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Computations of chemical systems' equilibrium properties and non-equilibrium dynamics have been suspected of being a "killer app" for quantum computers. This review highlights the recent advancements of quantum algorithms tackling complex sampling tasks in the key areas of computational chemistry: ground state, thermal state properties, and quantum dynamics calculations. We review a broad range of quantum algorithms, from hybrid quantum-classical to fully quantum, focusing on the traditional Monte Carlo family, including Markov chain Monte Carlo, variational Monte Carlo, projector Monte Carlo, path integral Monte Carlo, etc. We also cover other relevant techniques involving complex sampling tasks, such as quantum-selected configuration interaction, minimally entangled typical thermal states, entanglement forging, and Monte Carlo-flavored Lindbladian dynamics. We provide a comprehensive overview of these algorithms' classical and quantum counterparts, detailing their theoretical frameworks and discussing the potentials and challenges in achieving quantum computational advantages., Comment: 35 pages, 12 figures

Molecular quantum chemistry has seen enormous progress in the last few decades thanks to the more advanced and sophisticated numerical techniques and computing power. Following the recent interest in extending these capabilities to condensed-phase problems, we summarize basic knowledge of condensed-phase quantum chemistry for ones with experience in molecular quantum chemistry. We highlight recent efforts in this direction, including solving the electron repulsion integrals bottleneck and implementing hybrid density functional theory and wavefunction methods, and lattice dynamics for periodic systems within atom-centered basis sets. Many computational techniques presented here are inspired by the extensive method developments rooted in quantum chemistry. In this Focus Article, we selectively focus on the computational techniques rooted in molecular quantum chemistry, emphasize some challenges, and point out open questions. We hope our perspectives will encourage researchers to pursue this exciting and promising research avenue., Comment: 17 pages, 4 figures

This paper investigates the impact of breast density distribution on the generalization performance of deep-learning models on mammography images using the VinDr-Mammo dataset. We explore the use of domain adaptation techniques, specifically Domain Adaptive Object Detection (DAOD) with the Noise Latent Transferability Exploration (NLTE) framework, to improve model performance across breast densities under noisy labeling circumstances. We propose a robust augmentation framework to bridge the domain gap between the source and target inside a dataset. Our results show that DAOD-based methods, along with the proposed augmentation framework, can improve the generalization performance of deep-learning models (+5% overall mAP improvement approximately in our experimental results compared to commonly used detection models). This paper highlights the importance of domain adaptation techniques in medical imaging, particularly in the context of breast density distribution, which is critical in mammography.

The amount of data generated by Earth observation satellites can be enormous, which poses a great challenge to the satellite-to-ground connections with limited rate. This paper considers problem of efficient downlink communication of multi-spectral satellite images for Earth observation using change detection. The proposed method for image processing consists of the joint design of cloud removal and change encoding, which can be seen as an instance of semantic communication, as it encodes important information, such as changed multi-spectral pixels (MPs), while aiming to minimize energy consumption. It comprises a three-stage end-to-end scoring mechanism that determines the importance of each MP before deciding its transmission. Specifically, the sensing image is (1) standardized, (2) passed through a high-performance cloud filtering via the Cloud-Net model, and (3) passed to the proposed scoring algorithm that uses Change-Net to identify MPs that have a high likelihood of being changed, compress them and forward the result to the ground station. The experimental results indicate that the proposed framework is effective in optimizing energy usage while preserving high-quality data transmission in satellite-based Earth observation applications.

Beam Placement (BP) is a well-known problem in Low-Earth Orbit (LEO) satellite communication (SatCom) systems, which can be modelled as an NP-hard clique cover problem. Recently, quantum computing has emerged as a novel technology which revolutionizes how to solve challenging optimization problems by formulating Quadratic Unconstrained Binary Optimization (QUBO), then preparing Hamiltonians as inputs for quantum computers. In this paper, we study how to use quantum computing to solve BP problems. However, due to limited hardware resources, existing quantum computers are unable to tackle large optimization spaces. Therefore, we propose an efficient Hamiltonian Reduction method that allows quantum processors to solve large BP instances encountered in LEO systems. We conduct our simulations on real quantum computers (D-Wave Advantage) using a real dataset of vessel locations in the US. Numerical results show that our algorithm outperforms commercialized solutions of D-Wave by allowing existing quantum annealers to solve 17.5 times larger BP instances while maintaining high solution quality. Although quantum computing cannot theoretically overcome the hardness of BP problems, this work contributes early efforts to applying quantum computing in satellite optimization problems, especially applications formulated as clique cover/graph coloring problems.

Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $R=\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ $(u^2=0)$ and $s,n$ be positive integers such that $n$ is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring $R$ of length $2^sn$ and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and $2$-quasi-cyclic codes over $\mathbb{F}_{2^m}$ of length $2^{s+1}n$ can be obtained from self-dual cyclic code over $R$ of length $2^sn$ and by a Gray map preserving orthogonality and distances from $R$ onto $\mathbb{F}_{2^m}^2$., Comment: arXiv admin note: text overlap with arXiv:1811.11018, arXiv:1907.07107

Let $p$ be an odd prime number, $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $s$ a positive integer. Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over $\mathbb{F}_p$ with a specific type. On that basis, we give an explicit representation and enumeration for all distinct self-dual cyclic codes of length $p^s$ over the finite chain ring $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2=0)$. Moreover, We provide an efficient method to construct every self-dual cyclic code of length $p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ precisely., Comment: arXiv admin note: substantial text overlap with arXiv:1811.11018

Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $\lambda$ and $k$ be integers satisfying $\lambda,k\geq 2$ and denote $R=\mathbb{F}_{2^m}[u]/\langle u^{2\lambda}\rangle$. Let $\delta,\alpha\in \mathbb{F}_{2^m}^{\times}$. For any odd positive integer $n$, we give an explicit representation and enumeration for all distinct $(\delta+\alpha u^2)$-constacyclic codes over $R$ of length $2^kn$, and provide a clear formula to count the number of all these codes. As a corollary, we conclude that every $(\delta+\alpha u^2)$-constacyclic code over $R$ of length $2^kn$ is an ideal generated by at most $2$ polynomials in the residue class ring $R[x]/\langle x^{2^kn}-(\delta+\alpha u^2)\rangle$., Comment: arXiv admin note: text overlap with arXiv:1805.05595

Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$ and $s$ a positive integer. Using properties for Kronecker product of matrices and calculation for linear equations over $\mathbb{F}_{2^m}$, an efficient method for the construction of all distinct self-dual cyclic codes with length $2^s$ over the finite chain ring $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ $(u^2=0)$ is provided. On that basis, an explicit representation for every self-dual cyclic code of length $2^s$ over $\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}$ and an exact formula to count the number of all these self-dual cyclic codes are given.