Magic states are eigenstates of non-Pauli operators. One way of suppressing errors present in magic states is to perform parity measurements in their non-Pauli eigenbasis and postselect on even parity. Here we develop new protocols based on non-Pauli parity checking, where the measurements are implemented with the aid of pre-distilled multiqubit resource states. This leads to a two step process: pre-distillation of multiqubit resource states, followed by implementation of the parity check. These protocols can prepare single-qubit magic states that enable direct injection of single-qubit axial rotations without subsequent gate-synthesis and its associated overhead. We show our protocols are more efficient than all previous comparable protocols with quadratic error reduction, including the protocols of Bravyi and Haah.
 Earl T Campbell, Barbara M Terhal, and Christophe Vuillot. Roads towards fault-tolerant universal quantum computation. Nature, 549 (7671): 172, 2017. 10.1038/nature23460.
 Sergey Bravyi and Alexei Kitaev. Universal quantum computation with ideal Clifford gates and noisy ancillas. Phys. Rev. A, 71: 022316, 2005. 10.1103/PhysRevA.71.022316.
 Adam M. Meier, Bryan Eastin, and Emanuel Knill. Magic-state distillation with the four-qubit code. Quant. Inf. and Comp., 13: 195, 2013.
 Jeongwan Haah, Matthew B. Hastings, D. Poulin, and D. Wecker. Magic state distillation with low space overhead and optimal asymptotic input count. Quantum, 1: 31, October 2017. ISSN 2521-327X. 10.22331/q-2017-10-03-31.
 Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Asymptotically optimal approximation of single qubit unitaries by clifford and $t$ circuits using a constant number of ancillary qubits. Phys. Rev. Lett., 110: 190502, May 2013. 10.1103/PhysRevLett.110.190502.
 David Gosset, Vadym Kliuchnikov, Michele Mosca, and Vincent Russo. An algorithm for the t-count. Quant. Inf. & Comp., 14 (15-16): 1261-1276, 2014.
 Neil J Ross and Peter Selinger. Optimal ancilla-free clifford+ t approximation of z-rotations. Quant. Inf. and Comp., 16: 901, 2016.
 Adam Paetznick and Krysta M Svore. Repeat-until-success: Non-deterministic decomposition of single-qubit unitaries. Quant. Inf. & Comp., 14 (15-16): 1277-1301, 2014.
 Alex Bocharov, Martin Roetteler, and Krysta M. Svore. Efficient synthesis of probabilistic quantum circuits with fallback. Phys. Rev. A, 91: 052317, May 2015. 10.1103/PhysRevA.91.052317.
 Andrew J Landahl and Chris Cesare. Complex instruction set computing architecture for performing accurate quantum $ z $ rotations with less magic. arXiv preprint arXiv:1302.3240, 2013. URL https://arxiv.org/pdf/1302.3240.pdf.
 Guillaume Duclos-Cianci and David Poulin. Reducing the quantum-computing overhead with complex gate distillation. Phys. Rev. A, 91: 042315, Apr 2015. 10.1103/PhysRevA.91.042315.
 Earl T Campbell and Joe O'Gorman. An efficient magic state approach to small angle rotations. Quantum Science and Technology, 1 (1): 015007, 2016. doi:10.1088/2058-9565/1/1/015007.
 Earl T. Campbell and Mark Howard. Unifying gate synthesis and magic state distillation. Phys. Rev. Lett., 118: 060501, Feb 2017a. 10.1103/PhysRevLett.118.060501.
 Earl T. Campbell and Mark Howard. Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost. Phys. Rev. A, 95: 022316, Feb 2017b. 10.1103/PhysRevA.95.022316.
 Jeongwan Haah, Matthew B Hastings, D Poulin, and D Wecker. Magic state distillation at intermediate size. Quant. Inf. and Comp., 18: 0114, 2018.
 Matthew B. Hastings and Jeongwan Haah. Distillation with sublogarithmic overhead. Phys. Rev. Lett., 120: 050504, Jan 2018. 10.1103/PhysRevLett.120.050504.
 Daniel Gottesman and Isaac L. Chuang. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 402: 390, 1999. 10.1038/46503.
 Earl T. Campbell and Dan E. Browne. On the structure of protocols for magic state distillation. Lecture Notes in Computer Science, 5906: 20, 2009. 10.1007/978-3-642-10698-9_3. arXiv:0908.0838.
 R. Raussendorf, J. Harrington, and K. Goyal. A fault-tolerant one-way quantum computer. Annals of Physics, 321 (9): 2242 - 2270, 2006. ISSN 0003-4916. 10.1016/j.aop.2006.01.012.
 Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland. Surface codes: Towards practical large-scale quantum computation. Phys. Rev. A, 86: 032324, Sep 2012. 10.1103/PhysRevA.86.032324.
 Joe O'Gorman and Earl T. Campbell. Quantum computation with realistic magic-state factories. Phys. Rev. A, 95: 032338, Mar 2017. 10.1103/PhysRevA.95.032338.
 Jeongwan Haah and Matthew B Hastings. Codes and protocols for distilling $ t $, controlled-$ s $, and toffoli gates. arXiv preprint arXiv:1709.02832, 2017. URL https://arxiv.org/pdf/1709.02832.pdf.
 Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", Quantum 3, 128 (2019).
 Craig Gidney and Austin G. Fowler, "Efficient magic state factories with a catalyzed |CCZ⟩ to 2|T⟩ transformation", Quantum 3, 135 (2019).
 Xin Wang, Mark M. Wilde, and Yuan Su, "Efficiently computable bounds for magic state distillation", arXiv:1812.10145.
 Xin Wang, Mark M. Wilde, and Yuan Su, "Quantifying the magic of quantum channels", arXiv:1903.04483.
 Jeongwan Haah, "Towers of generalized divisible quantum codes", Physical Review A 97 4, 042327 (2018).
 Michael Beverland, Earl Campbell, Mark Howard, and Vadym Kliuchnikov, "Lower bounds on the non-Clifford resources for quantum computations", arXiv:1904.01124.
 James R. Seddon and Earl Campbell, "Quantifying magic for multi-qubit operations", arXiv:1901.03322.
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