  Phase estimation is a quantum algorithm for measuring the eigenvalues of a
Hamiltonian. We propose and rigorously analyse a randomized phase estimation
algorithm with two distinctive features. First, our algorithm has complexity
independent of the number of terms L in the Hamiltonian. Second, unlike
previous L-independent approaches, such as those based on qDRIFT, all sources
of error in our algorithm can be suppressed by collecting more data samples,
without increasing the circuit depth.
