1 citations · 1 across the 7 of their papers we have counts for
9 papers
Gregory Nested Picard Iteration Schemes for Open Quantum Systems Governed by the Lindblad Equation
Jiuhua Hu, Daniel Appelo, Yingda Cheng
Numerical simulation of quantum computing hardware and open quantum systems governed by the Lindblad equation is challenging due to the high dimensionality of the density matrix an…
Completely Positive and Trace Preserving Schemes with Tensor Train Compression for the Lindblad Equation
Peter DelMastro, Daniel Appelö, Yingda Cheng
We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is emp…
Arbitrary High Order Low-rank Completely Positive and Trace Preserving (CPTP) Schemes for Lindblad Equations with Time-dependent Hamiltonian
Jiuhua Hu, Daniel Appelo, Yingda Cheng
In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on neste…
A new cross approximation for Tucker tensors and its application in Tucker-Anderson Acceleration
Daniel Appelö, Yingda Cheng
This paper proposes two new algorithms related to the Tucker tensor format. The first method is a new cross approximation for Tucker tensors, which we call Cross-DEIM. Cross$^2…
lrAA: Low-Rank Anderson Acceleration
Daniel Appelo, Yingda Cheng
This paper proposes a new framework for computing low-rank solutions to nonlinear matrix equations arising from spatial discretization of nonlinear partial differential equations:…
High-Order Implicit Low-Rank Method with Spectral Deferred Correction for Matrix Differential Equations
Shun Li, Yan Jiang, Yingda Cheng
In this paper, we develop a low-rank method with high-order temporal accuracy using spectral deferred correction (SDC) to compute linear matrix differential equations. In [1], a lo…
Preconditioning Low Rank Generalized Minimal Residual Method (GMRES) for Implicit Discretizations of Matrix Differential Equations
Shixu Meng, Daniel Appelo, Yingda Cheng
This work proposes a new class of preconditioners for the low rank Generalized Minimal Residual Method (GMRES) for multiterm matrix equations arising from implicit timestepping of…
Kraus is King: High-order Completely Positive and Trace Preserving (CPTP) Low Rank Method for the Lindblad Master Equation
Daniel Appelo, Yingda Cheng
We design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserves…
Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
Daniel Appelö, Yingda Cheng
In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to cap…