Computational approaches for quantum many-body systems

Slides:

Advertisements

Similar presentations

APRIL 2010 AARHUS UNIVERSITY Simulation of probed quantum many body systems.

Advertisements

Matrix product states for the absolute beginner

CONFIGURABLE QUANTUM NETWORKS FOR ADVANCED COMPUTING (CoQuNAC) Irfan Siddiqi Lawrence Berkeley National Laboratory Department of Physics, University of.

Lecture 1: A New Beginning References, contacts, etc. Why Study Many Body Physics? Basis for new Devices Complex Emergent Phenomena Describe Experiments.

Andy Ferris International summer school on new trends in computational approaches for many-body systems Orford, Québec (June 2012) Multiscale Entanglement.

1 Quantum Monte Carlo Methods Jian-Sheng Wang Dept of Computational Science, National University of Singapore.

Magnetism in systems of ultracold atoms: New problems of quantum many-body dynamics E. Altman (Weizmann), P. Barmettler (Frieburg), V. Gritsev (Harvard,

Complexity of simulating quantum systems on classical computers Barbara Terhal IBM Research.

Modeling strongly correlated electron systems using cold atoms Eugene Demler Physics Department Harvard University.

Universal Optical Operations in Quantum Information Processing Wei-Min Zhang ( Physics Dept, NCKU )

Strongly Correlated Systems of Ultracold Atoms Theory work at CUA.

Entanglement Renormalization Frontiers in Quantum Nanoscience A Sir Mark Oliphant & PITP Conference Noosa, January 2006 Guifre Vidal The University of.

An Arbitrary Two-qubit Computation in 23 Elementary Gates or Less Stephen S. Bullock and Igor L. Markov University of Michigan Departments of Mathematics.

Coherence in Spontaneous Emission Creston Herold July 8, 2013 JQI Summer School (1 st annual!)

Exploring The Quantum Department of Physics Entering the FreezerThe Age of the Qubit HOTCOLD Quantum properties emerge at extremes of energy. We work with.

CLARENDON LABORATORY PHYSICS DEPARTMENT UNIVERSITY OF OXFORD and CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE Quantum Simulation Dieter.

Introduction to Tensor Network States Sukhwinder Singh Macquarie University (Sydney)

PITP ACTIVITIES A. RESEARCH NETWORKS A set of research networks coordinates INTERNATIONAL RESEARCH COLLABORATIONS, which.

Entanglement entropy and the simulation of quantum systems Open discussion with pde2007 José Ignacio Latorre Universitat de Barcelona Benasque, September.

Max Planck Institut of Quantum Optics (Garching) New perspectives on Thermalization Aspen (NON) THERMALIZATION OF 1D SYSTEMS: numerical studies.

A study of two-dimensional quantum dot helium in a magnetic field Golam Faruk * and Orion Ciftja, Department of Electrical Engineering and Department of.

CLARENDON LABORATORY PHYSICS DEPARTMENT UNIVERSITY OF OXFORD and CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE Quantum Simulation Dieter.

Quantum Monte Carlo methods applied to ultracold gases Stefano Giorgini Istituto Nazionale per la Fisica della Materia Research and Development Center.

The Ising Model Mathematical Biology Lecture 5 James A. Glazier (Partially Based on Koonin and Meredith, Computational Physics, Chapter 8)

Tunable Molecular Many-Body Physics and the Hyperfine Molecular Hubbard Hamiltonian Michael L. Wall Department of Physics Colorado School of Mines in collaboration.

1 Accelerator Modeling (SciDAC). 2 Magneto-rotational instability and turbulent angular momentum transport (INCITE)

Tensor networks and the numerical study of quantum and classical systems on infinite lattices Román Orús School of Physical Sciences, The University of.

Introduction to MERA Sukhwinder Singh Macquarie University.

Physics “Advanced Electronic Structure” Lecture 1. Theoretical Background Contents: 1. Historical Overview. 2. Basic Equations for Interacting Electrons.

Javier Junquera Introduction to atomistic simulation methods in condensed matter Alberto García Pablo Ordejón.

Quantum Computing: An Overview for non-specialists Mikio Nakahara Department of Physics & Research Centre for Quantum Computing Kinki University, Japan.

Introduction to Quantum Computing

The quantum kicked rotator First approach to “Quantum Chaos”: take a system that is classically chaotic and quantize it.

Physics 541 A quantum approach to condensed matter physics.

Hidden topological order in one-dimensional Bose Insulators Ehud Altman Department of Condensed Matter Physics The Weizmann Institute of Science With:

An Introduction to Quantum Computation Sandy Irani Department of Computer Science University of California, Irvine.

KITPC Max Planck Institut of Quantum Optics (Garching) Tensor networks for dynamical observables in 1D systems Mari-Carmen Bañuls.

Density matrix and its application. Density matrix An alternative of state-vector (ket) representation for a certain set of state-vectors appearing with.

Physics 1202: Lecture 34 Today’s Agenda Announcements: Extra creditsExtra credits –Final-like problems –Team in class –Teams 5 & 6 HW 10 due FridayHW 10.

QUANTUM PHYSICS BY- AHRAZ, ABHYUDAI AND AKSHAY LECTURE SECTION-5 GROUP NO. 6.

Christopher Monroe Joint Quantum Institute and Department of Physics NIST and University of Maryland Quantum Computation and Simulation.

Quantum simulations of high-energy physics models MAX-PLANCK INSTITUT FÜR PHYSIK January 27th, 2015 In collaboration with J. Pachos (Leeds) S. Kühn B.

Arnau Riera, Grup QIC, Universitat de Barcelona Universität Potsdam 10 December 2009 Simulation of the Laughlin state in an optical lattice.

I shall present a many body problem which is:

Fernando G.S.L. Brandão Microsoft Research MIT 2016

Quantum Information and Everything.

Atomic BEC in microtraps: Localisation and guiding

Algorithmic simulation of far-from- equilibrium dynamics using quantum computer Walter V. Pogosov 1,2,3 1 Dukhov Research Institute of Automatics (Rosatom),

Generalized DMRG with Tree Tensor Network

10. Quantum Monte Carlo Methods

2nd Lecture: QMA & The local Hamiltonian problem

On the collapses and revivals in the Rabi Hamiltonian

14. TMMC, Flat-Histogram and Wang-Landau Method

Coupled atom-cavity system

Debasis Sadhukhan HRI, Allahabad, India

Ehud Altman Anatoli Polkovnikov Bertrand Halperin Mikhail Lukin

Anatomy of a Phase Shift

Part II New challenges in quantum many-body theory:

3rd Lecture: QMA & The local Hamiltonian problem (CNT’D)

OSU Quantum Information Seminar

COT 6200 Quantum Computing Fall 2010

“Addition” of angular momenta – Chap. 15

PHY 741 Quantum Mechanics 12-12:50 AM MWF Olin 103

“Addition” of angular momenta – Chap. 15

郑公平河南师范大学第五届全国冷原子物理和量子信息青年学者学术讨论会

Thermodynamics and Statistical Physics

Computational approaches for quantum many-body systems

Computational approaches for quantum many-body systems

Introduction to topological superconductivity and Majorana fermions

Presentation transcript:

Computational approaches for quantum many-body systems HGSFP Graduate Days SS2019 Martin Gärttner

Organizational matters 90 min lecture + 90 min programming exercises Materials: https://www.kip.uni- heidelberg.de/user/marting/teaching/ss19_hgsfp_graddays Programming exercises: Python with Jupyter notebooks → Install Anaconda with Python 3 (https://jupyter.readthedocs.io/en/latest/install.html#id3) Alternative: https://jupyter.kip.uni-heidelberg.de → log in with your uni-id Active participation and feedback is essential!

Course overview Lecture 1: Introduction to many-body spin systems Quantum Ising model, Bloch sphere, tensor structure, exact diagonalization Lecture 2: Collective spin models LMG model, symmetry, semi-classical methods, Monte Carlo Lecture 3: Entanglement Mixed states, partial trace, Schmidt decomposition Lecture 4: Tensor network states Area laws, matrix product states, tensor contraction, AKLT model Lecture 5: DMRG and other variational approaches Energy minimization, PEPS and MERA, neural quantum states

Learning goals After today you will be able to … … interpret the evolution of a single spin in the Bloch sphere picture. … explain the complexity problem of quantum many-body systems and understand many-body spin Hamiltonians. … apply the spin toolbox to build and diagonalize many-body spin Hamiltonians. … study a quantum phase transition in the transverse field Ising model.

What is a spin? https://answergarden.ch/910798 Intrinsic angular momentum Electron spin Nuclear spin Polarizations of a photon Ground and excited level of atom/ion… States of a superconducting circuit… States 0 and 1 Unit of quantum information Physical spin Pseudo spin Two-level system Qubit

Why care about spins? Simple, but still shows fundamental physical phenomena Analytically solvable many-body problems Many condensed matter physics problems come in the form of spin models (magnetism, Hubbard models map so spin models in specific cases) Quantum computers are just many-spin systems

Quantum simulation Special purpose quantum computers Emulate (spin) model Hamiltonians in controlled experiments Overcome problem of quantum complexity Numerical methods for spin models Benchmark quantum simulators in tractable regimes Testing approximations using comparison to experiment Examples: Trapped ions (Bollinger, Monroe, Blatt) Rydberg atoms (Lukin, Broways, Weidemüller) Ultracold atoms in optical lattices (Greiner, Bloch) Nature 484, 489-492 (2012) Nature 551, 601-604 (2017) Nat. Phys. 8, 277-284 (2012) Nature 551, 579-584 (2017) Nature 561, 79-82 (2018) Science 342, 954-956 (2013) Nature 545, 462-466 (2017) Science 349, 842 (2015)