Related papers: Efficient Variational Quantum Linear Solver for St…
We apply preconditioning, which is widely used in classical solvers for linear systems $A\textbf{x}=\textbf{b}$, to the variational quantum linear solver. By utilizing incomplete LU factorization as a preconditioner for linear equations…
Variational quantum eigensolvers (VQEs) combine classical optimization with efficient cost function evaluations on quantum computers. We propose a new approach to VQEs using the principles of measurement-based quantum computation. This…
Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row…
Analysis of quantum processes, especially in the context of noise, errors, and decoherence is essential for the improvement of quantum devices. An intuitive representation of those processes modeled by quantum channels are Pauli transfer…
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…
Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
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…
Partial Differential Equations (PDEs) describe several problems relevant to many fields of applied sciences, and their discrete counterparts typically involve the solution of sparse linear systems. In this context, we focus on the analysis…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although…
This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…
We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Quantum Computing is believed to be the ultimate solution for quantum chemistry problems. Before the advent of large-scale, fully fault-tolerant quantum computers, the variational quantum eigensolver~(VQE) is a promising heuristic quantum…
This article presents a new method to compute matrices from numerical simulations based on the ideas of sparse sampling and compressed sensing. The method is useful for problems where the determination of the entries of a matrix constitutes…
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…
This paper introduces a novel approach to implementing non-unitary linear transformations of basis on quantum computational platforms, a significant leap beyond the conventional unitary methods. By integrating Singular Value Decomposition…
The variational quantum eigensolver (or VQE) uses the variational principle to compute the ground state energy of a Hamiltonian, a problem that is central to quantum chemistry and condensed matter physics. Conventional computing methods are…