In this paper, a method to reduce the profile of layered carpet cloaks is proposed. We analytically prove and numerically demonstrate that using a Low Index Material (LIM), a material with a relative dielectric constant smaller than 1, in construction of carpet cloaks can remarkably reduce their profiles. Using the proposed technique, a carpet cloak consisting of alternating LIM and silicon layers is designed to provide invisibility at visible wavelengths. The designed cloak has a profile that is 2.3 times smaller than a carpet cloak without LIM layers. To realize low index materials at optical wavelengths, silver-coated CdSe/CdS quantum dots dispersed in a polymer host are used. Quantum dots are utilized to compensate the loss of Silver and to achieve a low index medium with neglectable loss. The designed low profile carpet cloak is numerically analyzed showing a good performance for a wide range of incident angles which is the advantage of the proposed structure in comparison with metasurface-based carpet cloaks which work only for a very narrow range of incident angles.