  We formulate Grover's unstructured search algorithm as a chiral quantum walk,
where transitioning in one direction has a phase conjugate to transitioning in
the opposite direction. For small phases, this breaking of time-reversal
symmetry is too small to significantly affect the evolution: the system still
approximately evolves in its ground and first excited states, rotating to the
marked vertex in time $\pi \sqrt{N} / 2$. Increasing the phase does not change
the runtime, but rather changes the support for the 2D subspace, so the system
evolves in its first and second excited states, or its second and third excited
states, and so forth. Apart from the critical phases corresponding to these
transitions in the support, which become more frequent as the phase grows, this
reveals that our model of quantum search is robust against time-reversal
symmetry breaking.
