Enhancing detection of topological order by local error correction.

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.