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Enhancing detection of topological order by local error correction.

Iris Cong1, Nishad Maskara1, Minh C Tran1,2

  • 1Department of Physics, Harvard University, Cambridge, MA, 02138, USA.

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|February 20, 2024
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We introduce a new method, locally error-corrected decoration (LED), to identify and quantify topological states of matter. This robust technique works even with experimental noise, aiding quantum computation and the study of quantum spin liquids.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Science
  • Quantum Computation

Background:

  • Topologically-ordered states of matter are crucial for quantum computation due to properties like long-range entanglement and emergent gauge fields.
  • Characterizing these states is challenging due to their complex nature and sensitivity to noise.
  • Existing methods struggle with the practical demands of experimental realization.

Purpose of the Study:

  • To introduce a novel paradigm, locally error-corrected decoration (LED), for quantifying topological states.
  • To develop a method robust against incoherent noise, suitable for experimental applications.
  • To extend the applicability of topological state characterization to generic topological phases.

Main Methods:

  • Combined error correction techniques with renormalization-group flow concepts to create the LED paradigm.
  • Utilized numerical simulations of the toric code under various perturbations to validate LED.
  • Applied LED to an experimental realization of a quantum spin liquid on a Rydberg-atom simulator.

Main Results:

  • Demonstrated efficient and robust identification of topological order using LED.
  • Showcased LED's applicability in the presence of incoherent noise sources.
  • Provided new insights into a quantum spin liquid system via experimental application.

Conclusions:

  • Locally error-corrected decoration (LED) offers a powerful and practical approach for identifying topological order.
  • The LED method is suitable for realistic experimental conditions, including noisy environments.
  • LED is a versatile tool applicable to various topological phases, including those with non-abelian order.