Related papers: Iterative Power Algorithm for Global Optimization …
We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to…
In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for achieving quantum advantage in combinatorial optimization. However, its variational framework presents a long-standing challenge in selecting circuit parameters.…
The Partition Search Algorithm (PSA) and Iterative Quantum Optimization with an Adaptive Problem (IQOAP) are leading variational quantum algorithms for solving Shortest Vector Problem (SVP). However, each has limitations that restrict its…
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been…
We propose a machine-learning approach based on Bayesian optimization to build global potential energy surfaces (PES) for reactive molecular systems using feedback from quantum scattering calculations. The method is designed to correct for…
Quantum Approximate Optimization Algorithm (QAOA) is a promising quantum heuristic with empirical evidence of speedup over classical state-of-the-art for some problems. QAOA uses a parameterized circuit with $p$ layers, where higher $p$…
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…
We investigate the power iteration algorithm for the tensor PCA model introduced in Richard and Montanari (2014). Previous work studying the properties of tensor power iteration is either limited to a constant number of iterations, or…
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
We propose Selective Multiple Power Iterations (SMPI), a new algorithm to address the important Tensor PCA problem that consists in recovering a spike $\bf{v_0}^{\otimes k}$ corrupted by a Gaussian noise tensor $\bf{Z} \in…
The Quantum Approximate Optimization Algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization problems whose performance can only improve with the number of layers $p$. While QAOA holds promise as an algorithm that can…
Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…