Quantum Natural Gradient

By James Stokes, Josh A. Izaac, Nathan Killoran, Giuseppe Carleo. Quantum, 2019

537 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/4ff5d4b32fdbd4a1926bc1a4082f82caa903acaf

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Citations in the corpus

General parameter-shift rules for quantum gradients (2021, methodology): “Metric entries that belong to operations that commute within the circuit 10 can be computed block-wise without any auxiliary qubits, additional operations or deeper circuits [48].”
Barren plateaus in variational quantum computing (2024, unknown): “For example, one might assume that despite suppressed gradients, it is possible to find a loss-minimizing direction by using higher-order gradient information, gradient-free methods, quantum natural gradients 215,216 or other quantum Fisher information-based schemes.”
Challenges and opportunities in quantum machine learning (2022, methodology): “Quantum natural gradient [55, 56] adjusts the step size according to the local geometry of the landscape (based on the quantum Fisher information metric).”
Training Variational Quantum Algorithms Is NP-Hard. (2021, methodology): “Methods include standard BFGS optimization and extensions [6] and natural gradient descent [7], which has a favorable performance at least for certain easy instances [8].”
PennyLane: Automatic differentiation of hybrid quantum-classical computations (2018, methodology): “PennyLane currently has seven built-in optimizers, which work with the default Autograd interface: standard gradient descent, gradient descent with momentum, gradient descent with Nesterov momentum, Adagrad, Adam, RMSprop, and quantum natural gradient descent [ 45 ] .”
Variational quantum algorithms (2020, methodology): “U(θ)|ψ0〉 for some initial state |ψ0〉), are sometimes used in sophisticated optimization algorithms [71–73] (see Section IID) and variational quantum simulation [74–76]”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “[35] James Stokes, Josh Izaac, Nathan Killoran, and Giuseppe Carleo, “Quantum natural gradient,” Quantum 4, 269 (2020).”
Effect of data encoding on the expressive power of variational quantum-machine-learning models (2020, background): “A lot of work has been done to understand the practical details of this approach, leading to useful training strategies [3, 7, 8] and ways to emulate and extend classical machine learning methods [2, 9–12].”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “, quantum algorithms whose gates depend on continuous parameters that then are optimized by an external classical algorithm in order to extremalize the variational cost function [399, 538, 633, 654].”