File:Quantum phase estimation steps.png

English: The standard quantum phase estimation circuit utilizes three ancilla qubits. In this configuration, when the ancilla qubits are in the state ${\displaystyle |k\rangle }$, a controlled rotation, denoted as ${\displaystyle e^{-\pi \cdot H\cdot i\cdot 2^{k}}}$, is applied to the target state ${\displaystyle |\psi \rangle }$. This operation is a key component of the process. The term 'QFT' refers to the quantum Fourier transform, a fundamental quantum computing operation detailed by . In the final step of the process, the ancilla qubits are measured in the computational basis. This measurement causes the ancilla qubits to collapse to a specific eigenvalue of the Hamiltonian (${\displaystyle H}$), simultaneously collapsing the register qubits into an approximation of the corresponding energy eigenstate. This mechanism is central to the functioning of the quantum phase estimation circuit, allowing for the estimation of energy levels of the system under study. Figure reproduced without permission.^[1]