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Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common…

With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…

We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…

Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

Optimization by stochastic gradient descent is an important component of many large-scale machine learning algorithms. A wide variety of such optimization algorithms have been devised; however, it is unclear whether these algorithms are…

Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…

Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…

In quantum computing, the variational quantum algorithms (VQAs) are well suited for finding optimal combinations of things in specific applications ranging from chemistry all the way to finance. The training of VQAs with gradient descent…

Decoherence of quantum hardware is currently limiting its practical applications. At the same time, classical algorithms for simulating quantum circuits have progressed substantially. Here, we demonstrate a hybrid framework that integrates…

Zeroth-order optimization aims to minimize an objective function using only function evaluations, and is therefore fundamental in black-box optimization, hyperparameter tuning, bandit learning, and adversarial machine learning. While…

In a real Hilbert space setting, we study the convergence properties of an inexact gradient algorithm featuring both viscous and Hessian driven damping for convex differentiable optimization. In this algorithm, the gradient evaluation can…

Quantum control is valuable for various quantum technologies such as high-fidelity gates for universal quantum computing, adaptive quantum-enhanced metrology, and ultra-cold atom manipulation. Although supervised machine learning and…

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…

We develop a classical shadow tomography protocol utilizing the randomized measurement scheme based on hybrid quantum circuits, which consist of layers of two-qubit random unitary gates mixed with single-qubit random projective…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have…