Quantum Phase Estimation

• Use phase kickback to write phase of U to t qubits in counting register
• • Use a qubit to control U-gate, the qubit will turn proportionally to phase e^(2iπθ)
• • Repeat rotation appropriate number of times until phase theta as a number between 0 and 2t

Mathematical Foundation

• Setup
• Superposition - Apply n-bit Hadamard gate operation on counting register
• Controlled Unitary Operations - Need to introduce controlled unitary C−U
• Inverse Fourier Transform
• Measurement