This study will evaluate the efficacy, immunogenicity and safety of 9-valent human papillomavirus (9vHPV; V503) vaccine in Chinese women 20 to 45 years of age. The primary hypotheses are: 9vHPV vaccine reduces the incidence of HPV 31-, 33-, 45-, 52-, and 58-related 12-month persistent infection at least 1 month post Dose 3, compared with quadrivalent HPV (qHPV) vaccine in women 20 to 45 years of age who are seronegative at Day 1 and polymerase chain reaction (PCR) negative Day 1 through Month 7 to the relevant HPV type; and 9vHPV vaccine induces non-inferior competitive luminex immunoassay (cLIA) geometric mean titers (GMTs) for each of HPV 6, 11, 16, and 18 one month post Dose 3, compared with qHPV vaccine in women 20 to 45 years of age who are seronegative at Day 1 and PCR negative Day 1 through Month 7 to the relevant HPV type.