Enhancing Topological Order Parameters via Error Correction and Renormalization

Nishad Maskara, Harvard University

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The realization of topological order in the lab has been a long-coveted goal in both condensed matter and quantum computation. Nevertheless, verifying the preparation of these topological ordered states is still a particularly challenging task. The typical approach is to measure large loop operators, e.g. Wilson loops. However, these decay exponentially with the length of the loop, making it difficult to achieve significant signal to noise in practical experiments for large loops. In this paper, we address this challenge by introducing a class of order parameters for certifying topological phases. Our method applies local quantum error correction (QEC) and entanglement renormalization to amplify the signal from large Wilson loops in topological phases. Loop operators in the topological phase are correctable, so the signal increases as we iterate the procedure. In contrast, outside the topological phase the loops are uncorrectable, so the signal is suppressed. The method can also be naturally applied to mixed states with coherent and incoherent errors, which is crucial for certifying topological order in experiments. We demonstrate this method on numerical and experimental data for a perturbed toric code and Rydberg quantum spin liquid respectively.

Abstract Author(s): Nishad Maskara, Iris Cong, Guilia Semeghini, Minh Tran, Sona Najafi, Susanne Yelin, Soonwon Choi, Mikhail Lukin