Can quantum computers solve traveling salesman problem in polynomial time?

Can quantum computers solve traveling salesman problem in polynomial time?

The set of problems that can be solved by an universal quantum computer in “polynomial time” (with at most 1/3 probability of error) is called BQP. Travelling salesman problem is in complexity class called NP.

Has anyone solved the traveling salesman problem?

The traveling salesperson problem “isn’t a problem, it’s an addiction,” as Christos Papadimitriou, a leading expert in computational complexity, is fond of saying. Most computer scientists believe that there is no algorithm that can efficiently find the best solutions for all possible combinations of cities.

What type of problems can quantum computers 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 quantum computers solve Travelling salesman?

Quantum computing could speed up certain algorithms for solving the famous traveling salesman problem. The traveling salesman problem (TSP) can describe many situations, such as the optimization of electric wiring or business scheduling.

Is Travelling salesman NP-hard?

Thus we can say that the graph G’ contains a TSP if graph G contains Hamiltonian Cycle. Therefore, any instance of the Travelling salesman problem can be reduced to an instance of the hamiltonian cycle problem. Thus, the TSP is NP-Hard.

What problems Cannot be solved by computers?

Eight Problems A Computer Can’t Solve

• A computer won’t solve broad, poorly defined problems.
• A computer won’t save money by eliminating workers.
• A computer won’t clean up the errors in your manual procedures.
• A computer won’t do forecasting or trend analysis until a few years down the road.

Can a quantum computer solve the traveling salesman problem?

A quantum computer can solve classes of problems that no classical computer can efficiently solve, and perhaps that will someday include the traveling salesman problem. When your brute force options are too expensive and an efficient algorithm eludes you, don’t give up on ever solving the problem altogether.

What are the problems that are difficult to solve using classical computers?

Travelling Salesperson Problem (TSP), Dynamic Program- ming (DP), Quantum Computing (QC), Quantum Mechan- ics (QM), Quantum Bit (Qubit). Combinatorial Optimization problems, especially the problems that are categorized as NP-hard problems are often difficult to solve using classical computers.

How many possible routes can a quantum computer take?

Assuming you know that you begin and end at your home, there are six possible routes you can take… Even if no such solution exists, and it might not with a classical computer, the world of quantum computers offers unparalleled hope.

Are quantum algorithms better than classical computers?

Recently, quantum computing has been of great interest due to the possible advantage quantum computers may present over their classical counterparts. This motivates the research of quantum algorithms that present a speedup over the best classical solutions.