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@PHDTHESIS{Cerfontaine:768380,
      author       = {Cerfontaine, Pascal},
      othercontributors = {Bluhm, Jörg and DiVincenzo, David P.},
      title        = {{H}igh-fidelity single- and two-qubit gates for
                      two-electron spin qubits},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2019-09348},
      pages        = {1 Online-Ressource (xiii, 166 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2019},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2019},
      abstract     = {A key ingredient for fault-tolerant quantum computers are
                      sufficiently accurate logic gates on single and multiple
                      qubits in the presence of decohering noise. In this thesis,
                      we theoretically develop and experimentally demonstrate such
                      high-fidelity quantum gates for semiconductor-based quantum
                      computing. Specifically, we consider a qubit encoded in the
                      singlet and one triplet state of two electron spins in GaAs.
                      While its potential for optical coupling makes GaAs an
                      attractive material, highly auto-correlated magnetic field
                      noise from fluctuating nuclear spins leads to considerably
                      lower coherence times than for Si-based devices, where
                      nuclear spins can be removed by isotopic purification. In
                      addition to noise, the control methods used in earlier
                      experiments are based on unrealistic approximations. For
                      these reasons, fidelities well above 99 $\%,$ as required by
                      current quantum error correction (QEC) schemes, have not
                      been obtained before this thesis. To tackle these issues, we
                      extend the filter function formalism to describe quantum
                      gates and processes in the presence of experimentally
                      relevant non-Markovian noise. Since this formalism can
                      consider all relevant noise sources in a computationally
                      efficient manner, it can be used to find optimal control
                      pulses by numerical optimization, leading to predicted
                      single-qubit gate fidelities of 99.9 $\%.$ Furthermore, we
                      deal with the considerable control challenges associated
                      with this qubit type by experimental calibration of the
                      optimized control pulses. To this end, we extend our
                      previous experimental gate set calibration (GSC) routine to
                      remove systematic gate errors on an arbitrary number of
                      qubits. We apply the numerically optimized single-qubit
                      control pulses to our GaAs sample and experimentally
                      calibrate them with GSC. This procedure yields an average
                      gate fidelity of 99.50 ± 0.04 $\%$ and a low leakage rate
                      of 0.13 ± 0.03 $\%$ out of the computational subspace,
                      characterized by randomized benchmarking. We also optimize
                      realistic two-qubit control pulses, considering current
                      control hardware as well as interqubit Coulomb and exchange
                      coupling that cannot be fully turned off. Using measured
                      noise spectra, we show that two-qubit gate fidelities of
                      99.90 $\%$ can be reached in GaAs, while 99.99 $\%$ can be
                      achieved in Si. These results demonstrate that high-fidelity
                      gates can be realized even in the presence of nuclear spins
                      as in GaAs.},
      cin          = {132210 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)132210_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2019-09348},
      url          = {https://publications.rwth-aachen.de/record/768380},
}