Fault-tolerant magic state preparation with flag qubits

Christopher Chamberland1,2 and Andrew W. Cross1

1IBM T. J. Watson Research Center, Yorktown Heights, NY, 10598, United States
2Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes requires only three ancilla qubits, even with noisy Clifford gates. We compare the physical qubit and gate cost of our scheme to the magic state distillation protocol of Meier, Eastin, and Knill (MEK), which is efficient and uses a small stabilizer circuit. For low enough noise rates, we show that in some regimes the overhead can be improved by several orders of magnitude compared to the MEK scheme which uses Clifford operations encoded in the codes considered in this work.

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► References

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Cited by

[1] Ilkwon Sohn, Jeongho Bang, and Jun Heo, "Dynamic Concatenation of Quantum Error Correction in Integrated Quantum Computing Architecture", Scientific Reports 9, 3302 (2019).

[2] Xin Wang, Mark M. Wilde, and Yuan Su, "Efficiently computable bounds for magic state distillation", arXiv:1812.10145.

[3] Xin Wang, Mark M. Wilde, and Yuan Su, "Quantifying the magic of quantum channels", arXiv:1903.04483.

[4] Theerapat Tansuwannont, Christopher Chamberland, and Debbie Leung, "Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes", arXiv:1803.09758.

[5] Daniel Litinski, "Magic State Distillation: Not as Costly as You Think", arXiv:1905.06903.

[6] Yunong Shi, Christopher Chamberland, and Andrew W. Cross, "Fault-tolerant preparation of approximate GKP states", arXiv:1905.00903.

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