Related papers: Lower bounds to variational problems with guarante…
Estimating spectral gaps of quantum many-body Hamiltonians is a highly challenging computational task, even under assumptions of locality and translation-invariance. Yet, the quest for rigorous gap certificates is motivated by their broad…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
An analytical prediction is established of how an isolated many-body quantum system relaxes towards its thermal long-time limit under the action of a time-independent perturbation, but still remaining sufficiently close to a reference case…
Strongly interacting quantum systems described by non-stoquastic Hamiltonians exhibit rich low-temperature physics. Yet, their study poses a formidable challenge, even for state-of-the-art numerical techniques. Here, we investigate…
We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful…
A novel class of hybrid quantum-classical algorithms based on the variational approach have recently emerged from separate proposals addressing, for example, quantum chemistry and combinatorial problems. These algorithms provide an…
A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…
Elementary introduction to the application of Mathematica 3.0 to the solution of bound-state problems in quantum theory by standard variational procedures, with particular emphasis on the computation of precise upper bounds on energy levels…
This paper is concerned with the analysis of the randomized subspace iteration for the computation of low-rank approximations. We present three different kinds of bounds. First, we derive both bounds for the canonical angles between the…