The problems which are calculated, such as finding prime factors of an integer, take non-polynomial (NP) time on a classical computer to solve. But NP problems, as opposed to NP-hard, can by definition be confirm in P (polynomial) time on a classical computer. Therefore, we can easily confirm that the answer is correct using classical computers.
On an aside, I used the example of prime factorization because it is one of the most well known problems that can be accelerated via quantum computing using Shor’s algorithm. Using Shor’s algorithm on a quantum computer, an integer can be factorized in P time. This is opposed to NP time on a classical computer.
Also, note that this acceleration provided by Shor’s algorithm is what people are talking about when they say “quantum breaks encryption”. I don’t like when people say that though because quantum computers don’t break all encryption schemes. In fact, there is only one mainstream encryption scheme which is susceptible and that is RSA. Don’t get me wrong, if RSA is comprised that would compromise a LOT of legacy systems. But we already have new public key ciphers, such as elliptic curves, which are ready to replace RSA once quantum computers become large enough to actually implement an attack against RSA.
The problems which are calculated, such as finding prime factors of an integer, take non-polynomial (NP) time on a classical computer to solve. But NP problems, as opposed to NP-hard, can by definition be confirm in P (polynomial) time on a classical computer. Therefore, we can easily confirm that the answer is correct using classical computers.
On an aside, I used the example of prime factorization because it is one of the most well known problems that can be accelerated via quantum computing using Shor’s algorithm. Using Shor’s algorithm on a quantum computer, an integer can be factorized in P time. This is opposed to NP time on a classical computer.
Also, note that this acceleration provided by Shor’s algorithm is what people are talking about when they say “quantum breaks encryption”. I don’t like when people say that though because quantum computers don’t break all encryption schemes. In fact, there is only one mainstream encryption scheme which is susceptible and that is RSA. Don’t get me wrong, if RSA is comprised that would compromise a LOT of legacy systems. But we already have new public key ciphers, such as elliptic curves, which are ready to replace RSA once quantum computers become large enough to actually implement an attack against RSA.