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We present a scheme for magic state distillation using punctured polar codes. Our results build on some recent work by Bardet et al. (ISIT, 2016) who discovered that polar codes can be described algebraically as decreasing monomial codes. Using this powerful framework, we construct tri-orthogonal quantum codes (Bravyi et al., PRA, 2012) that can be used to distill magic states for the T gate. An advantage of these codes is that they permit the use of the successive cancellation decoder whosearXiv:1811.03112v2 fatcat:t2ds663j55a2ja7opjj6mdlbzq