Quantum Natural Gradient

2020/05/25 by James Stokes, Josh Izaac, Nathan Killoran +1 · 1 citation
Computer Science · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Parallel Computing and Optimization Techniques

paper · pdf · doi:10.22331/q-2020-05-25-269

openalex publication_date 2020/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Path-SGD: Path-Normalized Optimization in Deep Neural Networks
• Adam: A Method for Stochastic Optimization
• A Quantum Approximate Optimization Algorithm
• Natural Gradient Works Efficiently in Learning
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Three Factors Influencing Minima in SGD
• Quantum Computing in the NISQ era and beyond
• Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
• PennyLane: Automatic differentiation of hybrid quantum-classical computations

Cited by

• A Review of Variational Quantum Algorithms: Insights into Fault-Tolerant Quantum Computing
• Giuseppe Carleo [wikipedia]