Related papers: Time evolution of Matrix Product States
The investigation of the behavior of both classical and quantum systems on non-Euclidean surfaces near the phase transition point represents an interesting research area of modern physics. In the case of classical spin systems, a…
Dynamical electronic- and vibrational-structure theories have received a growing interest in the last years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular…
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems but are restricted to moderately entangled states as the number of parameters scales exponentially with the…
We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
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…
We introduce evolved quantum Boltzmann machines as a variational ansatz for quantum optimization and learning tasks. Given two parameterized Hamiltonians $G(\theta)$ and $H(\phi)$, an evolved quantum Boltzmann machine consists of preparing…
We introduce a novel approach for estimating the spectrum of quantum many-body Hamiltonians, and more generally, of Hermitian operators, using quantum time evolution. In our approach we are evolving a maximally mixed state under the…
The density-matrix renormalization group method has become a standard computational approach to the low-energy physics as well as dynamics of low-dimensional quantum systems. In this paper, we present a new set of applications, available as…
In a recent work we presented a recursive algorithm to compute the matrix elements of a generic Gaussian transformation in the photon-number basis. Its purpose was to evolve a quantum state by building the transformation matrix and…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
In this work, we consider the imaginary time evolution of matrix product states. We present a novel quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed-up the…
We review different tensor network approaches to study the spreading of operators in generic nonintegrable quantum systems. As a common ground to all methods, we quantify this spreading by means of the Frobenius norm of the commutator of a…
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
Tensor network methods as presented in our open source Matrix Product States software have opened up the possibility to study many-body quantum physics in one and quasi-one-dimensional systems in an easily accessible package similar to…