Abstract
We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance error correction codes. Here we apply it to a wider range of quantum protocols and identify circuit structures that allow for efficient calculation of the exact success probability and even the final distribution of output states. As examples, we apply our method to the Bernstein–Vazirani algorithm and the Steane [[7,1,3]] quantum error correction code and compare the results to Monte Carlo simulations.
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Acknowledgments
We would like to thank Andrew Cross, Ryan Sheehan, Alonzo Hernandez and Silas Fradley for useful discussions. This project was supported by Office of the Director of National Intelligence (ODNI)—Intelligence Advanced Research Project Activity (IARPA) through Army Research Office Grant No. W911NF-10-1-0231 and Department of Interior Contract No. D11PC20167. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US Government.
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Janardan, S., Tomita, Y., Gutiérrez, M. et al. Analytical error analysis of Clifford gates by the fault-path tracer method. Quantum Inf Process 15, 3065–3079 (2016). https://doi.org/10.1007/s11128-016-1330-z
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DOI: https://doi.org/10.1007/s11128-016-1330-z