Quantum Computer Search Algorithms: Can We Outperform the Classical Search Algorithms?

Abstract

Quantum Computers are not limited to just two states. Qubits, the basic unit of quantum computing have the power to exist in more than one state at a time. While the classical computers only perform operations by manipulation of classical bits having two values 0 and 1, quantum bits can represent data in multiple states. This property of inheriting multiple states at a time is called superposition which gives quantum computers tremendous power over classical computers. With this power, the algorithms designed on quantum computers to solve search queries can yield result significantly faster than the classical algorithms. There are four types of problems that exist: Polynomial (P), Non-Deterministic Polynomial (NP), Non-Deterministic Polynomial Complete (NP-complete) and Non-Deterministic Polynomial hard (NP-hard). P problems can be solved in the polynomial amount of time like searching a database for an item. However, when the size of the search space grows, it becomes difficult to compute solutions even for P problems. Quantum algorithms like Grover’s algorithm has reduced the time complexity of some of the classical algorithm problems from N to \(\sqrt{N}\). Variants of Grover’s algorithm like Quantum Partial Search propose changes that yield not exact but closer results in time even lesser than Grover’s algorithm. NP problems are the problems whose solution if known can be verified in polynomial amount time. Factorization of prime numbers which is considered to be an NP problem took an exponential amount of time when solved using the classical computer while the Shor’s quantum computing algorithm computes it in polynomial time. Factorization is also a class of bounded-error quantum polynomial time (BQP) problems which are decision problems solved by quantum computers in polynomial time. There are problems to which if a solution is found can solve every problem Of NP class, these are NP-complete problems. The power of Qubits could be exploited in the future to come up with solutions for NP-complete problems in the future.