Day 29　Quantum Protocols and Quantum Algorithms

Understanding Quantum Teleportation
1.Creates an entangled pair of qubits(one to Bob and one to Alice)
-> Entangled qubits could be written in Dirac Notation
2.Alice applies CNOT gate to q1(controlled by |ψ⟩ the qubit she is trying to send Bob)
3.Alice applies Hadamard gate to |ψ⟩
-> (H⊗I⊗I)(CNOT⊗I)(|q⟩⊗|ψ⟩)
4.Alice measures both q1 and |ψ⟩
5.Alice stores result in two classical bits then sends to Bob
6.Bob applies the following gates depending on the state of classical bits:
00 -> Do nothing
01 -> Apply X gate
10 -> Apply Z gate
11 -> Apply ZX gate

Difference between Superdense Coding and Quantum Teleportation
Quantum teleportation

• Destroys the quantum state of a qubit in one location
• Recreates it on a qubit at a distant location(shared entanglement)
  Superdense coding
• Send two classical bits to another party using single qubit

Deutsch-Jozsa Algorithm

• Constant function returns all 0's or all 1's
• Balanced function returns 0's for exactly half and 1's for the other half

Bernstein-Vazirani Algorithm

• extension of Deutsch-Josza algorithm

Quantum Fourier Transform(QFT)

• Quantum implementation of discrete Fourier transform over amplitudes of wavefunction
• QFT|State in Computational Basis⟩ -> |State in Fourier Basis⟩