Related papers: Tensor-Programmable Quantum Circuits for Solving D…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
In scientific computing, the formulation of numerical discretisations of partial differential equations (PDEs) as untrained convolutional layers within Convolutional Neural Networks (CNNs), referred to by some as Neural Physics, has…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…
Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding…
We introduce and extend the outer product and contractive product of tensors and matrices, and present some identities in terms of these products. We offer tensor expressions of derivatives of tensors, focus on the tensor forms of…
Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks…
For the solution of time-dependent nonlinear differential equations, we present variational quantum algorithms (VQAs) that encode both space and time in qubit registers. The spacetime encoding enables us to obtain the entire time evolution…
Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…
Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…
One of the most important topics in quantum scientific computing is solving differential equations. In this paper, generalized quantum functional expansion (QFE) framework is proposed. In the QFE framework, a functional expansion of…
In this work, we present a case study in implementing a variational quantum algorithm for solving the Poisson equation, which is a commonly encountered partial differential equation in science and engineering. We highlight the practical…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Quantum computers are considered as a part of the family of the reversible, lineary-extended, dynamical systems (Quanputers). For classical problems an operational reformulation is given. A universal algorithm for the solving of classical…
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering related fields. They are in general non-sparse and non-unitary. In this paper, we present efficient quantum circuits…
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized…
This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…