Related papers: Matrix Product State on a Quantum Computer

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.

In stochastic modeling, there has been a significant effort towards finding predictive models that predict a stochastic process' future using minimal information from its past. Meanwhile, in condensed matter physics, matrix product states…

We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a…

For quantum many-body systems in one dimension, computational complexity theory reveals that the evaluation of ground-state energy remains elusive on quantum computers, contrasting the existence of a classical algorithm for temperatures…

Embedding high-dimensional data into resource-limited quantum devices remains a significant challenge for practical quantum machine learning. In multimodal face anti-spoofing, while linear compression methods such as principal component…

Incorporating conservation laws explicitly into matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used…

Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…

We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…

The property of quantum many-body systems under spatial reflection and the relevant physics of renormalization group (RG) procedure are revealed. By virtue of the matrix product state (MPS) representation, various attributes for…

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…

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…

Simulating the nonequilibrium dynamics of thermal states is a fundamental problem across scales from high energy to condensed matter physics. Quantum computers may provide a way to solve this problem efficiently. Preparing a thermal state…

We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…

We construct exact eigenstates of quantum many-body systems with Hamiltonians that are not frustration-free in matrix product form, based on a local error cancellation ansatz motivated by the Derrida-Evans-Hakim-Pasquier method for finding…

We introduce an efficient algorithm for the systematic design of shallow-depth quantum circuits capable of preparing many-body quantum states represented as Matrix Product States (MPS). The proposed method leverages Schmidt spectrum…

Direct numerical simulation (DNS) of turbulent reactive flows has been the subject of significant research interest for several decades. Accurate prediction of the effects of turbulence on the rate of reactant conversion, and the subsequent…

Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum…

Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…

We propose the simulation of quantum-optical systems in the ultrastrong-coupling regime using a variational quantum algorithm. More precisely, we introduce a short-depth variational form to prepare the groundstate of the multimode Dicke…

Solving the ground state of quantum many-body systems remains a fundamental challenge in physics and chemistry. Recent advancements in quantum hardware have opened new avenues for addressing this challenge. Inspired by the quantum-enhanced…