Related papers: Quantum locally linear embedding for nonlinear dim…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
The imaginary-time evolution method is widely known to be efficient for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of…
Estimating the difference between quantum data is crucial in quantum computing. However, as typical characterizations of quantum data similarity, the trace distance and quantum fidelity are believed to be exponentially-hard to evaluate in…
Partial differential equation (PDE) models with multiple temporal/spatial scales are prevalent in several disciplines such as physics, engineering, and many others. These models are of great practical importance but notoriously difficult to…
Distributed architectures are gaining prominence in quantum machine learning as a means to overcome hardware limitations and enable scalable quantum information processing. In this context, we analyze the design and performance of…
Large language models (LLMs) demand substantial computational and memory resources, posing challenges for efficient deployment. Two complementary approaches have emerged to address these issues: token-adaptive layer execution, which reduces…
Quantum computing has emerged as a promising platform for simulating strongly correlated systems in chemistry, for which the standard quantum chemistry methods are either qualitatively inaccurate or too expensive. However, due to the…
Quantum Embeddings (QE) are essential for loading classical data into quantum systems for Quantum Machine Learning (QML). The performance of QML algorithms depends on the type of QE and how features are mapped to qubits. Traditionally, the…
The integration of quantum computing into classical machine learning architectures has emerged as a promising approach to enhance model efficiency and computational capacity. In this work, we introduce the Quantum Kernel-Based Long…
We present a general framework for applying linear quantum error mitigation (QEM) techniques directly to physical qubits within a logical qubit to suppress logical errors. By exploiting the linearity of quantum error correction (QEC), we…
Quantum Annealing (QA) is a quantum computing paradigm for solving combinatorial optimization problems formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. An essential step in QA is minor embedding, which maps the…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective…
Since its introduction in 2000, the locally linear embedding (LLE) has been widely applied in data science. We provide an asymptotical analysis of the LLE under the manifold setup. We show that for the general manifold, asymptotically we…
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of…
This paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in…
The multiscale simulation of heterogeneous materials is a popular and important subject in solid mechanics and materials science due to the wide application of composite materials. However, the classical FE2 (finite element2) scheme can be…
In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…