Related papers: Solving nonlinear PDEs with Quantum Neural Network…

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…

Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…

This work studies quantum algorithms to solve high-dimensional stochastic differential equations (SDEs) $\mathrm{d} \mathbf{X}_t = A(t) \mathbf{X}_t \mathrm{d} t + B(t) \mathrm{d} \mathbf{W}_t$. Aiming for a speed-up in the dimension $N$ of…

The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…

Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a…

The variational quantum algorithm (VQA) with a parametrized quantum circuit is widely applicable to near-term quantum computing, but its fundamental issues that limit optimization performance have been reported in the literature. For…

Quantum computers show potential for achieving computational advantage over classical computers, with many candidate applications in combinatorial optimisation. We present an application level benchmarking framework for near-term quantum…

We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the…

Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…

Variational quantum algorithms (VQA) have emerged as a promising quantum alternative for solving optimization and machine learning problems using parameterized quantum circuits (PQCs). The design of these circuits influences the ability of…

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…

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…

Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…

Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…

We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it…

In this work, we present a Gauss-Newton based quantum algorithm (GNQA) for combinatorial optimization problems that, under optimal conditions, rapidly converges towards one of the optimal solutions without being trapped in local minima or…

Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead,…

The variational quantum eigensolver (VQE), a type of variational quantum algorithm, is a hybrid quantum-classical algorithm to find the lowest-energy eigenstate of a particular Hamiltonian. We investigate ways to optimize the VQE solving…

Variational quantum algorithms (VQAs) have emerged as a leading paradigm in near-term quantum computing, yet their performance can be hindered by the so-called barren plateau problem, where gradients vanish exponentially with system size or…