What kinds of problems can quantum computing solve?
Quantum computers can solve NP-hard problems that classical computers are unable to solve. Currently, the two most important and notable complexity classes are “P” and “NP.” P represents problems that can be solved in polynomial time by a classical computer. For instance, asking if a number is prime belongs to P.
Can a quantum computer solve the halting problem?
No, quantum computers (as understood by mainstream scientists) cannot solve the halting problem. We can already simulate quantum circuits with normal computers; it just takes a really long time when you get a decent number of qubits involved. (Quantum computing provides exponential speedups for some problems.)
Can TSP be solved in polynomial time?
The only known way to verify that a provided solution is the shortest possible solution is to actually solve TSP. Since it takes exponential time to solve NP, the solution cannot be checked in polynomial time.
Can quantum computers solve problems that classical computers cannot?
Computer scientists have been searching for years for a type of problem that a quantum computer can solve but that any possible future classical computer cannot. Now they’ve found one.
How many hints does a quantum computer need to solve pH?
In fact, a quantum computer needs just one hint, while even with unlimited hints, there’s no algorithm in PH that can solve the problem. “This means there is a very efficient quantum algorithm that solves that problem,” said Raz.
Can quantum computers solve cryptography?
However, a quantum computer has the computational ability to find solutions to the cryptographic algorithms in use today. Cryptographic problems that use factoring are excellent examples of problems that can be solved with a quantum computer because both the input and output are each a single number.
What is BQP in quantum computing?
They defined this class to contain all the decision problems — problems with a yes or no answer — that quantum computers can solve efficiently. Around the same time they also proved that quantum computers can solve all the problems that classical computers can solve. That is, BQP contains all the problems that are in P. 1.