Quantum Natural Gradient
James Stokes, Josh Izaac, Nathan Killoran, Giuseppe Carleo
Abstract
A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.
Topics & Concepts
MathematicsTensor (intrinsic definition)DiagonalQuantumQuantum algorithmGeneralizationMetric (unit)Gradient descentPure mathematicsMathematical analysisQuantum mechanicsComputer sciencePhysicsGeometryArtificial intelligenceArtificial neural networkEconomicsOperations managementQuantum Computing Algorithms and ArchitectureQuantum Information and CryptographyParallel Computing and Optimization Techniques