Related papers: Gradient methods for variational optimization of p…
Recently developed neural network-based wave function methods are capable of achieving state-of-the-art results for finding the ground state in real space. In this work, a neural network-based method is used to compute excited states. We…
We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field…
We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as…
We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…
The tensor network algorithm, a family of prevalent numerical methods for quantum many-body problems, aptly captures the entanglement properties intrinsic to quantum systems, enabling precise representation of quantum states. However, its…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
Efficient optimization of quantum systems is a necessity for reaching fault tolerant thresholds. A standard tool for optimizing simulated quantum dynamics is the gradient-based \textsc{grape} algorithm, which has been successfully applied…
In this paper we combine concepts from Riemannian Optimization and the theory of Sobolev gradients to derive a new conjugate gradient method for direct minimization of the Gross-Pitaevskii energy functional with rotation. The conservation…
Projected entangled pair states (PEPS) provide a natural ansatz for the ground states of gapped, local Hamiltonians in which global characteristics of a quantum state are encoded in properties of local tensors. We develop a framework to…
We introduce a class of bipartite entangled continuous variable states that are positive under partial transposition operation, i.e., PPT bound entangled. These states are based on realistic preparation procedures in optical systems, being…
Several tensor networks are built of isometric tensors, i.e. tensors satisfying $W^\dagger W = \mathrm{I}$. Prominent examples include matrix product states (MPS) in canonical form, the multiscale entanglement renormalization ansatz (MERA),…
Global optimization heuristics are popular to optimize hard non-convex problems. Despite their irrefutably large cost-to-solution, in the lack of other working greedy or convex approaches, global optimization algorithms remain the…