A quantum computer can solve the mathematical basis of all encryption (factoring primes and discrete logarithms) by simulating multiple values simultaneously via superposition and entanglement, making Shor's algorithm feasible on sufficiently large machines.
Charles and Preston explain the core mechanism: classical computers must try one solution at a time (like guessing a pin code digit by digit), while quantum computers use superposition to simulate multiple states simultaneously and entanglement with interference to converge on the correct answer almost instantly.
transcript
Charles Edwards: essentially, a quantum computer is trying to replicate the quantum state and physics, which is, you know, potentially being in multiple values at the same time. So that where that becomes interesting in programming and especially what we're talking about here in encryption is you can essentially model multiple values at the same time and zero in on an optimization really quickly. So if you're trying to guess a password, if it's just a pin code and a lock and it is scrolling through the numbers and if it's got three different number options, you can get there eventually, it'll take you a while. But with a quantum machine, you can basically simulate all of them at once more or less and solve things really quick.
explains mechanism · 1