Related papers: Variational methods for solving high dimensional q…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
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…
To solve nonlinear partial differential equations (PDEs) is one of the most common but important tasks in not only basic sciences but also many practical industries. We here propose a quantum variational (QuVa) PDE solver with the aid of…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical variational algorithm that produces an upper-bound estimate of the ground-state energy of a Hamiltonian. As quantum computers become more powerful and go beyond the…
This paper presents a hybrid quantum-classical approach to prime factorization. The proposed algorithm is based on the Variational Quantum Eigensolver (VQE), which employs a classical optimizer to find the ground state of a given…
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There…
Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that…
Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…
We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest.…
This thesis explores the application of the Symmetry-Breaking/Symmetry-Restoration methodology on quantum computers to better approximate a Hamiltonian's ground state energy within a variational framework in many-body physics. This involves…
We propose a numerical method to solve the Wigner equation in quantum systems of spinless, non-relativistic particles. The method uses a spectral decomposition into $L^2(\mathbb{R}^d)$ basis functions in momentum-space to obtain a system of…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit…
In this work, we develop a highly efficient representation of functions and differential operators based on Fourier analysis. Using this representation, we create a variational hybrid quantum algorithm to solve static, Schr\"odinger-type,…
We perform quantum simulation on classical and quantum computers and set up a machine learning framework in which we can map out phase diagrams of known and unknown quantum many-body systems in an unsupervised fashion. The classical…
We propose a neural-network variational quantum algorithm to simulate the time evolution of quantum many-body systems. Based on a modified restricted Boltzmann machine (RBM) wavefunction ansatz, the proposed algorithm can be efficiently…
Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and thermalization that challenge classical computational methods due to their volume-law entanglement content. In this work, we explore…
Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying…
Variational approaches are among the most powerful modern techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in…