Related papers: Efficient higher-order matrix product operators fo…
We investigate the application of matrix product states to the Hubbard model in one spatial dimension with both of open and periodic boundary conditions. We develop the variatinal method that the optimization of the variational parameters…
We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate…
Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive…
We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time…
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…
The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized…
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
We present a general method for simulating lattice gauge theories in low dimensions using infinite matrix product states (iMPS). A central challenge in Hamiltonian formulations of gauge theories is the unbounded local Hilbert space…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
The finite-element approach to lattice field theory is both highly accurate (relative errors $\sim1/N^2$, where $N$ is the number of lattice points) and exactly unitary (in the sense that canonical commutation relations are exactly…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a…
We introduce an algorithm that is simultaneously memory-efficient and low-scaling for applying ab initio molecular Hamiltonians to matrix-product states (MPS) via the tensor-hypercontraction (THC) format. These gains carry over to Krylov…
We present explicit matrix product operator (MPO) representations for the local conserved quantities of the spin-$1/2$ XYZ chain. Through these MPO representations, we simplify the coefficients appearing in the local conserved quantities…
In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg--Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this…