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Imagine a scenario where you inherit a bank vault brimming with delicious pies, but there's a catch—the access code is encrypted with the number 314191. The tantalizing aroma of pie is just out of reach, and you're faced with a cryptographic puzzle that only a quantum computer can solve. How do we crack this code and satisfy our sweet tooth? Let's dive into the world of quantum computing and Shor's algorithm to find out.
Have you ever wondered what it would take to break encryption protocols using quantum mechanics? In this article, we'll explore how Shor's algorithm can factorize large numbers, effectively unlocking the secrets behind encrypted codes. But first, let's pose a question: What if there was a way to guess the factors of a large number quickly and efficiently?
Enter the realm of quantum computing, where the laws of quantum mechanics allow us to perform computations that are beyond the capabilities of classical computers. Here's where Shor's algorithm comes into play. It leverages the power of quantum superposition and Fourier transform to guess the factors of a large number with unprecedented speed.
Let's start with a simple guess—101. Does it share a factor with 314191? No, it doesn't. But what if we could find a special power, p, such that 101^p is just one more than a multiple of 314191? This is where our quantum computer steps in, raising 101 to any power and calculating the remainder when divided by 314191.
But how does it work? By starting with a superposition of all numbers up to 314191, the quantum computer computes the powers of 101 and their remainders. When we measure the state of the remainders, we get one output, say, 74126. This remainder corresponds to a superposition of powers that are all "p" apart, as explained in our previous video.
Now, the magic happens: we apply a quantum Fourier transform to this superposition. This transform outputs a superposition of multiples of 1/p, which we can measure to find a random value. Repeating this process several times, we start to notice a pattern—a common factor of all those values. In our case, that common factor is 1/4347, indicating that p is 4347.
But what if our initial guess is wrong? No problem! We just start over with a new guess, say, 127, and repeat the process. This time, we find that the corresponding p is 17388. Using Euclid's algorithm, we discover that 829 and 379 are the factors of 314191, and voilà! The vault opens, and the pies are ours to enjoy.
So, what does this mean for our digital lives? If you want to ensure your online accounts are more secure than the pie-filled bank vault in this scenario, consider using a password manager like Dashlane. It generates and securely stores long, unique passwords for each of your accounts, alerting you to weak passwords and even offering a VPN service.
Ready to simplify and secure your online life? Visit dashlane.com/minutephysics to learn more and get 10% off Dashlane Premium with the promo code minutephysics.
In conclusion, while quantum computing may seem like a distant concept, it has real-world applications that can solve complex problems and make our lives easier—starting with the pie in this case!
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