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

We consider performing phase estimation under the following conditions: we are given only one copy of input state, state does not have to be an eigenstate unitary, and must measured. Most quantum algorithms make assumptions that them unsuitable for this 'coherent' setting, leaving textbook approach. present novel phase, energy, amplitude both conceptually computationally simpler than method, featuring a smaller query complexity ancilla footprint. They do require Fourier transform, they sorting network compute median several estimates. Instead, use block-encoding techniques estimate bit at time, all amplification via singular value transformation. These improved subroutines accelerate performance Metropolis sampling Bayesian inference.