Despite significant overhead reductions since its first proposal, magic state distillation is often considered to be a very costly procedure that dominates the resource cost of fault-tolerant quantum computers. The goal of this work is to demonstrate that this is not true. By writing distillation circuits in a form that separates qubits that are capable of error detection from those that are not, most logical qubits used for distillation can be encoded at a very low code distance. This significantly reduces the space-time cost of distillation, as well as the number of qubits. In extreme cases, it can cost less to distill a magic state than to perform a logical Clifford gate on full-distance logical qubits.
 A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Phys. Rev. A 86, 032324 (2012).
 C. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, Surface code quantum computing by lattice surgery, New J. Phys. 14, 123011 (2012).
 R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Encoding electronic spectra in quantum circuits with linear T complexity, Phys. Rev. X 8, 041015 (2018).
 E. T. Campbell and M. Howard, Unified framework for magic state distillation and multiqubit gate synthesis with reduced resource cost, Phys. Rev. A 95, 022316 (2017a).
 T. Jochym-O'Connor and S. D. Bartlett, Stacked codes: Universal fault-tolerant quantum computation in a two-dimensional layout, Phys. Rev. A 93, 022323 (2016).
 J. Haah, M. B. Hastings, D. Poulin, and D. Wecker, Magic state distillation with low space overhead and optimal asymptotic input count, Quantum 1, 31 (2017).
 Y. Li, A magic state’s fidelity can be superior to the operations that created it, New J. Phys. 17, 023037 (2015).
 J. Lodyga, P. Mazurek, A. Grudka, and M. Horodecki, Simple scheme for encoding and decoding a qubit in unknown state for various topological codes, Scientific Rep. 5, 8975 (2015).
 L. Lao et al., Preparing high-fidelity magic states with low costs, in preparation.
 Cramming more power into a quantum device, https://www.ibm.com/blogs/research/2019/03/ power-quantum-device/, accessed: 2019-05-09.
 K. Wright, K. Beck, S. Debnath, J. Amini, Y. Nam, N. Grzesiak, J.-S. Chen, N. Pisenti, M. Chmielewski, C. Collins, et al., Benchmarking an 11-qubit quantum computer, arXiv:1903.08181 (2019).
 E. T. Campbell and M. Howard, Unifying gate synthesis and magic state distillation, Phys. Rev. Lett. 118, 060501 (2017b).
 Dominic W. Berry, Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush, "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization", arXiv:1902.02134.
 Craig Gidney and Martin Ekerå, "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits", arXiv:1905.09749.
 Y. Herasymenko and T. E. O'Brien, "A diagrammatic approach to variational quantum ansatz construction", arXiv:1907.08157.
 Ryuji Takagi and Hiroyasu Tajima, "Universal limitations on implementing resourceful unitary evolutions", arXiv:1909.01336.
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