Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates

Abstract

Geometric quantum gates are often expected to be more resilient than dynamical gates against certain types of error, which would make them ideal for robust quantum computing. However, this is still up for debate due to seemingly conflicting results in the literature. Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate. For any control Hamiltonian that produces a geometric gate, we find that under certain common conditions one can construct another control Hamiltonian that produces an equivalent dynamical gate with identical noise sensitivity (as characterized by the filter function). Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant single-qubit scenarios and providing explicit examples of equivalent geometric and dynamical gates.

12 pages, 10 figures

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Cited by in corpus (7)

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• Reverse engineering of one-qubit filter functions with dynamical invariants
• Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing
• Nonadiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition
• An automated geometric space curve approach for designing dynamically corrected gates
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Engineered Robustness for Nonadiabatic Geometric Quantum Gates