  We prove the genus-one restriction of the all-genus
Landau-Ginzburg/Calabi-Yau conjecture of Chiodo and Ruan, stated in terms of
the geometric quantization of an explicit symplectomorphism determined by
genus-zero invariants. This provides the first evidence supporting the
higher-genus Landau-Ginzburg/Calabi-Yau correspondence for the quintic
threefold, and exhibits the first instance of the "genus zero controls higher
genus" principle, in the sense of Givental's quantization formalism, for
non-semisimple cohomological field theories.
