Lecture 20 - Grover's Algorithm

Monday, 5/20/24 (week 8, lesson 1):

  1. This week’s Th. office hours moved to 11:10-12!
  2. Next week: T follows a Monday schedule – T activity will take place in class, 3:10-4 pm, T and W!
  3. Read 6.8, 7.2 (incl. all subsections)
  4. Read lecture slides on Quantum algorithms pp. 17-22

![[Physics CPE 345 Quantum Computing Lecture slides Weeks 8 and 9 Quantum algorithms 240520 2.pdf#page=11]]

![[Physics CPE 345 Quantum Computing Lecture slides Weeks 8 and 9 Quantum algorithms 240520 2.pdf#page=12]]

For instance, if we do:

![[Physics CPE 345 Quantum Computing Lecture slides Weeks 8 and 9 Quantum algorithms 240520 2.pdf#page=16]]

|ψ0⟩=|1⟩ is the entry we are looking for|ψ1⟩=12(|0⟩+|1⟩)⊗12(|0⟩−|1⟩)|ψ2⟩=cX|ψ1⟩=12(|00⟩−|01⟩+|11⟩−|10⟩)=12(|0⟩−|1⟩)⊗12(|0⟩−|1⟩)

Then doing the diffuser/amplifer:

|ψ3⟩=H⊗2|ψ2⟩=12(12(|0⟩+|1⟩)−12(|0⟩−|1⟩))⊗...=|1⟩⊗|1⟩|ψ4⟩=X0|ψ3⟩=|0⟩⊗|1⟩|ψ5⟩=Z0|ψ4⟩=|0⟩⊗|1⟩|ψ6⟩=X0|ψ5⟩=|1⟩⊗|1⟩|ψ7⟩=H0|ψ6⟩=12(|0⟩−|1⟩)⊗|1⟩=12(|01⟩−|11⟩)