🤖 AI Summary
This work systematically compares the performance trade-offs between native topological fusion readout and grouped Pauli measurements for implementing the Fibonacci anyon Hamiltonian on noisy intermediate-scale quantum hardware. Leveraging Floquet evolution and variational quantum eigensolver (VQE) circuits, the study employs a covariance-aware mean squared error metric to assess energy estimation accuracy. It provides the first quantitative characterization of the trade-off between compilation and measurement costs for these two approaches and introduces a general criterion tailored to two-dimensional topological models. The results reveal that fusion readout simultaneously reduces both mean squared error and sampling variance in Floquet circuits, whereas in VQE settings, grouped Pauli measurements yield marginally higher accuracy at the cost of increased variance—thereby establishing clear guidelines for selecting optimal measurement strategies across different computational scenarios.
📝 Abstract
Recent demonstrations of non-Abelian braiding of graph vertices on noisy intermediate-scale quantum (NISQ) superconducting processor, and the experimental realization of topological order in general on various quantum hardware platforms necessitate an important question: when does a native (topological) fusion readout genuinely help for topological anyonic Hamiltonians implemented on NISQ hardware? We use the Fibonacci anyons chain as a concrete model for understanding the trade-off between measurement cost and compilation cost in that setting. The comparison is made against a simple grouped-Pauli baseline, and is scored by a covariance-aware mean-squared-error (MSE) of the full energy estimator. We based our benchmark on two different important classes of quantum circuits, namely Floquet time-evolved and variational quantum eigensolver quantum circuits, with the underlying Hamiltonian consisting of both braiding and fusion interaction. Our analysis found that there is not a uniform best method across both problems: the fusion readout method performed better on Floquet-type circuits on both the MSE and covariance-aware sampling variance, while the grouped Pauli method performed better on VQE on the MSE but worse on sampling variance. We derive scaling laws, and compute shot-budget crossover points, where one method is operationally favored above the other. The relevance of this work extends beyond Fibonacci chains to two-dimensional topological models compiled on superconducting and other qubit-native platforms, and can be used as a guide in answering the question of when one should measure in the native operator basis of the target physics, or when it is better to fall back on Pauli-basis reconstruction.