title: Experimental estimation of average fidelity of a Clifford gate on a 7-qubit quantum processor.
abstract: One of the major experimental achievements in the past decades is the ability to control quantum systems to high levels of precision. To quantify the level of control we need to characterize the dynamical evolution. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10^{8} experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to at least 87.5% if the signal's decay due to decoherence is taken into account. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Dawei
authors.initials: D
authors.lastname: Lu
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.|Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.
authors.forename: Hang
authors.initials: H
authors.lastname: Li
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Denis-Alexandre
authors.initials: DA
authors.lastname: Trottier
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Jun
authors.initials: J
authors.lastname: Li
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Aharon
authors.initials: A
authors.lastname: Brodutch
authors.affiliation: Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Anthony P
authors.initials: AP
authors.lastname: Krismanich
authors.affiliation: Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Ahmad
authors.initials: A
authors.lastname: Ghavami
authors.affiliation: Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Gary I
authors.initials: GI
authors.lastname: Dmitrienko
authors.affiliation: State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China.|Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.
authors.forename: Guilu
authors.initials: G
authors.lastname: Long
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Baugh
authors.affiliation: Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.|Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada.|Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada.
authors.forename: Raymond
authors.initials: R
authors.lastname: Laflamme