相关论文: Dynamically Evolving Bond-Dimensions within the on…

We investigate ensembles of Matrix Product States (MPSs) generated by quantum circuit evolution followed by projection onto MPSs with a fixed bond dimension $\chi$. Specifically, we consider ensembles produced by: (i) random sequential…

We consider a decision-making problem where the environment varies both in space and time. Such problems arise naturally when considering e.g., the navigation of an underwater robot amidst ocean currents or the navigation of an aerial…

The curse of dimensionality is ubiquitous in both numerical and data-driven methods. This is particularly severe for space-time methods, which treat the combined space-time domain simultaneously. We investigate the effectiveness of a…

Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…

Matrix Product State (MPS) is a versatile tensor network representation widely applied in quantum physics, quantum chemistry, and machine learning, etc. MPS sampling serves as a critical fundamental operation in these fields. As the…

We introduce a method to simulate open quantum many-body dynamics by combining time-dependent variational Monte Carlo (tVMC) with quantum trajectory techniques. Our approach unravels the Lindblad master equation into an ensemble of…

It is by now well-known that ground states of gapped one-dimensional (1d) quantum-many body systems with short-range interactions can be studied efficiently using classical computers and matrix product state techniques. A corresponding…

Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…

In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…

Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J.…

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices…

We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying…

We combine the Density Matrix Renormalization Group (DMRG) with Matrix Product State tangent space concepts to construct a variational algorithm for finding ground states of one dimensional quantum lattices in the thermodynamic limit. A…

Time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in TD-DMRG,…

We adapt the time-evolving block decimation (TEBD) algorithm, originally devised to simulate the dynamics of 1D quantum systems, to simulate the time-evolution of non-equilibrium stochastic systems. We describe this method in detail; a…

Matrix Product States form the basis of powerful simulation methods for ground state problems in one dimension. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the "area law". In…

An algorithm for the simulation of the evolution of slightly entangled quantum states has been recently proposed as a tool to study time-dependent phenomena in one-dimensional quantum systems. Its key feature is a time-evolving…

We study a restricted class of correlator product states (CPS) for a spin-half chain in which each spin is contained in just two overlapping plaquettes. This class is also a restriction upon matrix product states (MPS) with local dimension…

Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional…