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Comparing Experiments to the Fault-Tolerance Threshold.

Richard Kueng1,2,3, David M Long1, Andrew C Doherty1

  • 1Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, 2006 New South Wales, Australia.

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|November 9, 2016
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Quantum computing experiments aim for error rates below fault-tolerance thresholds. This study bridges the gap between average error rates from randomized benchmarking and worst-case thresholds, crucial for quantum error correction.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Error Correction

Background:

  • Achieving fault-tolerant quantum computation requires error rates below a critical threshold.
  • Randomized benchmarking is a standard technique for measuring average gate error rates in quantum experiments.
  • A discrepancy exists between average error rates from benchmarking and worst-case error thresholds required for fault tolerance.

Purpose of the Study:

  • To reconcile the difference between experimentally measured average error rates and theoretical worst-case error thresholds.
  • To establish a framework for comparing these two distinct measures of quantum gate errors.
  • To identify the specific noise sources responsible for the mismatch between average and worst-case error metrics.

Main Methods:

  • Derivation of analytical relationships between average error rates and worst-case error quantities.
  • Analysis of various physical noise models relevant to quantum computing.
  • Quantification of the required error control levels for coherent errors.

Main Results:

  • Coherent errors are identified as the primary cause for the significant divergence between average and worst-case error rates.
  • Quantitative relations are established to compare experimentally measured average errors with fault-tolerance thresholds.
  • The study provides metrics for assessing the necessary precision in controlling coherent errors.

Conclusions:

  • Accurate comparison of quantum gate performance requires understanding the impact of coherent errors on error metrics.
  • The derived relations are essential for validating experimental progress towards fault-tolerant quantum computing.
  • This work facilitates a more direct assessment of whether current quantum systems meet fault-tolerance requirements.