# Optimization schemes for unitary tensor-network circuit

@article{Haghshenas2020OptimizationSF, title={Optimization schemes for unitary tensor-network circuit}, author={Reza Haghshenas}, journal={arXiv: Strongly Correlated Electrons}, year={2020} }

We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also the conjugate-gradient method with an effective line search. We present the benchmarking calculations for different network structures by studying the Heisenberg model in a strongly disordered magnetic field and a tensor-network $QR$-decomposition.

#### 2 Citations

Fast tensor disentangling algorithm

- Physics
- SciPost Physics
- 2021

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement.
However, many of the previously used iterative algorithms to minimize… Expand

The Variational Power of Quantum Circuit Tensor Networks

- Physics
- 2021

Reza Haghshenas,1, ∗ Johnnie Gray,1, † Andrew C. Potter,2, 3 and Garnet Kin-Lic Chan1, ‡ Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Tensor Network States and Geometry

- Mathematics, Physics
- 2011

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different… Expand

A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

- Physics, Computer Science
- 2013

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for… Expand

Uni10: an open-source library for tensor network algorithms

- Mathematics
- 2015

We present an object-oriented open-source library for developing tensor network algorithms written in C++ called Uni10. With Uni10, users can build a symmetric tensor from a collection of bonds,… Expand

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

- Physics, Mathematics
- 2008

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected… Expand

Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz

- Physics
- 2011

The goal of this manuscript is to provide an introduction to the multi-scale entanglement renormalization ansatz (MERA) and its application to the study of quantum critical systems. Only systems in… Expand

Unifying projected entangled pair state contractions

- Computer Science, Physics
- 2013

A new strategy is introduced, based on the idea of clusters, that unifies previous methods for the approximate contraction of a tensor network of projected entangled pair states and interpolates naturally between the cheapest and most imprecise and the most costly and most precise method. Expand

Conjugate gradient algorithm for optimization under unitary matrix constraint

- Mathematics, Computer Science
- Signal Process.
- 2009

This paper proposes a conjugate gradient (CG) algorithm on the Lie group of unitary matrices U(n) and shows that the proposed algorithm outperforms other existing algorithms in terms of convergence speed and computational complexity. Expand

Optimization algorithms exploiting unitary constraints

- Mathematics, Computer Science
- IEEE Trans. Signal Process.
- 2002

This paper presents novel algorithms that iteratively converge to a local minimum of a real-valued function f (X) subject to the constraint that the columns of the complex-valued matrix X are… Expand

Learning Relevant Features of Data with Multi-scale Tensor Networks

- Mathematics, Physics
- ArXiv
- 2018

Inspired by coarse-graining approaches used in physics, it is shown how similar algorithms can be adapted for data based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Expand

Variational ansatz-based quantum simulation of imaginary time evolution

- Computer Science, Mathematics
- npj Quantum Information
- 2019

This work proposes a variational algorithm that is hybrid, suitable for error mitigation and can exploit shallow quantum circuits, and can be implemented with current quantum computers, and uses it to find the ground-state energy of many-particle systems. Expand