Amplitude encoding stores information in the absolute values of the amplitudes associated with quantum basis states. Quantum Fourier transform converts between this representation and phase encoding, where information resides in the phases of complex amplitudes. section 5.5 section 5.3.4
In quantum phase estimation, amplitude encoding supports readout through a short conversion pipeline:
- Encode eigenphase information in the relative phases of multiple control qubits. section 5.3.5
- Apply the inverse quantum Fourier transform to convert phase encoding into amplitude encoding. section 5.3.5
- Measure the control register, where larger amplitudes give higher probabilities to better eigenphase approximations. section 5.3.5
Two-bit quantum phase estimation
Quantum phase estimation uses two control qubits, applies controlled operations to encode an eigenphase in their relative phases, and then uses inverse QFT so the basis state representing the best two-bit approximation has the largest amplitude and measurement probability. section 5.3.5
Figure 5.8 In quantum phase estimation algorithm, we use multiple control qubits to encode the information about the eigenphase in phases of their states. Then, we use inverse quantum Fourier transform to convert that information from phase encoding to amplitude encoding, increasing the amplitude of the basis state that encodes the eigenphase compared to the amplitudes of other states. Finally, we measure the control qubits, reading out the bits of the phase as measurement results with high probability.
Trace the visual sequence from phase encoding through inverse quantum Fourier transform to measurement of the eigenphase bits. section 5.3.5
