Quantum Natural Gradient with Geodesic Corrections for Small Shallow Quantum Circuits

Halla, Mourad

Published Jan 1, 2025• 0 citations

Abstract

The Quantum Natural Gradient (QNG) method enhances optimizationin variational quantum algorithms (VQAs) by incorporating geometric insights fromthe quantum state space through the Fubini-Study metric. In this work, we extendQNG by introducing higher-order integrators and geodesic corrections using theRiemannian Euler update rule and geodesic equations, deriving an updated rule for theQuantum Natural Gradient with Geodesic Correction (QNGGC). We also develop anefficient method for computing the Christoffel symbols necessary for these corrections,leveraging the parameter-shift rule to enable direct measurement from quantumcircuits. Through theoretical analysis and practical examples, we demonstrate thatQNGGC significantly improves convergence rates over standard QNG, highlightingthe benefits of integrating geodesic corrections into quantum optimization processes.Our approach paves the way for more efficient quantum algorithms, leveraging theadvantages of geometric methods.

DOI: 10.3204/pubdb-2025-01396

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