How Shor's Algorithm Factors 314191

The video explains how quantum computers, specifically using Shor's algorithm, can factor large numbers to break encryption. It demonstrates the process of using a quantum computer to find factors of a number by making random guesses, using superposition, and applying a quantum Fourier transform. The video also covers the use of Euclid's algorithm to verify the factors found. The example used involves factoring the number 314,191 to break an encryption, illustrating the steps and calculations involved in the process.

What is the primary purpose of Shor's Algorithm as discussed in the video?

• To simulate classical computers

• To perform basic arithmetic operations

• To factor large numbers quickly

• To encrypt data using large numbers

In the process of using Shor's Algorithm, what is the significance of finding the power p?

• It is used to determine the period of the superposition

• It is used to calculate the remainder

• It is used to find a better guess for a factor

• It helps in encrypting the number

What role does the quantum Fourier transform play in Shor's Algorithm?

• It encrypts the number

• It finds the common factor

• It calculates the remainder

• It picks out the frequency of the superposition

Why was the initial guess of 101 not successful in factoring 314,191?

• Because the resulting power was odd

• Because 101 is a prime number

• Because 101 shares a factor with 314,191

• Because the quantum computer failed

What are the final factors of 314,191 as determined by Shor's Algorithm?

• 829 and 379

• 314 and 191

• 101 and 127

• 4,347 and 17,388