Related papers: Improved Quantum Algorithms for Eigenvalues Findin…
Quadratic Unconstrained Binary Optimization (QUBO) is a general-purpose modeling framework for combinatorial optimization problems and is a requirement for quantum annealers. This paper utilizes the eigenvalue decomposition of the…
Multipartite entanglement is a crucial resource for a wide range of quantum information processing tasks, including quantum metrology, quantum computing, and quantum communication. The verification of multipartite entanglement, along with…
The eigenvalue density of a matrix plays an important role in various types of scientific computing such as electronic-structure calculations. In this paper, we propose a quantum algorithm for computing the eigenvalue density in a given…
Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…
Variational quantum algorithms have been acknowledged as a leading strategy to realize near-term quantum advantages in meaningful tasks, including machine learning and combinatorial optimization. When applied to tasks involving classical…
Accurate computation of multiple eigenvalues of quantum Hamiltonians is essential in quantum chemistry, materials science, and molecular spectroscopy. Estimating excited-state energies is challenging for classical algorithms due to…
We study a quantum-algorithmic framework for parameterizing partial differential equations (PDEs). For a broad class of problems in which the discretized parameter field admits a diagonal representation, block-encodings of diagonal…
Determining the ground state of a many-body Hamiltonian is a central problem across physics, chemistry, and combinatorial optimization, yet it is often classically intractable due to the exponential growth of Hilbert space with system size.…
Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block encoded matrices, a central task that lies at the heart of most prominent…
We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
In this paper, we introduce a major advancement in Quantum Singular Value Transformation (QSVT) through the development of Feedforward QSVT (FQSVT), a framework that significantly enhances the efficiency and robustness of quantum algorithm…
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…
Quantum computing has emerged as a powerful potential accelerator for computational fluid dynamics (CFD), but whether this promise can be realized in practice depends on how fluid information is encoded on quantum hardware. This review…
In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have…
Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and…
Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…