Unconstrained tree tensor simulations for high-dimensional quantum many-body simulations
Simone Montangero University of Padova - Department of Physics and Astronomy
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Path-integral Optimization and AdS/CFT
Tadashi Takayanagi Yukawa Institute for Theoretical Physics
Equivariant Elliptic Cohomology
Nora Ganter University of Melbourne
Special Topics in Astrophysics - Numerical Hydrodynamics - Lecture 19
Daniel Siegel University of Greifswald
Effective Fly-Bys: Gravitational Waves from Dynamical Capture Binaries
Nicholas Loutrel Princeton University
A measurement-based variational quantum eigensolver
Luca Dellantonio University of Waterloo
Query complexity and cutoffs in AdS3/CFT2
Bartek Czech Tsinghua University
Emergent classicality for large channels and states
Daniel Ranard California Institute of Technology (Caltech)
Dimensional Expressivity Analysis for Quantum Circuits
Tobias Hartung Deutsches Elektronen-Synchrotron DESY
Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry
Bianca Dittrich Perimeter Institute for Theoretical Physics
Unconstrained tree tensor simulations for high-dimensional quantum many-body simulations
Simone Montangero University of Padova - Department of Physics and Astronomy
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.Path-integral Optimization and AdS/CFT
Tadashi Takayanagi Yukawa Institute for Theoretical Physics
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.Equivariant Elliptic Cohomology
Nora Ganter University of Melbourne
The subject of equivariant elliptic cohomology finds itself at the interface of topology, string theory, affine representation theory, singularity theory and integrable systems. These connections were already known to the founders of the discipline, Grojnowski, Segal, Hopkins, Devoto, but have come into sharper focus in recent years with a number of remarkable developments happening simultaneously: First, there are the geometric constructions, due to Kitchloo, Rezk and Spong, Berwick-Evans and Tripathy, building on the older program of Stolz-Teichner, and of course Segal. These are now all known to be equivalent to Grojnowski's original definition, thanks to work of Spong. Second, there are new applications, to integrable systems (Aganagic-Okounkov, Felder-Rimanyi-Varchenko-Tarasov) and to representation theory (Yang-Zhao-Zhong, G-Ram). Finally, there is the work of Weber-Rimanyi-Kumar, who build on the techniques of Borisov and Libgober to define Schubert classes in equivariant elliptic cohomology (with an added dynamical parametre), recovering the stable envelopes in type A. This talk will give a gentle introduction to the topic and attempt an overview over these recent developments.
Special Topics in Astrophysics - Numerical Hydrodynamics - Lecture 19
Daniel Siegel University of Greifswald
Effective Fly-Bys: Gravitational Waves from Dynamical Capture Binaries
Nicholas Loutrel Princeton University
Compact binaries may be formed dynamically in globular clusters, with large (close to unity) orbital eccentricity and emitting gravitational waves within the detection band of ground based detectors. The gravitational waves from such sources resemble more a discrete set of bursts than the continuous signal of their quasi-circular counterparts. I here discuss the construction of new analytic waveforms for such systems, which rely on treating the problem as a perturbation of a parabolic fly-by. I will discuss the results of parameter estimation with these waveforms for binary black holes, and the inclusion of tidal effects for binary neutron stars.
A measurement-based variational quantum eigensolver
Luca Dellantonio University of Waterloo
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.Query complexity and cutoffs in AdS3/CFT2
Bartek Czech Tsinghua University
A quantum state is a map from operators to real numbers that are their expectation values. Evaluating this map always entails using some algorithm, for example contracting a tensor network. I propose a novel way of quantifying the complexity of a quantum state in terms of "query complexity": the number of times an efficient algorithm for computing correlation functions in the given state calls a certain subroutine. I construct such an algorithm for a general "state at a cutoff" in 1+1-dimensional field theory. The algorithm scans cutoff-sized intervals for operators whose expectation values will be computed. It can be written as a Matrix Product State, with individual matrices performing translations in the space of (cutoff-sized) intervals and reading off consecutive operator inputs. If we take the queried subroutine to be a translation in the space of intervals, query complexity counts "how many" intervals the algorithm visits--a notion of distance in the space of intervals. A unique distance function is consistent with the requisite notion of translations; therefore the query complexity of a state at a cutoff is unambiguously defined. In holographic theories, the query complexity evaluates to the integral of the Ricci scalar on a spatial slice enclosed by the bulk cutoff, which in pure AdS3 agrees with the volume proposal but otherwise departs from it.Emergent classicality for large channels and states
Daniel Ranard California Institute of Technology (Caltech)
In a quantum measurement process, classical information about the measured system spreads through the environment. In contrast, quantum information about the system becomes inaccessible to local observers. In this talk, I will present a result about quantum channels indicating that an aspect of this phenomenon is completely general. We show that for any evolution of the system and environment, for everywhere in the environment excluding an O(1)-sized region we call the "quantum Markov blanket," any locally accessible information about the system must be approximately classical, i.e. obtainable from some fixed measurement. The result strengthens the earlier result of arXiv:1310.8640 in which the excluded region was allowed to grow with total environment size. I will also discuss applications to many-body physics.
Dimensional Expressivity Analysis for Quantum Circuits
Tobias Hartung Deutsches Elektronen-Synchrotron DESY
"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)."Tensor network description of 3D Quantum Gravity and Diffeomorphism Symmetry
Bianca Dittrich Perimeter Institute for Theoretical Physics
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.Towards a realistic holographic tensor network: From p-adic CFT to (minimal) CFT2
Ling-Yan Hung Tsinghua University
The success of the Ryu-Takayanagi formula suggests a profound connection between the AdS/CFT correspondence and tensor networks. There are since many works on constructing examples, although it is very difficult to make them explicit and quantitative. We will discuss some new progress in the toy example of p-adic CFT where its tensor network dual was previously constructed explicitly [ arXiv:1703.05445 , arXiv:1812.06059, arXiv:1902.01411], and how some analogue of Einstein equation on the graph emerges as we consider RG flow of these CFTs. These progresses inspire us to find a way to construct explicit holographic tensor networks of more realistic CFTs based on their connection with topological models with one higher dimension, at least in CFT2. We will present some preliminary results and works in progress.