Related papers: Variational Quantum Linear Solver
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Simulating nonlinear partial differential equations (PDEs) such as the Navier--Stokes (NS) equations remains computationally intensive, especially when implicit time integration is used to capture multiscale flow dynamics. This work…
Simulating response properties of molecules is crucial for interpreting experimental spectroscopies and accelerating materials design. However, it remains a long-standing computational challenge for electronic structure methods on classical…
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization…
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
Variational Quantum Algorithms (VQAs) are expected to be promising algorithms with quantum advantages that can be run at quantum computers in the close future. In this work, we review simple rules in basic quantum circuits, and propose a…
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need…
Linear systems of equations can be found in various mathematical domains, as well as in the field of machine learning. By employing noisy intermediate-scale quantum devices, variational solvers promise to accelerate finding solutions for…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
We present hybrid quantum-classical pipelines for solving the Duffing equation that leverage Carleman linearization and the Variational Quantum Linear Solver (VQLS). First, we demonstrate that Carleman linearization accurately approximates…
Simulating quantum circuits using classical computers can accelerate the development and validation of quantum algorithms. Our newly developed algorithm, variational quantum search (VQS), has shown an exponential advantage over Grover's…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Given a linear system of equations $A\boldsymbol{x}=\boldsymbol{b}$, quantum linear system solvers (QLSSs) approximately prepare a quantum state $|\boldsymbol{x}\rangle$ for which the amplitudes are proportional to the solution vector…
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engineering domains. For instance, in aerodynamics, the PDE…
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…