Chris Bernhardt

“Popular descriptions of quantum algorithms describe them as being much faster than regular algorithms. This speedup, it is explained, comes from being able to put the input into a superposition of all possible inputs and then performing the algorithm on the superposition. Consequently, instead of running the algorithm on just one input, as you do classically, you can run the algorithm using “quantum parallelism” on all possible inputs at the same time.”
― Chris Bernhardt, Quantum Computing for Everyone

“If a problem can be solved in polynomial time we say it belongs to the complexity class P. So the problem that consists of multiplying two numbers together belongs to P. Suppose that instead of solving the problem, someone gives you the answer and you just have to check that the answer is correct. If this process of checking that an answer is correct takes polynomial time, then we say the problem belongs to complexity class NP.* The problem of factoring a large number into the product of two primes belongs to NP.”
― Chris Bernhardt, Quantum Computing for Everyone