mechanics, the success of this quantum computer proves its effectiveness. The potential of quantum computers is exciting and it is eagerly anticipated to see the first one in action.
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Wikipedia said:
In 2001, the first 7-qubit quantum computer became the first to run Shor's algorithm. It factored the number 15.

If we can actually build quantum computers then Quantum Mechanics and its principles, such as superposition of states, really must be very accurate. Not being a physicist, this is surprising to me, but in a good way. I'm familiar with some of Quantum Mechanics' "oddities" and I've always wondered if it has gone down a path where it is only valid because verifying some of its predictions isn't easy. But there's no way a Quantum Computer would work without the principle of superposition, and regarding Quantum Computation I've always held the "see it to believe it" approach. Of course i will only really believe when i see a Quantum Computer break an RSA encription in polynomial time. We already have the algorithm, by Shor, all we need is the machine. If Quantum Computers are possible then this is all very exciting, these machines are beasts and extraordinarily powerful.
I'll wait impatiently for the first one. :smile:
 
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Originally Posted by Wikipedia
In 2001, the first 7-qubit quantum computer became the first to run Shor's algorithm. It factored the number 15.

But what result did it get?:rofl:
 
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HallsofIvy said:
But what result did it get?:rofl:

Well, since it knew 15 with absolute precision it got a result of approximately 3 and approximately 5. :smile:

-Dan
 

1. What is Shor's algorithm and how does it relate to quantum computers?

Shor's algorithm is a quantum algorithm that can efficiently factor large numbers. It relies on the unique properties of quantum computers, such as superposition and entanglement, to solve the factoring problem much faster than classical computers.

2. Why is factoring 15 considered a significant problem for quantum computers?

Factoring 15 is a significant problem for quantum computers because it is the smallest number that can demonstrate the power of Shor's algorithm. While it may seem like a small number, factoring 15 is still a difficult problem for classical computers and solving it on a quantum computer demonstrates the potential for tackling larger and more complex factoring problems.

3. How does Shor's algorithm factor numbers on a quantum computer?

Shor's algorithm uses a combination of classical and quantum operations to factor numbers. First, the number to be factored is converted into a quantum state using quantum gates. Then, the quantum state is measured multiple times to obtain the factors of the original number. The quantum circuit used in Shor's algorithm is designed to take advantage of the quantum properties of superposition and entanglement to efficiently solve the factoring problem.

4. Can Shor's algorithm be used for other types of problems besides factoring?

While Shor's algorithm is primarily known for its ability to factor numbers, it can also be adapted to solve other types of problems. For example, it has been used to solve the discrete logarithm problem, which is important in cryptography. However, Shor's algorithm is limited to solving problems that can be expressed as a mathematical function, so it cannot be used for all types of problems.

5. Are there any challenges or limitations to implementing Shor's algorithm on quantum computers?

Yes, there are several challenges and limitations to implementing Shor's algorithm on quantum computers. One major challenge is the need for a large number of qubits, which are the basic units of quantum information. Shor's algorithm requires a significant number of qubits to solve larger factoring problems, and current quantum computers do not have enough qubits to make this possible. Additionally, quantum computers are prone to errors, which can affect the accuracy of the results obtained from Shor's algorithm. Finally, there are also challenges in creating and controlling the complex quantum circuits required for Shor's algorithm to run.

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