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@PHDTHESIS{Heuen:977865,
      author       = {Heußen, Sascha Heinrich},
      othercontributors = {Müller, Markus and DiVincenzo, David P.},
      title        = {{A}pplications of fault-tolerant topological quantum error
                      correction in near-term devices},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-00957},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2024},
      abstract     = {Quantum computers can theoretically facilitate solving
                      problems that classical supercomputers may only solve with
                      resources – like computation time – exponentially
                      growing with the size of the problem instance. Such devices
                      are widely believed to require quantum error correction to
                      reach the level of reliability that is needed to run useful
                      large-scale quantum algorithms. A fault-tolerant system
                      design can help to achieve practical computational
                      advantages from quantum computers built from noisy
                      components. In this thesis, we demonstrate how modern
                      fault-tolerant quantum circuit designs can be used to
                      systematically suppress noise, which is detrimental to the
                      information stored and processed by the quantum computer.
                      For this purpose, we employ small topological quantum error
                      correcting codes that are suitable for experimental devices.
                      We develop a numerical simulation technique that is capable
                      of efficiently simulating adaptive sequences of quantum
                      circuits built from components with weak noise on a
                      classical computer. Failure of the whole system in this case
                      becomes a rare event, with high-fidelity physical
                      operations, which may be attainable in practice due to the
                      impressive improvements of experimental control
                      capabilities. Then, using active quantum error correction
                      can become a fruitful endeavor to suppress failure rates
                      even further. The quantum computation can be sustained for
                      in principle arbitrarily long times this way. We show that
                      the first experimental realization of an encoded
                      fault-tolerant universal quantum gate set in a trapped-ion
                      quantum computer can be accurately modeled by a
                      few-parameter noise model that is only informed by the
                      infidelities of experimental operations. The effectiveness
                      of fault-tolerant implementations is showcased by the
                      superior performance of magic state preparation compared to
                      non-fault-tolerant approaches. Subsequently, we study the
                      effect of improved noise strengths on physical operations in
                      order to gain an advantage of logical qubit operation over
                      physical qubits. Additionally, we provide a new circuit for
                      fault-tolerant unitary logical qubit initialization that
                      eliminates the need for in-sequence measurements, which pose
                      major roadblocks for experimental realizations of
                      fault-tolerant protocols. Further developing these ideas, we
                      propose and analyze a measurement- free quantum error
                      correction scheme, which is fully fault-tolerant with
                      respect to any type of noise on all components of the
                      circuit. This may enable fault-tolerant quantum error
                      correction in experimental architectures that struggle with
                      implementations of fast and reliable in-sequence
                      measurements and feed-forward corrections. We show via
                      numerical simulations that the scheme can potentially
                      achieve lower logical failure rates than a conventional
                      fault-tolerant quantum error correction scheme when
                      implemented in a neutral-atom quantum computer. Our findings
                      contribute to the advancement of practical fault-tolerant
                      quantum computation. They serve to realize primitives of
                      error-corrected universal quantum computation using
                      state-of-the-art and near-term devices.},
      cin          = {137310 / 130000},
      ddc          = {530},
      cid          = {$I:(DE-82)137310_20140620$ / $I:(DE-82)130000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-00957},
      url          = {https://publications.rwth-aachen.de/record/977865},
}