Related papers: Many-Body Eigenstates from Quantum Manifold Optimi…
The exploration of neural network quantum states has become widespread in the studies of complicated quantum many-body systems. However, achieving high precision remains challenging due to the exponential growth of Hilbert space size and…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite…
Using the trajectory conception of state we give a simple demonstration that the quantum state of a many-body system may be expressed as a set of states in three-dimensional space, one associated with each particle. It follows that the…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
Classical simulation of quantum physics is a central approach to investigating physical phenomena. Quantum computers enhance computational capabilities beyond those of classical resources, but it remains unclear to what extent existing…
Neural-network state representations of quantum many-body systems are attracting great attention and more rigorous quantitative analysis about their expressibility and complexity is warranted. Our analysis of the restricted Boltzmann…
Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space,…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…
Variational methods have offered controllable and powerful tools for capturing many-body quantum physics for decades. The recent introduction of expressive neural network quantum states has enabled the accurate representation of a broad…
While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this work, we introduce an alternative…
We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one entry…
We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
Quantum embedding theories are powerful tools for approximately solving large-scale strongly correlated quantum many-body problems. The main idea of quantum embedding is to glue together a highly accurate quantum theory at the local scale…
Many-body quantum systems present a rich phenomenology which can be significantly altered when they are in contact with an environment. In order to study such setups, a number of approximations are usually performed, either concerning the…
Finding the precise location of quantum critical points is of particular importance to characterise quantum many-body systems at zero temperature. However, quantum many-body systems are notoriously hard to study because the dimension of…