Related papers: Localized density matrix minimization and linear s…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements $f(H)_{ij}$ decay rapidly…
As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
An exact method to compute the entire equilibrium reduced density matrix for systems characterized by a system-bath Hamiltonian is presented. The approach is based upon a stochastic unraveling of the influence functional that appears in the…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We…
We propose a technique for calculating and understanding the eigenvalue distribution of sums of random matrices from the known distribution of the summands. The exact problem is formidably hard. One extreme approximation to the true density…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
We present a protocol that allows the estimation of any density matrix element for continuous-variable quantum states, without resorting to the complete reconstruction of the full density matrix. The algorithm adaptatively discretizes the…
Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…
We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including $\ell_1$ regularization and structured output…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
In this article, we analyse the domain mapping method approach to approximate statistical moments of solutions to linear elliptic partial differential equations posed over random geometries including smooth surfaces and bulk-surface…
An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational…