Enhancing Detection of Topological Order by Local Error Correction

Abstract

The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states -- locally error-corrected decoration (LED) -- by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.

Corrected minor typos. Added new results on generalizations to non-abelian topological phases, and connections between LED and topological entanglement negativity

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• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
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• Enhancing Quantum Memory Lifetime with Measurement-Free Local Error Correction and Reinforcement Learning
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• Attention to Quantum Complexity
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Shortcuts to Analog Preparation of Non-Equilibrium Quantum Lakes