Towards a better understanding of the matrix product function approximation algorithm in application to quantum physics

Abstract

We recently introduced a method to approximate functions of Hermitian Matrix Product Operators or Tensor Trains that are of the form $\mathsf{Tr}f(A)$. Functions of this type occur in several applications, most notably in quantum physics. In this work we aim at extending the theoretical understanding of our method by showing several properties of our algorithm that can be used to detect and correct errors in its results. Most importantly, we show that there exists a more computationally efficient version of our algorithm for certain inputs. To illustrate the usefulness of our finding, we prove that several classes of spin Hamiltonians in quantum physics fall into this input category. We finally support our findings with numerical results obtained for an example from quantum physics.

17 pages, comments very welcome

References in corpus (5)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• Time evolution algorithms for Matrix Product States and DMRG
• Computations in Quantum Tensor Networks

Cited by in corpus (1)

• Efficient approximation for global functions of matrix product operators