Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation

Understand

We consider performing phase estimation under the following conditions: we are given only one copy of the input state, the input state does not have to be an eigenstate of the unitary, and the state must not be measured.

• Most quantum estimation algorithms make assumptions that make them unsuitable for this 'coherent' setting, leaving only the textbook approach.
• We present novel algorithms for phase, energy, and amplitude estimation that are both conceptually and computationally simpler than the textbook method, featuring both a smaller query complexity and ancilla footprint.
• They do not require a quantum Fourier transform, and they do not require a quantum sorting network to compute the median of several estimates.