Related papers: Time-evolution methods for matrix-product states
Time-dependent density matrix renormalization group method with a matrix product ansatz is employed for explicit computation of non-equilibrium steady state density operators of several integrable and non-integrable quantum spin chains,…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
(Please refer to arXiv:1810.08050, which has completely different aims but contains all the main contents of this paper) In this work, we propose to access the information of criticality and excitations of one-dimensional quantum systems by…
We propose a new method for computing the ground state properties and the time evolution of infinite chains based on a transverse contraction of the tensor network. The method does not require finite size extrapolation and avoids explicit…
A matrix product state approach to non-Markovian, classical and quantum processes is discussed. In the classical case, the Radon-Nikodym derivative of all processes can be embedded into quantum measurement procedure. In the both cases,…
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time…
We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our…
This paper is devoted to the description of the evolution of states of quantum many-particle systems within the framework of a one-particle density operator, which enables to construct the kinetic equations in scaling limits in the presence…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
The time-evolving matrix product operator (TEMPO) method has become a very competitive numerical method for studying the real-time dynamics of quantum impurity problems. For small impurities, the most challenging calculation in TEMPO is to…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
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…
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum…
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…
As a contribution to the field of quantum mereology, we study how a change of tensor product structure in a finite-dimensional Hilbert space affects its entanglement properties. In particular, we ask whether, given a time-evolving state,…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…