Tensor Network Simulation Methods for Open Quantum Lattice Models

A complex quantum system cannot be perfectly isolated from its surroundings and is typically subject to incoherent processes. Dissipation and/or an external drive can move the system away from thermal equilibrium to a non-equilibrium regime. Often, dissipation is an unwanted feature which is minimised as much as possible, while in others cases, it can be harnessed to stabilise interesting phases of matter. The subject of this thesis is the development of tensor network techniques to probe the dynamics and steady state properties of many-body open quantum systems. Our theoretical understanding of many-body open quantum systems is greatly aided by numerical techniques. However, numerical methods are remarkably limited by the exponential growth of many-body Hilbert spaces. Tensor network methods are a class of numerical techniques which aim to circumvent the exponential growth of Hilbert space by representing the quantum state as a network of tensors. Doing so allows for an efficient representation and manipulation of the quantum state. In the first part of this thesis, a tensor network method is presented in a Cluster Mean Field framework. This method integrates a one-dimensional Lindblad master equation by dividing the system into finite sized clusters, each represented by a tensor network. The effective master equation is integrated in real time using a sweeping Time Evolving Block Decimation algorithm and the method is used to investigate the steady properties of a dissipative Jaynes-Cummings-Hubbard model with a two-photon drive where a finite size scaling of the cluster sizes allows for comparison with equilibrium models. The simulation of two-dimensional open quantum lattice models are the subject of the second part of the thesis. The Infinite Projected Entangled Pair Operator is used as an ansatz for the density matrix of a system on an infinite square lattice. The key development is a method to optimise the truncation of enlarged tensor bonds in a way which is appropriate for mixed states. The method is tested against exactly solvable cases and literature results. In the final chapter, the algorithm is applied to a dissipative anisotropic XY-model and revealing the nature of a transition parameterised by the strength of dissipation

Stable iPEPO Tensor-Network Algorithm for Dynamics of Two-Dimensional Open Quantum Lattice Models

Being able to accurately describe the dynamics steady states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite projected entangled pair operator ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimizing an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising, driven-dissipative hard-core boson, and dissipative anisotropic X Y models in non-mean-field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables us to study regimes that are accessible to current experiments but lie well beyond the applicability of existing techniques

Towards adiabatic quantum computing using compressed quantum circuits

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization.Comment: 11 pages, 8 figure

Realization of quantum signal processing on a noisy quantum computer

Quantum signal processing (QSP) is a powerful toolbox for the design of quantum algorithms and can lead to asymptotically optimal computational costs. Its realization on noisy quantum computers without fault tolerance, however, is challenging because it requires a deep quantum circuit in general. We propose a strategy to run an entire QSP protocol on noisy quantum hardware by carefully reducing overhead costs at each step. To illustrate the approach, we consider the application of Hamiltonian simulation for which QSP implements a polynomial approximation of the time evolution operator. We test the protocol by running the algorithm on Quantinuum's H1-1 trapped-ion quantum computer powered by Honeywell. In particular, we compute the time dependence of bipartite entanglement entropies for an Ising spin chain and find good agreement with exact numerical simulations. To make the best use of the device, we determine optimal experimental parameters by using a simplified error model for the hardware and numerically studying the trade-off between Hamiltonian simulation time, polynomial degree, and total accuracy. Our results are the first step in the experimental realization of QSP-based quantum algorithms.Comment: 15 pages, 8 figure

ESL Student Perceptions of VLE Effectiveness at a University in South Korea

The purpose of this study is to determine students’ perception of the advantages, effects on language skills, suggestions for improvement, and limitations regarding the use of a VLE (Blackboard) and their differences according to gender, year, number of Blackboard courses taken, and computer literacy. The respondents of this study were 686 randomly selected university students enrolled in English classes at the University of Suwon in South Korea. An adapted survey questionnaire consisting of 33 items was administered to the students. The Mean was used to determine the students’ perceptions in the four areas followed by t-test and ANOVA to determine the differences in the students’ perceptions. The results showed that the students had a somewhat disagree rating in the areas of Advantages, Language, and Limitations and somewhat agree rating in the area of Suggestions. Significant differences were found in the students’ perceptions in the four areas when grouped according to gender and computer literacy; a significant difference was found in the area of Limitations when grouped according to year; and no significant differences were found according to number of Blackboard courses taken

Regulatory T cells and their role in rheumatic diseases: a potential target for novel therapeutic development

Regulatory T cells have an important role in limiting immune reactions and are essential regulators of self-tolerance. Among them, CD4+CD25high regulatory T cells are the best-described subset. In this article, we summarize current knowledge on the phenotype, function, and development of CD4+CD25high regulatory T cells. We also review the literature on the role of these T cells in rheumatic diseases and discuss the potential for their use in immunotherapy

Classically optimized Hamiltonian simulation

Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that the classically optimized circuits can be orders of magnitude more accurate than Trotter product formulas.Comment: 6 pages, 5 figure