Related papers: Quantum algorithm for linear matrix equations
We present a systematic pathway for solving differential equations within the quantum linear systems framework by combining block encoding with Quantum Singular Value Transformation (QSVT). The approach is demonstrated on a complex…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
In this note we construct a solution of a matrix interval linear equation of the form X=AX+B (the discrete stationary Bellman equation) over partially ordered semirings, including the semiring of nonnegative real numbers and all idempotent…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a…
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
While quantum algorithms for solving large scale systems of linear equations offer potentially exponential speedups, their application has largely been confined to sparse matrices. This work extends the scope of these algorithms to a broad…
Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…
We introduce a quantum linear system solving algorithm based on the Kaczmarz method, a widely used workhorse for large linear systems and least-squares problems that updates the solution by enforcing one equation at a time. Its simplicity…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…