TENSOR NETWORKS: FROM SIMULATIONS TO HOLOGRAPHY III

America/Toronto
Perimeter Institute

Perimeter Institute

Karl Jansen (Deutsches Elektronen-Synchrotron), Lena Funcke (Perimeter Institute), Michal Heller (Max Planck Institute for Gravitational Physics), Stefan Kühn (The Cyprus Institute), Sukhbinder Singh (Max Planck Institute for Gravitational Physics), Volker Schomerus (Deutsches Elektronen-Synchrotron)
Description

This workshop aims to stimulate the exchange between different research areas where tensor network techniques are applied, in particular lattice gauge theories, holography and condensed matter physics.

Registration
Registration for "Tensor Networks: From Simulations to Holography III"
Participants
  • Aaron Szasz
  • Aleksandr Berezutskii
  • Alexander Jahn
  • Amit Anand
  • Anderson Misobuchi
  • Andreas Bauer
  • Andreas Wipf
  • Andrew Frey
  • Ashley Milsted
  • Augustine Kshetrimayum
  • Ben Kitching-Morley
  • Beni Yoshida
  • Bianca Dittrich
  • ChunJun Cao
  • Clement Delcamp
  • David Hui
  • David Kaplan
  • David Schaich
  • Dimitrios Bachtis
  • Dimitrios Patramanis
  • Dominik Neuenfeld
  • Dongsheng Ge
  • Eduardo Bardales
  • Esperanza Lopez
  • Francisco Zuniga Frias
  • Georgios Chnitidis
  • Georgios Styliaris
  • Giancarlo Camilo
  • Giovanni Ramirez Garcia
  • Guifre Vidal
  • Haoxing Du
  • Isaac De Vlugt
  • Ivan Kukuljan
  • Jacob Bridgeman
  • James Osborn
  • Jamie Gill
  • Jan Boruch
  • Jan de Boer
  • Javier Molina-Vilaplana
  • Jeff greensite
  • Johannes Knaute
  • Jon Yard
  • José Garre-Rubio
  • Juan Carrasquilla
  • Jutho Haegeman
  • Karl Jansen
  • Keun-Young Kim
  • Kevin Slagle
  • Kritika Khanwal
  • Lena Funcke
  • Leo Shaposhnik
  • Lorenz Mayer
  • Luan Martins Veríssimo
  • Manuel Schneider
  • Marcel Niedermeier
  • Matteo Rizzi
  • Matthew Steinberg
  • Matthew Wingate
  • Matthias Volk
  • MOHAMMED SHITU
  • Mohsin Iqbal
  • Muhammad Asaduzzaman
  • Namrata Joshi
  • Nelson Lachini
  • Nick Hunter-Jones
  • Nouman Butt
  • Patrick Dreher
  • Pawel Caputa
  • Pedro Ribeiro
  • Philippe Faist
  • Przemek Witaszczyk
  • Raghav Govind Jha
  • Riley Chien
  • Robert Myers
  • Roger Melko
  • Roman Orus
  • Sam Cree
  • Samuel Desrosiers
  • Sanjoy Saha
  • Sergey Pirogov
  • Shan-Ming Ruan
  • Shawna Skelton
  • ShengHsuan Lin
  • Simon Catterall
  • Simran Singh
  • Stam Nicolis
  • Stefan Kühn
  • Sujay Kazi
  • Sukhbinder Singh
  • Tibor Rakovszky
  • Tim Hsieh
  • Timo Eckstein
  • Troy Sewell
  • Tucker Carrington
  • Xiao-Yong Jin
    • 08:00 08:50
      Talk 1 50m
      Speaker: Subir Sachdev (Harvard University)
    • 08:50 09:00
      Coffee Break 10m
    • 09:00 09:50
      Talk 2 50m
      Speaker: Frank Verstraete (University of Vienna & University of Ghent)
    • 09:50 13:00
      Extended Break 3h 10m
    • 13:00 13:50
      Talk 3 50m
      Speaker: Jens Eisert (Free University of Berlin)
    • 13:50 14:00
      Coffee Break 10m
    • 14:00 14:50
      Tensor networks for LGT: beyond 1D 50m

      The suitability of tensor network ansatzes for the description of physically relevant states in one dimensional lattice gauge theories (LGT) has been demonstrated in the last years by a large amount of systematic studies, including abelian and non-abelian LGTs, and including scenarios where traditional Monte Carlo approaches fail due to a sign problem. While this establishes a solid motivation to extend the program to higher dimensions, a similar systematic study in two dimensions using PEPS requires dealing with specific considerations. Besides a larger computational costs associated to the higher spatial dimension, the presence of plaquette terms in LGTs hinders the efficiency of the most up-to-date PEPS algorithms. With a newly developed update strategy, nevertheless, such terms can be treated by the most efficient techniques. We have used this method to perform the first ab initio iPEPS study of a LGT in 2+1 dimensions: a Z3 invariant model, for which we have determined the phase diagram.

      Speaker: Mari-Carmen Banuls (Max Planck Institute of Quantum Optics)
    • 14:50 15:00
      Coffee Break 10m
    • 15:00 18:00
      Informal Hang Out Time via Remo
    • 08:00 08:50
      Quantum Cellular Automata, Tensor Networks, and Area Laws 50m

      Quantum Cellular Automata are unitary maps that preserve locality and respect causality. I will show that in one spatial dimension they correspond to matrix product unitary operators, and that one can classify them in the presence of symmetries, giving rise to phenomenon analogous to symmetry protection. I will then show that in higher dimensions, they correspond to other tensor networks that fulfill an extra condition and whose bond dimension does not grow with the system size. As a result, they satisfy an area law for the entanglement entropy they can create. I will also define other classes of non-unitary maps, the so-called quantum channels, that either respect causality or preserve locality and show that, whereas the latter obey an area law for the amount of quantum correlations they can create, as measured by the quantum mutual information, the former may violate it. Additionally, neither of them can be expressed as tensor networks with a bond dimension that is independent of the system size.

      Speaker: Ignacio Cirac (Max Planck Institute of Quantum Optics)
    • 08:50 09:00
      Coffee Break 10m
    • 09:00 09:50
      Fun with replicas and holographic tensor networks 50m
      Speaker: Michael Walter (University of Amsterdam)
    • 09:50 13:00
      Extended Break 3h 10m
    • 13:00 13:15
      A tensor-network approach to fixed-point models of topological phases 15m
      Speaker: Andreas Bauer (Free University Berlin)
    • 13:15 13:30
      Custom Fermionic Codes for Quantum Simulation 15m
      Speaker: Riley Chien (Dartmouth College)
    • 13:30 13:45
      Quantum Extremal Islands Made Easy: Complexity on the brane 15m

      We examine holographic complexity in the doubly holographic model to study quantum extremal islands. We focus on the holographic complexity=volume (CV) proposal for boundary subregions in the island phase. Exploiting the Fefferman-Graham expansion of the metric and other geometric quantities near the brane, we derive the leading contributions to the complexity and interpret these in terms of the generalized volume of the island derived from the higher curvature action for the brane gravity. Motivated by these results, we propose a generalization of the CV proposal for higher curvature theories of gravity. Further, we provide two consistency checks of our proposal by studying Gauss-Bonnet gravity and f(R) gravity in the bulk.

      Speaker: Shan-Ming Ruan (Perimeter Institute)
    • 13:45 14:00
      Coffee Break 15m
    • 14:00 14:50
      Talk 7 50m
      Speaker: Steven White (University of California, Irvine)
    • 14:50 15:00
      Coffee Break 10m
    • 15:00 18:00
      Informal Hang Out Time via Remo
    • 08:00 08:50
      Talk 8 50m
      Speaker: Ling-Yan Hung (Fudan University )
    • 08:50 09:00
      Coffee Break 10m
    • 09:00 09:50
      Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry 50m

      In contrast to the 4D case, there are well understood theories of quantum gravity for the 3D case. Indeed, 3D general relativity constitutes a topological field theory (of BF or equivalently Chern-Simons type) and can be quantized as such. The resulting quantum theory of gravity offers many interesting lessons for the 4D case.

      In this talk I will discuss the quantum theory which results from quantizing 3D gravity as a topological field theory. This will also allow a derivation of a holographic boundary theory, together with a geometric interpretation of the boundary observables.

      The resulting structures can be interpreted in terms of tensor networks, which provide states of the boundary theory.
      I will explain how a choice of network structure and bond dimensions constitutes a complete gauge fixing of the diffeomorphism symmetry in the gravitational bulk system. The theory provides a consistent set of rules for changing the gauge fixing and with it the tensor network structure. This provides an example of how diffeomorphism symmetry can be realized in a tensor network based framework.

      I will close with some remarks on the 4D case and the challenges we face there.

      Speaker: Bianca Dittrich (Perimeter Institute)
    • 09:50 13:00
      Extended Break 3h 10m
    • 13:00 13:50
      Dimensional Expressivity Analysis for Quantum Circuits 50m

      "Besides tensor networks, quantum computations (QC) as well use a Hamiltonian formulation to solve physical problems. Although QC are presently very limited, since only small number of qubits are available, they have the principal advantage that they straightforwardly scale to higher dimensions. A standard tool in the QC approach are Variational Quantum Simulations (VQS) which form a class of hybrid quantum-classical algorithms for solving optimization problems. For example, the objective may be to find the ground state of a Hamiltonian by minimizing the energy. As such, VQS use parametric quantum circuit designs to generate a family of quantum states (e.g., states obeying physical symmetries) and efficiently evaluate a cost function for the given set of variational parameters (e.g., energy of the current quantum state) on a quantum device. The optimization is then performed using a classical feedback loop based on the measurement outcomes of the quantum device.

      In the case of energy minimization, the optimal parameter set therefore encodes the ground state corresponding to the given Hamiltonian provided that the parametric quantum circuit is able to encode the ground state. Hence, the design of parametric quantum circuits is subject to two competing drivers. On one hand, the set of states, that can be generated by the parametric quantum circuit, has to be large enough to contain the ground state. On the other hand, the circuit should contain as few quantum gates as possible to minimize noise from the quantum device. In other words, when designing a parametric quantum circuit we want to ensure that there are no redundant parameters.

      In this talk, I will consider the parametric quantum circuit as a map from parameter space to the state space of the quantum device. Using this point of view, the set of generated states forms a manifold. If the quantum circuit is free from redundant parameters, then the number of parameters is precisely the dimension of the manifold of states. This leads us to the notion of dimensional expressivity analysis. I will discuss means of analyzing a given parametric design in order to remove redundant parameters as well as any unwanted symmetries (e.g., a gate whose only effect is a change in global phase). Time permitting, I may discuss the manifold of physical states as well since this will allow us to decide whether or not a parametric quantum circuit can express all physical states (thereby ensuring that the ground state can be expressed as well)."

      Speaker: Tobias Hartung (Deutsches Elektronen-Synchrotron)
    • 13:50 14:00
      Coffee Break 10m
    • 14:00 14:20
      Discussion Session: Prospects of continuous Tensor Networks versus discrete Tensor Networks for field theories
    • 14:20 14:40
      Discussion Session: Lattice gauge theories with Tensor Networks
    • 14:40 15:00
      Discussion Session: Tensor Networks in Holography and Gravity
    • 15:00 18:00
      Informal Hang Out Time via Remo
    • 08:00 08:50
      Talk 10 50m
      Speaker: Bartek Czech (Tsinghua University)
    • 08:50 09:00
      Coffee Break 10m
    • 09:00 09:50
      Thirring model from tensor networks - phase structure and real-time dynamics 50m

      In this talk, we report on our studies of the Thirring model using MPS techniques. The Thirring model is a quantum field theory describing self-interactions of the Dirac field in 1+1 dimensions. It evinces a non-trivial zero-temperature phase structure in the mass-interaction plane, with gapless (critical) and gapped (massive) phases separated by a Berezinskii-Kosterlitz-Thousless-type transition. To investigate this phase structure, we examined the entanglement entropy, the fermion bilinear condensate and two types of correlation functions. We also show our preliminary results of the real-time dynamics of the Thirring model, using variational uniform MPS and time-dependent variational principle.
      Co-Authors:
      Mari Carmen Banuls, Max-Planck Institute of Quantum Optics
      Hao-Ti Hung, National Taiwan University
      Ying-Jer Kao, National Taiwan University
      C.-J. David Lin, National Chiao-Tung University
      Yu-Ping Lin, University of Colorado at Boulder
      Amit Singh, National Chiao-Tung University
      David T. L. Tan, National Chiao-Tung University

      Speaker: Krzysztof Cichy (Adam Mickiewicz University)
    • 09:50 13:00
      Extended Break 3h 10m
    • 13:00 13:50
      A measurement-based variational quantum eigensolver 50m

      In this talk I will speak about the meeting point of two models that have raised interest in the community in the last years. From one side, we looked at measurement-based quantum computing (MBQC), which is an alternative to circuit-based quantum computing. Instead of modifying a state via gates, MBQC achieves the same result by measuring auxiliary qubits in a graph. From the other side, we considered variational quantum eigensolvers (VQEs), that are one of the most successful tools for exploiting quantum computers in the NISQ era. In our work, we present two measurement-based VQE schemes. The first introduces a new approach for constructing variational families. The second provides a translation of circuit-based to measurement-based schemes. Both schemes offer problem-specific advantages in terms of the required resources and coherence times. We apply them, respectively, to the Schwinger model and the two-dimensional Z(2) lattice gauge theory.

      Speaker: Luca Dellantonio (University of Waterloo)
    • 13:50 14:00
      Coffee Break 10m
    • 14:00 14:50
      Extracting universal data of critical quantum spin chains from periodic uniform matrix product states 50m

      We explain how periodic uniform matrix product states (puMPS) can be used to extract universal data of critical quantum spin chains. We show that puMPS and puMPS Bloch states accurately capture the ground state and low-energy excited states of critical quantum spin chains up to several hundreds of spins. This enables us to extract (i) scaling dimensions, conformal spins of scaling operators, (ii) spectral renormalization group flows between CFTs, (iii) lattice realizations of scaling operators, and operator product expansion coefficients, (iv) emergent symmetries such as superconformal symmetry, and (v) universal tripartite entanglement of the ground state, including entanglement of purification and reflected entropy. We give examples how each of these is achieved and discuss potential applications to open problems.

      In collaboration with Ash Milsted, Mike Zaletel, Guifre Vidal

      Speaker: Yijian Zou (X, the Moonshot Factory)
    • 14:50 15:00
      Coffee Break 10m
    • 15:00 18:00
      Informal Hang Out Time via Remo
    • 08:00 08:50
      Path-integral Optimization and AdS/CFT 50m

      In this talk we will start with a review of path-integraloptimization, which provides a useful description of non-unitary tensor networks for Euclidean path-integrals in CFTs. We will explain an emergence of AdS geometry in this method and an interpretation as a computational complexity. Next we will give its application to analytical calculations of entanglement of purification, which was quite recently reproduced by numerical calculations. Finally, we would like to present a derivation of a path-integral optimization method directly from the AdS/CFT.

      Speaker: Tadashi Takayanagi (Yukawa Institute for Theoretical Physics)
    • 08:50 09:00
      Coffee Break 10m
    • 09:00 09:50
      Unconstrained tree tensor simulations for high-dimensional quantum many-body simulations 50m

      We present some recent results on the development of efficient unconstrained tree tensor networks algorithms and their application to high-dimensional many-body quantum systems. In particular, we present our results on topological two-dimensional systems, two-dimensional Rydberg atom systems, and two- and three-dimensional lattice gauge theories in presence of fermonic matter. Finally, we present their application to the study of open many-body quantum systems and in particular to the computation of the entanglement of formation in critical many-body quantum systems, resulting in the generalization of the Calabrese-Cardy formula to open systems.

      Speaker: Simone Montangero (Padova University)
    • 09:50 13:00
      Extended Break 3h 10m
    • 13:00 13:50
      An overview of Wavelets and MERA 50m

      The use of wavelet-based constructions has led to significant progress in the analytic understanding of holographic tensor networks, such as the multi-scale entanglement renormalization ansatz (MERA). In this talk I will give an overview of the (past and more recently established) connections between wavelets and MERA, and the discuss the important results that have followed. I will also discuss work currently underway that exploits the wavelet-MERA connection in order to produce new families of wavelets that are optimal for certain tasks, such as image compression.

      Speaker: Glen Evenbly (University of Sherbrooke)
    • 13:50 14:00
      Coffee Break 10m
    • 14:00 14:20
      Discussion Session: Higher-dimensional gauge theories with Tensor Networks
    • 14:20 14:40
      Discussion Session: Machine learning and Tensor Networks
    • 14:40 15:00
      Discussion Session: Quantum computing and Tensor Networks
    • 15:00 18:00
      Informal Hang Out Time via Remo