Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

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Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.
© Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. M. M. thanks M. Guta for valuable discussions. We gratefully acknowledge support by the Austrian Science Fund (FWF) through the SFB FoQuS (FWF Project No. F4002-N16), as well as the Institut für Quantenoptik und Quanteninformation GmbH. E. A. M. is a recipient of a DOC grant from the Austrian Academy of Sciences. P. S. was supported by the Austrian Science Foundation (FWF) Erwin Schrödinger Stipendium 3600-N27. The research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via the U.S. Army Research Office Grant No. W911NF-16-1-0070. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the view of the U.S. Army Research Office. We also acknowledge support by U.S. A.R.O. through Grant No. W911NF-14-1-010, the Spanish MINECO Grant No. FIS2012-33152, and the CAM Research Consortium QUITEMAD+ S2013/ICE-2801.
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