Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the noisy intermediate-scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time, to the best of our knowledge. We obtained the dissociation curve of the He-H + cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications.
Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the noisy intermediate-scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time, to the best of our knowledge. We obtained the dissociation curve of the He-H + cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications.
We investigate the performance of the quantum natural gradient (QNG) optimizer in the presence of noise. Specifically, we evaluate the efficacy of QNG within the quantum approximate optimization algorithm for finding the ground state of the transverse field Ising model. Its performance is benchmarked against the vanilla gradient descent optimizer across two prominent quantum computing platforms: Rydberg atoms and superconducting circuits. Our analysis includes simulations under both idealized noise-free conditions and realistic noisy environments based on calibration data from actual devices. Results demonstrate that QNG consistently outperforms vanilla gradient descent, exhibiting faster convergence on average and greater robustness against random initializations of parameters. This robustness is attributed to the distance regularization in parameter space inherent to QNG. Additionally, QNG achieves a higher convergence rate to the solution, effectively avoiding certain local minima. These findings highlight QNG as a promising tool for optimizing variational quantum algorithms in noisy intermediate-scale quantum devices.
The Variational Quantum Eigensolver (VQE) is one of the most promising algorithms for current quantum devices. It employs a classical optimizer to iteratively update the parameters of a variational quantum circuit in order to search for the ground state of a given Hamiltonian. The efficacy of VQEs largely depends on the optimizer employed. Recent studies suggest that Quantum Natural Gradient Descent (QNG) can achieve faster convergence than vanilla gradient descent (VG), but at the cost of additional quantum resources to estimate Fubini-Study metric tensor in each optimization step. The Fubini-Study metric tensor used in QNG is related to the entire quantum state space and does not incorporate information about the target Hamiltonian. To take advantage of the structure of the Hamiltonian and address the limitation of additional computational cost in QNG, we propose Hamiltonian-aware Quantum Natural Gradient Descent (H-QNG). In H-QNG, we propose to use the Riemannian pullback metric induced from the lower-dimensional subspace spanned by the Hamiltonian terms onto the parameter space. We show that H-QNG inherits the desirable features of both approaches: the low quantum computational cost of VG and the reparameterization-invariance of QNG. We also validate its performance through numerical experiments on molecular Hamiltonians, showing that H-QNG achieves faster convergence to chemical accuracy while requiring fewer quantum computational resources.
Abstract The efficient optimization of variational quantum algorithms (VQAs) is critical for their successful application in quantum computing. The Quantum Natural Gradient (QNG) method, which leverages the geometry of quantum state space, has demonstrated improved convergence compared to standard gradient descent (Stokes et al. in Quantum 4:269, 2020). In this work, we introduce the Modified Conjugate Quantum Natural Gradient (CQNG), an optimization algorithm that integrates QNG with principles from the nonlinear conjugate-gradient method. Unlike QNG, which employs a fixed learning rate, CQNG dynamically adjusts its hyperparameters at each step, enhancing both efficiency and flexibility. Numerical simulations show that CQNG achieves faster convergence and reduces quantum-resource requirements compared to QNG across various optimization scenarios, even when strict conjugacy conditions are not fully satisfied—hence the term “Modified Conjugate.” These results highlight CQNG as a promising optimization technique for improving the performance of VQAs.
The efficient optimization of variational quantum algorithms (VQAs) is critical for their successful application in quantum computing. The Quantum Natural Gradient (QNG) method, which leverages the geometry of quantum state space, has demonstrated improved convergence compared to standard gradient descent [Quantum 4, 269 (2020)]. In this work, we introduce the Modified Conjugate Quantum Natural Gradient (CQNG), an optimization algorithm that integrates QNG with principles from the nonlinear conjugate-gradient method. Unlike QNG, which employs a fixed learning rate, CQNG dynamically adjusts its hyperparameters at each step, enhancing both efficiency and flexibility. Numerical simulations show that CQNG achieves faster convergence and reduces quantum-resource requirements compared to QNG across various optimization scenarios, even when strict conjugacy conditions are not fully satisfied--hence the term ``Modified Conjugate.'' These results highlight CQNG as a promising optimization technique for improving the performance of VQAs.
The efficient optimization of variational quantum algorithms (VQAs) is critical for their successful application in quantum computing. The Quantum Natural Gradient (QNG) method, which leverages the geometry of quantum state space, has demonstrated improved convergence compared to standard gradient descent [Quantum 4, 269 (2020)]. In this work, we introduce the Modified Conjugate Quantum Natural Gradient (CQNG), an optimization algorithm that integrates QNG with principles from the nonlinear conjugate gradient method. Unlike QNG, which employs a fixed learning rate, CQNG dynamically adjusts hyperparameters at each step, enhancing both efficiency and flexibility. Numerical simulations show that CQNG achieves faster convergence than QNG across various optimization scenarios, even when strict conjugacy conditions are not always satisfied -- hence the term ``Modified Conjugate.'' These results highlight CQNG as a promising optimization technique for improving the performance of VQAs.
Abstract Variational Quantum Algorithms (VQAs) are widely regarded as the most promising route to practical quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) hardware, but their trainability is threatened by the barren plateau phenomenon, in which cost-function gradients vanish exponentially with system size and circuit depth. Standard first-order optimizers, which treat the parameter space of a parameterized quantum circuit (PQC) as flat Euclidean space, are especially vulnerable to this effect and to the additional gradient suppression introduced by hardware noise. This extended treatment presents (i) a from-first-principles derivation of Quantum Natural Gradient (QNG) descent, tracing its lineage from Amari's classical information geometry [1] through the Fubini-Study metric to the Quantum Fisher Information Matrix (QFIM); (ii) a complete taxonomy of barren-plateau mechanisms (expressibility-induced, entanglement-induced, cost-function-locality-induced, and noise-induced); (iii) a comparative survey of the broader NISQ optimizer landscape (SPSA, Adam, COBYLA, Rotosolve, Quantum Natural SPSA, and reduced-cost QFIM estimators); and (iv) a controlled simulation study comparing QNG against vanilla gradient descent on a 4-qubit weighted MaxCut problem under three physically motivated NISQ noise models. Across 50 independent trials, QNG raised the convergence success rate from 30% to 95%, reduced the mean iteration count to convergence by a factor of roughly 6, and achieved a 16% net wall-clock speedup despite the added per-iteration cost of QFIM estimation. We give the full theoretical basis for these gains, an exhaustive discussion of their limitations, an A-to-Z glossary of the field's terminology, and a staged roadmap toward physical hardware validation. Figure placements throughout the document are annotated with detailed image-generation prompts so that the accompanying visual assets can be produced independently of this text.