AI summaryⓘ
The authors study when a special measurement technique called fusion readout is helpful for quantum systems involving Fibonacci anyons on near-term quantum computers. They compare this fusion method to a simpler measurement approach using grouped Pauli operators, judging which works better by how accurately each estimates the system's energy. Testing two types of quantum circuits, they find fusion readout works better for one kind (Floquet circuits), while grouped Pauli is better for another (variational circuits) in some ways. They also figure out when it makes sense to use one method over the other based on resource costs. Their results can guide how to measure topological quantum systems on different hardware platforms.
Non-Abelian braidingFibonacci anyonsFusion readoutGrouped Pauli measurementNoise intermediate-scale quantum (NISQ)Variational Quantum Eigensolver (VQE)Floquet circuitsTopological orderQuantum measurementEnergy estimation
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.