Variational quantum algorithms (VQAs) offer some promising characteristics for carrying out optimization tasks in noisy intermediate-scale quantum devices. These algorithms aim to minimize a cost function by optimizing the parameters of a quantum parametric circuit. Thus, the overall performance of these algorithms, heavily depends on the classical optimizer which sets the parameters. In the last years, some gradient-based and gradient-free approaches have been applied to optimize the parameters of the quantum circuit. In this work, we follow the second approach and propose the use of estimation of distribution algorithms for the parameter optimization in a specific case of VQAs, the quantum approximate optimization algorithm. Our results show an statistically significant improvement of the cost function minimization compared to traditional optimizers.
Variational quantum algorithms (VQAs) offer some promising characteristics for carrying out optimization tasks in noisy intermediate-scale quantum devices. These algorithms aim to minimize a cost function by optimizing the parameters of a quantum parametric circuit. Thus, the overall performance of these algorithms, heavily depends on the classical optimizer which sets the parameters. In the last years, some gradient-based and gradient-free approaches have been applied to optimize the parameters of the quantum circuit. In this work, we follow the second approach and propose the use of estimation of distribution algorithms for the parameter optimization in a specific case of VQAs, the quantum approximate optimization algorithm. Our results show an statistically significant improvement of the cost function minimization compared to traditional optimizers.
Variational quantum algorithms (VQAs) are hybrid approaches between classical and quantum computation, where a classical optimizer proposes parameter configurations for a quantum parametric circuit which is iteratively sampled. The overall performance of the algorithm depends on how the classical optimizer tunes the parameters of the quantum circuit. Several gradient-free and gradient-based approaches have been proposed in the literature to face this task. Estimation of distribution algorithms (EDAs) are a type of evolutionary algorithms where a probabilistic model is updated and sampled at each generation to optimize a cost function. EDAs have shown to be able to achieve good solutions in a reasonable computation time for different optimization problems, and thus, we believe that this algorithm can be a good option to overcome VQAs challenges such as the Barren plateaus phenomenon. In this paper, we study the use of three different EDAs, characterized by different probabilistic model complexities, to tune the parameters of two different VQAs to solver the Max Cut problem and to a VQA to simulate the behaviour of a molecule. Three EDA variants are compared to some state-of-the-art optimizers widely used for this task. Our results show statistical significant improvement of the EDA variants compared to different optimizers, and identify the VQAs characteristics that best fit to each EDA type. We also perform an analysis of the main EDAs hyper-parameters.
In recent years, variational quantum algorithms (VQA) have been receiving a great deal of attention, demonstrating their applicability in a wide range of tasks and implementable even in the noisy quantum processors currently available [1]. A VQA is a hybrid quantum-classical algorithm where a problem is encoded in a cost function that can be efficiently evaluated on a parametric quantum device and the minimum represents the desired solution. A classical optimizer can then be used to tune the parameters of the quantum device in order to minimize the loss function and find the optimal solution (Fig. 1). In the field of quantum computing, one of the main promising platforms is based on the use of single photons and integrated photonic circuits since photons are a natural choice for transferring information and have different degree of freedom that can be to encode the information. Moreover the use of integrated photonic allow the realization of compact and table complex interferometers with a high number of control parameters. Even if there are few applications [2], [3], VQA with photonic platforms remains a relatively unexplored subject. One of the main problems is the application of the classical optimizer to the photonic platform since most of the algorithms are based on the estimation of the gradient of the cost function with the finite difference method but that can not be applied to a noisy apparatus.
Parameterized quantum circuits (PQCs) play an essential role in the application of variational quantum algorithms (VQAs) in noisy intermediate-scale quantum (NISQ) devices. The PQCs are a leading candidate to achieve a quantum advantage in NISQ devices and have already been applied in various domains such as quantum chemistry, quantum machine learning, combinatorial optimization, and many others. There is no single definitive way to optimize PQCs. The most commonly used methods are based on computing the gradient via the parameter-shift rule to use classical gradient descent (GD) optimizers like Adam, stochastic GD, and others. In addition, sequential single-qubit optimizers have been proposed, such as Rotosolve, Free-Axis Selection (Fraxis), Free-Quaternion Selection (FQS), and hybrid algorithms from the aforementioned optimizers. We further develop hybrid algorithms than those represented in the previous work by drawing inspiration from the early stopping method used in classical machine learning. The switch between the optimizers depends on the previous cost function values compared to the previous ones. We introduce two new hybrid algorithms that are more robust and scalable, and they outperform previous hybrid methods in terms of convergence towards the global minima across various cost functions. In addition, we find that they are feasible for NISQ devices with different noise profiles.
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) offer a promising path toward using near-term quantum hardware for applications in academic and industrial research. These algorithms aim to find approximate solutions to quantum problems by optimizing a parametrized quantum circuit using a classical optimization algorithm. A successful VQA requires fast and reliable classical optimization algorithms. Understanding and optimizing how off-the-shelf optimization methods perform in this context is important for the future of the field. In this work, we study the performance of four commonly used gradient-free optimization methods [sequential least-squares quadratic programming, constrained optimization by linear approximations, the covariance matrix adaptation evolutionary strategy (CMA-ES), and the simultaneous perturbation stochastic approximation (SPSA)] to find ground-state energies of a range of small chemistry and material science problems. We test a telescoping sampling scheme (where the accuracy of the cost-function estimate provided to the optimizer is increased as the optimization converges) for all methods, demonstrating mixed results across our range of optimizers and problems chosen. We further hyperparameter tune two of the four optimizers (CMA-ES and SPSA) across a large range of models and demonstrate that with appropriate hyperparameter tuning, CMA-ES is competitive with and sometimes outperforms SPSA (which is not observed in the absence of hyperparameter tuning). Finally, we investigate the ability of an optimizer to beat the ``sampling-noise floor'' given by the sampling noise of each cost-function estimate provided to the optimizer. Our results demonstrate the necessity for tailoring and hyperparameter tuning known optimization techniques for inherently noisy variational quantum algorithms and that the variational landscape that one finds in a VQA is highly problem and system dependent. This provides guidance for future implementations of these algorithms in experiments.
The exponential runtime of quantum simulators on classical machines, along with long queue times and high costs associated with real quantum devices, presents significant challenges for the efficient optimization of Variational Quantum Algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), and Quantum Neural Networks (QNNs). To address these limitations, we propose a novel approach, DyPP (Dynamic Parameter Prediction), which accelerates the convergence of VQAs by leveraging regular trends in the parameter weights to update parameters efficiently. We introduce two techniques for optimal prediction performance: Naive Prediction (NaP) and Adaptive Prediction (AdaP). Through extensive experimentation and training of multiple QNN models on various datasets, we demonstrate that DyPP achieves a speedup of approximately 2.25×compared to standard training methods, while also providing improved accuracy (up to 2.3% higher) and lower loss (up to 6.1% reduction) with minimal storage and computational overhead. We further evaluate DyPP’s effectiveness in VQE for molecular ground-state energy estimation and in QAOA for graph MaxCut. Our results show that, on average, DyPP leads to a speedup of up to 3.1× for VQE and 2.91× for QAOA compared to traditional optimization, while requiring up to 3.3× fewer shots (i.e., repeated circuit executions). Even in the presence of hardware noise, DyPP outperforms existing optimization techniques, delivering up to 3.33× speedup and requiring 2.5× fewer shots, thereby enhancing the efficiency of VQAs.