Related papers: Quantum Levenberg--Marquardt Algorithm for optimiz…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
In this paper, we give quantum algorithms for two fundamental computation problems: solving polynomial systems over finite fields and optimization where the arguments of the objective function and constraints take values from a finite field…
We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it…
The advent of quantum computing processors with possibility to scale beyond experimental capacities magnifies the importance of studying their applications. Combinatorial optimization problems can be one of the promising applications of…
In this paper, we study the generalized problem that minimizes or maximizes a multi-order complex quadratic form with constant-modulus constraints on all elements of its optimization variable. Such a mathematical problem is commonly…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian…
A programmable quantum processor is a fundamental model of quantum computation. In this model, any quantum channel can be approximated by applying a fixed universal quantum operation onto an input state and a quantum `program' state, whose…
Many computer vision applications need to recover structure from imperfect measurements of the real world. The task is often solved by robustly fitting a geometric model onto noisy and outlier-contaminated data. However, recent theoretical…
A Quantum Natural Gradient (QNG) algorithm for optimization of variational quantum circuits has been proposed recently. In this study, we employ the Langevin equation with a QNG stochastic force to demonstrate that its discrete-time…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
We introduce Power Bundle Adjustment as an expansion type algorithm for solving large-scale bundle adjustment problems. It is based on the power series expansion of the inverse Schur complement and constitutes a new family of solvers that…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here, we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to…
Neighborhood Preserving Embedding (NPE) is an important linear dimensionality reduction technique that aims at preserving the local manifold structure. NPE contains three steps, i.e., finding the nearest neighbors of each data point,…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
Quantum Computing aims to streamline machine learning, making it more effective with fewer trainable parameters. This reduction of parameters can speed up the learning process and reduce the use of computational resources. However, in the…
We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…
Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and…