Magic state parity-checker with pre-distilled components

Earl T. Campbell and Mark Howard

Department of Physics & Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom.

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Abstract

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.

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Cited by

[1] Daniel Litinski, "Magic State Distillation: Not as Costly as You Think", Quantum 3, 205 (2019).

[2] Daniel Litinski, "A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery", Quantum 3, 128 (2019).

[3] Earl Campbell, Ankur Khurana, and Ashley Montanaro, "Applying quantum algorithms to constraint satisfaction problems", Quantum 3, 167 (2019).

[4] Earl Campbell, "Random Compiler for Fast Hamiltonian Simulation", Physical Review Letters 123 7, 070503 (2019).

[5] James R. Seddon and Earl T. Campbell, "Quantifying magic for multi-qubit operations", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475 2227, 20190251 (2019).

[6] Xin Wang, Mark M Wilde, and Yuan Su, "Quantifying the magic of quantum channels", arXiv:1903.04483, New Journal of Physics 21 10, 103002 (2019).

[7] Craig Gidney and Austin G. Fowler, "Efficient magic state factories with a catalyzed |CCZ⟩ to 2|T⟩ transformation", Quantum 3, 135 (2019).

[8] Michael Beverland, Earl Campbell, Mark Howard, and Vadym Kliuchnikov, "Lower bounds on the non-Clifford resources for quantum computations", arXiv:1904.01124.

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

[10] Jeongwan Haah, "Towers of generalized divisible quantum codes", Physical Review A 97 4, 042327 (2018).

The above citations are from Crossref's cited-by service (last updated 2019-12-06 10:44:13) and SAO/NASA ADS (last updated 2019-12-06 10:44:15). The list may be incomplete as not all publishers provide suitable and complete citation data.