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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
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Microfluidic Platform with Multiplexed Electronic Detection for Spatial Tracking of Particles
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Published on: March 13, 2017

Surface code threshold in the presence of correlated errors.

E Novais1, Eduardo R Mucciolo

  • 1Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André, São Paulo 09210-170, Brazil.

Physical Review Letters
|February 7, 2013
PubMed
Summary
This summary is machine-generated.

We found that correlated errors in quantum computing surface codes are linked to phase transitions in statistical models. This connection helps determine error thresholds based on environmental factors.

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Area of Science:

  • Quantum computing
  • Quantum error correction
  • Condensed matter physics

Background:

  • Correlated errors pose a significant challenge to achieving fault-tolerant quantum computation.
  • The fidelity of quantum error correction codes, like the surface code, is sensitive to the nature of errors.
  • Understanding error mechanisms is crucial for designing robust quantum algorithms.

Purpose of the Study:

  • To investigate the fidelity of the surface code under correlated errors induced by a bosonic environment.
  • To establish a connection between error thresholds and phase transitions in a relevant statistical model.
  • To provide a framework for relating error thresholds to physical parameters of the environment.

Main Methods:

  • Mapping the time evolution of the surface code after one error correction cycle to a statistical spin model.
  • Analyzing the statistical spin model for phase transitions in the thermodynamic limit.
  • Relating the critical behavior of the spin model to the error threshold of the surface code.

Main Results:

  • The existence of an error threshold for the surface code is shown to be equivalent to an order-disorder phase transition in the mapped statistical model.
  • The error threshold is directly related to the parameters of the bosonic bath and the spatial correlation range of the errors.
  • A precise connection is established between quantum error correction fidelity and critical phenomena in statistical mechanics.

Conclusions:

  • The study provides a novel perspective on quantum error correction by linking it to phase transitions.
  • The findings offer a method to predict and potentially mitigate correlated errors by understanding environmental coupling.
  • This work advances the theoretical understanding of fault-tolerant quantum computing in realistic noisy environments.