  Quantum computing technologies promise to revolutionize calculations in many
areas of physics, chemistry, and data science. Their power is expected to be
especially pronounced for problems where direct analogs of a quantum system
under study can be encoded coherently within a quantum computer. A first step
toward harnessing this power is to express the building blocks of known
physical systems within the language of quantum gates and circuits. In this
paper, we present a quantum calculation of an archetypal quantum system:
neutrino oscillations. We define gate arrangements that implement the neutral
lepton mixing operation and neutrino time evolution in two-, three-, and
four-flavor systems. We then calculate oscillation probabilities by coherently
preparing quantum states within the processor, time evolving them unitarily,
and performing measurements in the flavor basis, with close analogy to the
physical processes realized in neutrino oscillation experiments, finding
excellent agreement with classical calculations. We provide recipes for
modeling oscillation in the standard three-flavor paradigm as well as
beyond-standard-model scenarios, including systems with sterile neutrinos,
non-standard interactions, Lorentz symmetry violation, and anomalous
decoherence.
