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The leading approach to fault tolerant quantum computing requires a continual supply of magic states.
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In fact one of two different gates on the input state will have occurred, depending on the outcome of the measurement – but these gates are related by a rotation that can be performed fault-tolerantly
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E. T. Campbell, arXiv:1406.3055
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J. Łodyga, P. Mazurek, A. Grudka, and M. Horodecki, arXiv:1404.2495
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