Related papers: Time-evolution methods for matrix-product states
For an infinite system of particles arriving in and departing from a habitat $X$ -- a locally compact Polish space with a positive Radon measure $\chi$ -- a Markov process is constructed in an explicit way. Along with its location $x\in X$,…
We consider the problem of model reduction for Markovian quantum systems whose dynamics are described by a time-dependent Lindblad generator -- notably, as arising in the presence of external control. Our approach, which builds upon Krylov…
Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix $\rho_1$, obtained by…
A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this…
Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved…
We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational…
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 discuss a new mechanism leading to a matrix product form for the stationary state of one-dimensional stochastic models. The corresponding algebra is quadratic and involves four different matrices. For the example of a…
Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for…
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential…
This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…
Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix $\rho(t)$. Because $\rho$ contains both classical and quantum-mechanical probabilities it…
Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponential growth of resources. Tensor network approaches, in…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We reconsider and analyze in detail the problem of particle production in the time dependent background of $c=1$ matrix model where the Fermi sea drains away at late time. In addition to the moving mirror method, which has already been…
Minimally entangled typical thermal states (METTS) are a construction that allows one to to solve for the imaginary time evolution of quantum many body systems. By using wave functions that are weakly entangled, one can take advantage of…
Matrix product states, a key ingredient of numerical algorithms widely employed in the simulation of quantum spin chains, provide an intriguing tool for quantum phase transition engineering. At critical values of the control parameters on…
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
Exact matrix product state representations for a type of scale-invariant states are presented, which describe highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes in one-dimensional quantum…