GROVER'S ALGORITHM

more background information Quantum states (|0⟩, |1⟩, |+⟩, |-⟩) can be represented as a superposition. |ψ⟩= α|0⟩+ β|1⟩

|α|^2+ |β|^2=1

α=√(1-p,) β=e^jφ √p, 0≤p≤1,0≤φ<2π

|ψ⟩=√(1-p)|0⟩+ e^jφ √p,|1⟩

e^jφ is the phase

The phase can be used to offset the qubit. There are different gates we can use to do the offsets (T, S, Z etc.)

A phase change example can be found here. https://quantum-computing.ibm.com/composer/d065727b7bdddc3f658e2ad8badeb1ba.

Grover's Algorithm

Grover's algorithm shows the exponential advantage of a quantum computer. It is a search algorithm that provides a huge improvement to a regular classical sorting algorithm. This is because Quantum Mechanics systems can be in a state of superposition and algorithms can simultaneously examine multiple states. A search for an item from a random list of n items can be obtained in O(√n)steps.