What can quantum computers do more efficiently than regular computers?

Quantum computers vs classical computers

Quantum computers can perform certain types of computations much more efficiently than classical computers. The most significant advantage of quantum computers is that they can perform certain operations exponentially faster than classical computers. This is due to the unique properties of quantum mechanics. 

Unique properties of quantum mechanics

• quantum parallelism
• quantum entanglement

One of the most important applications of quantum computers is in the field of quantum algorithms, such as Shor's algorithm and Grover's algorithm. 

• Shor's algorithm:

• It can be used to factorize large numbers efficiently, which is crucial for breaking many encryption systems. 

• Grover's algorithm:

• It can be used to search an unsorted database quadratically faster than any classical algorithm.

Another important area where quantum computers have the potential to be much more powerful than classical computers is in simulating quantum systems. Due to the exponential scaling of the Hilbert space with the number of qubits, even a small quantum computer with only a few dozen qubits can represent an exponentially large classical system.

Summary:

Quantum computers can perform certain computations exponentially faster than classical computers, including factoring large integers, solving systems of linear equations, and simulating quantum systems.

Use case of factorization in quantum computing: 

The use case of factorization in quantum computing is Shor's algorithm, which is a quantum algorithm for factoring integers that were discovered by mathematician Peter Shor in 1994. 

 It is the most efficient known classical algorithm for this task. The algorithm can be used to break RSA and other public key cryptosystems that are based on the difficulty of factoring large integers, thereby solving one of the most important problems in classical computer science and a major open problem in mathematical research. 

In the year 1994, Shor's algorithm was first implemented on a quantum computer with a 7-qubit NMR quantum computer. Since then, the largest factorization that has been performed using this algorithm is on a 21-qubit quantum computer, which factorized the number 15 into 3 and 5.