  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. Instead, they use block-encoding
techniques to compute the estimate one bit at a time, performing all
amplification via singular value transformation. These improved subroutines
accelerate the performance of quantum Metropolis sampling and quantum Bayesian
inference.
