22 citations · 45 across the 14 of their papers we have counts for
14 papers
Basis-update and Galerkin time integration in canonical matrix-product-state form
Maximilian Fröhlich, Richard M. Milbradt, Martin Eigel +3
Matrix product state algorithms must enlarge their bond spaces as entanglement grows and compress them to control cost. We formulate basis-update and Galerkin (BUG) time integratio…
Time Evolution on Hybrid Tensor Networks -- A Novel and Parallelizable Algorithm
Tobias V. Bauer, Richard M. Milbradt, Christian B. Mendl
We develop a novel time-evolution algorithm for matrix product states based on the recently introduced hybrid tensor network (hTN) framework. We retain the tensors close to the bou…
A Short Note on the Generators of Controlled Quantum Gates
Richard M. Milbradt, Christian B. Mendl
We present the analytical generators for arbitrary multi-qubit controlled gates. Closed forms for the generating Hamiltonians are given for gates with both multiple control and tar…
Efficient Application of Tensor Network Operators to Tensor Network States Through Successive Deterministic Compression
Richard M. Milbradt, Shuo Sun, Christian B. Mendl +2
We introduce an algorithm to apply tree tensor network operators to tree tensor network states followed by compression. Especially when applying a matrix product operator to matrix…
Tree Tensor Networks Methods for Efficient Calculation of Molecular Vibrational Spectra
Shuo Sun, Richard M. Milbradt, Stefan Knecht +2
We develop and employ general Tree Tensor Networks (TTNs) to compute the vibrational spectra for two model systems: a set of 64-dimensional coupled oscillators and acetonitrile. We…
Quantum circuit simulation with a local time-dependent variational principle
Aaron Sander, Maximilian Fröhlich, Mazen Ali +6
Classical simulations of quantum circuits are vital for assessing potential quantum advantage and benchmarking devices, yet they require sophisticated methods to avoid the exponent…
Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators
Hazar Çakır, Richard M. Milbradt, Christian B. Mendl
This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A g…
Large-scale stochastic simulation of open quantum systems
Aaron Sander, Maximilian Fröhlich, Martin Eigel +6
Understanding the precise interaction mechanisms between quantum systems and their environment is crucial for advancing stable quantum technologies, designing reliable experimental…
A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
Emiliano Godinez-Ramirez, Richard Milbradt, Christian B. Mendl
Tensor networks offer a valuable framework for implementing Lindbladian dynamics in many-body open quantum systems with nearest-neighbor couplings. In particular, a tensor network…
PyTreeNet: A Python Library for easy Utilisation of Tree Tensor Networks
Richard M. Milbradt, Qunsheng Huang, Christian B. Mendl
In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library…
State Diagrams to determine Tree Tensor Network Operators
Richard M. Milbradt, Qunsheng Huang, Christian B. Mendl
This work is concerned with tree tensor network operators (TTNOs) for representing quantum Hamiltonians. We first establish a mathematical framework connecting tree topologies with…
Correlations in Disordered Solvable Tensor Network States
Daniel Haag, Richard M. Milbradt, Christian B. Mendl
Solvable matrix product and projected entangled pair states evolved by dual and ternary-unitary quantum circuits have analytically accessible correlation functions. Here, we invest…
On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond
Mihail Stoian, Richard Milbradt, Christian B. Mendl
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contrac…
Ternary unitary quantum lattice models and circuits in dimensions
Richard Milbradt, Lisa Scheller, Christopher Aßmus +1
We extend the concept of dual unitary quantum gates to quantum lattice models in dimensions, by introducing and studying ternary unitary four-particle gates, which are unit…