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Quantum and Quantum-Inspired Optimizers

This page collects optimizers from two adjacent settings. The first is the optimization of variational quantum circuits, where shot noise and the quantum geometry of the parameter space drive the design of measurement-frugal, gradient-free, and natural-gradient methods. The second is quantum-inspired and quantum-hardware optimization of classical neural networks, where quantum fluctuations, adiabatic evolution, or annealer sampling replace or augment the classical training loop.

Optimizers for variational quantum circuits

Optimizer Venue Paper Code
SPSA IEEE Transactions on Automatic Control 1992 Multivariate stochastic approximation using a simultaneous perturbation gradient approximation official
iCANS Quantum 2020 An Adaptive Optimizer for Measurement-Frugal Variational Algorithms community
NFT Physical Review Research 2020 Sequential minimal optimization for quantum-classical hybrid algorithms official
Quantum Natural Gradient Quantum 2020 Quantum Natural Gradient official
Rosalin arXiv 2020 Operator Sampling for Shot-frugal Optimization in Variational Algorithms community
QN-SPSA Quantum 2021 Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information official
Rotosolve / Rotoselect Quantum 2021 Structure optimization for parameterized quantum circuits community
Quantum Analytic Descent Physical Review Research 2022 Quantum Analytic Descent official
SGLBO npj Quantum Information 2022 Stochastic gradient line Bayesian optimization for efficient noise-robust optimization of parameterized quantum circuits community
SantaQlaus arXiv 2023 SantaQlaus: A resource-efficient method to leverage quantum shot-noise for optimization of variational quantum algorithms
ExcitationSolve Communications Physics 2025 Fast gradient-free optimization of excitations in variational quantum eigensolvers official
Kernel Descent Scientific Reports 2025 Introducing the kernel descent optimizer for variational quantum algorithms
QUIVER arXiv 2026 Adaptive directional gradients for parameterised quantum circuits
WSBD AISTATS 2026 WSBD: Freezing-Based Optimizer for Quantum Neural Networks official
H-QNG arXiv 2025 Efficient Hamiltonian-aware Quantum Natural Gradient Descent for Variational Quantum Eigensolvers
WA-QNG Quantum Science and Technology 2026 Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver
CQNG EPJ Quantum Technology 2025 Modified Conjugate Quantum Natural Gradient
Momentum-QNG Physica A 2024 Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm official
qBang Quantum 2024 Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes official
EGT (Exact Geodesic Transport) arXiv 2025 Quantum optimization with exact geodesic transport
TGF / TGFQS arXiv 2026 Two-Gate Extensions of Free Axis and Free Quaternion Selection for Sequential Optimization of Parameterized Quantum Circuits
SGD (Superpositional Gradient Descent) IEEE QAI 2025 Superpositional Gradient Descent: Harnessing Quantum Principles for Model Training
Scalable On-Hardware QNN training (parallelised parameter-shift rule) arXiv 2026 Scalable On-Hardware Training of Quantum Neural Networks and Application to Clinical Data Imputation
QM-quantization optimizer (Schrodinger gradient-flow) arXiv 2026 Quantum mechanical framework for quantization-based optimization: from Gradient flow to Schroedinger equation

Quantum-inspired and quantum-hardware methods

Optimizer Venue Paper Code
Quantum Adam Scientific Reports 2018 Optimization of neural networks via finite-value quantum fluctuations
RBM training on a D-Wave annealer Frontiers in Physics 2021 Training Restricted Boltzmann Machines With a D-Wave Quantum Annealer
Quantum Hamiltonian Descent (QHD) arXiv 2023 Quantum Hamiltonian Descent official
Universal AQC neural-network training Frontiers in Artificial Intelligence 2024 Training neural networks with universal adiabatic quantum computing
QHDOPT INFORMS Journal on Computing 2025 QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent official
Stochastic Quantum Hamiltonian Descent (SQHD) arXiv 2025 Stochastic Quantum Hamiltonian Descent
QIASO AIMS Mathematics 2026 The quantum-inspired adaptive superposition optimization for neural network training