  Quantum annealing is a powerful alternative model for quantum computing,
which can succeed in the presence of environmental noise even without error
correction. However, despite great effort, no conclusive proof of a quantum
speedup (relative to state of the art classical algorithms) has been shown for
these systems, and rigorous theoretical proofs of a quantum advantage generally
rely on exponential precision in at least some aspects of the system, an
unphysical resource guaranteed to be scrambled by random noise. In this work,
we propose a new variant of quantum annealing, called RFQA, which can maintain
a scalable quantum speedup in the face of noise and modest control precision.
Specifically, we consider a modification of flux qubit-based quantum annealing
which includes random, but coherent, low-frequency oscillations in the
directions of the transverse field terms as the system evolves. We show that
this method produces a quantum speedup for finding ground states in the Grover
problem and quantum random energy model, and thus should be widely applicable
to other hard optimization problems which can be formulated as quantum spin
glasses. Further, we show that this speedup should be resilient to two
realistic noise channels ($1/f$-like local potential fluctuations and local
heating from interaction with a finite temperature bath), and that another
noise channel, bath-assisted quantum phase transitions, actually accelerates
the algorithm and may outweigh the negative effects of the others. The
modifications we consider have a straightforward experimental implementation
and could be explored with current technology.
