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Venue: R620, Physics Building, NTHU.

Day1, 8/28: DMRG and MPS
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Steven White: (online)
Introduction to entanglement, DMRG, and tensor networks.

Abstract: Quantum mechanics of many particles is exponentially complex, but many states of interest--including almost all ground states--are simpler because they have low entanglement.  I will introduce what entanglement is, how to measure it, and how it naturally leads to approximate approaches for solving quantum systems, including the original method, the density matrix renormalization group.  I will also discuss a few of the many extensions since the development of DMRG, which now comprise the broad field of tensor networks.
10:15-10:45 Coffee break: Morning break
10:45-12:00 Ian McCulloch:
Matrix Product Operators.

Abstract: I will introduce Matrix Product Operators (MPO's) as a way to represent observables and other operators in the form of a tensor network.  As well as being a convenient form for use with MPS algorithms, MPO techniques can be used to obtain many useful quantities, such as higher moments of operators and useful approximations to the time evolution operator.
12:00-14:00 Take photo & Lunch
14:00-15:15 Manuel Schneider:
Projected Entangled Pair States (PEPS) and tensor network states in more than one dimension.

Abstract: Matrix Product States (MPSs) provide a powerful toolbox to study many body systems in one spatial dimension. However, they are not well suited for systems in more than one dimension because of the limited entanglement entropy of the states they can represent. Therefore, other tensor network architectures are needed. I will give an overview of different tensor network states for approximating physical states in more than one spatial dimension. The Projected Entangled Pair State (PEPS) will be discussed in more details.  A PEPS is a direct generalization of an MPS in higher dimensions.  The ground state of a Hamiltonian can be simulated with an imaginary time evolution acting on a PEPS. Further approximations are needed during the tensor update process and when calculating expectation values. The details of the algorithm will be explained for systems in two spatial dimensions.
15:15-15:45 Coffee break: Afternoon break
15:45-18:00 Tutorial: Matrix product state applications
Day2, 8/29: 2D Tensor Network
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Chia-Min Chung:
Simulations for finite-temperature systems using Tensor Network.

Abstract: In this talk I will introduce how to use Tensor Network to represent a density matrix at finite temperature. More specifically, I will introduce two algorithms for finite temperature systems. The first one is called purification, which represents a density matrix by a pure state. The second one is called minimally entangled typical thermal states (METTS), which combine the tensor network and Monte Carlo simulations. I will discuss the advantages and the limitations of the both algorithms in terms of entanglement.
10:15-10:45 Coffee break: Morning break
10:45-12:00 Pochung Chen:
Real Space Renormalization Group via Tenor Network.

Abstract: In this talk, I will discuss how to reincarnate the concept of real space renormalization group in modern tensor network language. As an example, I perform tensor network based finite-size scaling analysis for the two-dimensional classical Ising model. I consider an infinite strip and use the higher-order tensor renormalization group method to renormalize the transfer matrix, from which the correlation length, spontaneous magnetization, and latent heat can be evaluated. I show that, by applying standard finite-size scaling techniques, critical temperature Tc and critical exponents nu, beta, alpha can be accurately determined. Furthermore, the conformal data can be accurately extracted. In contrast to the early real space renormalization group method, here the results can be systematically improved. In addition, I will discuss the nature crossover length scale included by the finite bond dimension. Finally, I will discuss the quantum-classical correspondence and how to define entanglement for the classical models and the link to the conformal field theory.
12:00-14:00 Lunch
14:00-15:15 Jutho Haegeman: (online)
Time-dependence with matrix product states.  

Abstract: We will explain how to use matrix product states to find approximate solutions of the time-dependent Schrodinger equation. We will discuss the time-dependent variational principle, which projects the Schrodinger equation within the manifold of matrix product states, and elaborate on some of its properties and its relation to variational optimisation. We will also discuss methods that approximate the time-evolution operator itself, which can then be applied to matrix product states. This typically increases the bond dimension and requires a subsequent truncation step. Finally, we will highlight some relevant applications of these methods.
15:15-15:45 Coffee break: Afternoon break
15:45-18:00 Tutorial: 2D tensor network

Day3, 8/30: Applications of Tensor Network and Quantum Computing
Time Title/Speaker
08:30-09:00 Registration
09:00-10:15 Miles Stoudenmire: (online)
Quantum-Inspired Classical Algorithms for Functions of Continuous Variables.

Abstract: Quantum computing has primarily been motivated by the goal of running quantum algorithms, in the form of quantum circuits, on specially built quantum hardware. But what if we can run certain classes of quantum circuits on classical hardware for a wide range of inputs? Could we get the benefits of quantum computing without a quantum computer? Surprisingly, the answer may be yes. I will introduce a technique for representing functions of continuous variables in terms of quantum states which can generally be captured very well by tensor networks. Important operations on these functions, such as convolving two functions or taking a Fourier transform, can be written as very compact matrix product operators (MPO). In the case of taking a Fourier transform, the resulting method can systematically be faster and scale better than the fast Fourier transform (FFT). I will discuss current use cases for tasks such as solving differential equations and applications to classical and quantum physics research.
10:15-10:45 Coffee break: Morning break
10:45-12:00 Ying-Jer Kao:
When tensor networks meet quantum circuits.

Abstract: In this talk, I will discuss the role tensor networks can play in the modern era of circuit-based quantum computing. First, I will introduce how to map tensor networks to quantum circuits and some examples of implementing classical TN algorithms on quantum computers. Secondly, I will introduce a hybrid framework of synergy of the classical tensor networks and quantum circuits to perform machine learning tasks. Finally, I will discuss potential directions going forward.
12:00-14:00 Lunch
14:00-15:15 Hsiu-Chuan Hsu: Basics of quantum computing

This talk starts from the basic concepts, including the circuit model, Bloch sphere, entanglement generation and measurement. After the fundamentals, examples of simulations on quantum computers are introduced and discussed. Lastly, the challenge of noisy qubits and noise mitigation methods are addressed.

Notice for the tutorial:

In order to run the tutorial session smoothly, it is suggested that the attendees prepare a python environment with qiskit and register an IBM Q account beforehand. The qiskit installation can be found here . To register for a user account, go to the IBM Q website and click ‘Create an IBMid account’. 

After successful registration and login, click the
  This is an image

icon on the top right corner,  go to ‘Account settings,’  and find the “API token.” We will copy the token into the code in the tutorial.
15:15-15:45 Coffee break: Afternoon break
15:45-18:00 Tutorial for quantum computing: Hsiu-Chuan Hsu