Quantum algorithm

• 1: Deutsch algorithm
  • Example1: Constant function
  • Example2: Balanced function
• 2: Deutsch-Jozsa algorithm
  • Example1: Constant function
  • Example2: Balanced function
• 3: Bernstein-Vazirani algorithm
  • Example1: \(a=101\)
  • Example2: \(a=111\)
• 4: Simon algorithm
  • Example1: the secret key \(s=3=11_{(2)}\)
  • Example2: the secret key \(s=1=01_{(2)}\)
  • Example3: the secret key \(s=2=10_{(2)}\)
• 5: 2-bit quantum teleportation
  • Example1: Transmission data \(\left| x \right\rangle=(\left| 0 \right\rangle + \left| 1 \right\rangle)/\sqrt{2}\) (H gate)
  • Example2: Transmission data \(\left| x \right\rangle=\left| 0 \right\rangle\) (No gate)
  • Example3: Transmission data \(\left| x \right\rangle=\left| 1 \right\rangle\) (X gate)
  • Example4: Transmission data \(\left| x \right\rangle=- \left| 1 \right\rangle\) (X gate, Z gate)
  • Example5: Transmission data \(\left| x \right\rangle=i \left| 1 \right\rangle\) (Y gate)
• 6: Grover algorithm
  • 6-1: Search method of Grover algorithm
    • (1) Superposition state with equal probability amplitude
    • (2) Marking by phase inversion of search solution
    • (3) Inversion around the mean value of the probability amplitude (diffusion conversion)
  • 6-2: In case of another search solution
    • (1) Search solution \(\left | 0 \right\rangle\)
    • (2) Search solution \(\left | 1 \right\rangle\)
    • (3) Search solution \(\left | 2 \right\rangle\)
• 7: Quantum Fourier Transform
  • 7-1: Quantum Fourier Transform \(QFT_4\)
  • 7-2: Quantum Fourier Transform \(QFT_{N}\)
  • 7-3: Inverse quantum Fourier Transform \(QFT^{-1}_{N}\)
• 8: Phase estimation problem
  • 8-1: Phase estimation problem with 3 qubits
• 9: Shor algorithm
  • 9-1: Classical factorization algorithm
  • 9-2: The Quantum circuit
  • 9-3: Quantum oracle
• 10: Quantum Error Correction
  • 10-1: Quantum error correction of bit inversion error
  • 10-2: Quantum error correction of phase inversion error
• 11: Quantum Tunnelling
  • Example1: When there is a potential barrier
  • Example2: When there is no potential barrier
• References