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Showing 1 to 14 of 14 for “"matrix product states"”.
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Exotic vortices in superfluids and matrix product states for quantum optimization and machine learning
… is energetically favorable in the ground state. Matrix product state (MPS) based methods are currently regarded as one of the most powerful tools to study the low-energy physics of one-dimensional many-body quantum systems. In this work we find a connection between MPS in the left canonical form …
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Finite and infinite matrix product states for Gutzwiller projected mean-field wavefunctions and their applications to quantum spin systems
… and understanding magnetically disordered ground states of 2D or quasi-2D quantum spin systems has been an important research theme in recent years. Many of these states show exotic quantum orders that cannot be understood in the context of Landau-Ginzburg order parameters. With few exceptions, 2D …
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Algebraic, geometric and numerical methods for Tensor Network Varieties
… in cases relevant for applications, such as matrix product states and projected entangled pairs states. We then focus on the study of the linear span of uniform matrix product states, which are translation invariant tensor network varieties associated to the cyclic graph. We provide …
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Implementing a Lattice Formulation of the Schwinger Modelwith Periodic Boundary Conditions Using Tensor Networks
… the local optimization steps used in the density matrix renormalization group (DMRG) algorithm for finding the ground state of a quantum system. However, due to practical constraints, I still use matrix product states and matrix product operators with open boundary conditions. I demonstrate the …
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Algebraic geometry for tensor networks, matrix multiplication, and flag matroids
… tensor networks, and more specifically: uniform matrix product states. We use methods from nonlinear algebra and algebraic geometry to answer questions about topology, defining equations, and identifiability of uniform matrix product states. By an interplay of theorems from algebra, geometry, and …
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Characterizing and measuring properties of continuous-variable quantum states
… to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also …
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EXOTIC PHASES IN A SPIN-1 BOSONIC FLUX SYSTEM
We study, using the optimisation of matrix product states, the ground state properties of an interacting spin-1 hardcore boson model on a ladder in a transverse magnetic field at zero temperature. At unit filling in the strong-interacting regime, we observe a Mott insulator phase characterised by a …
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Efficient classical simulation of spin networks
… the dynamics of more complicated spin networks. Matrix Product States (MPS) define a wavefunction anzatz that approximates slightly entangled quantum systems using poly(n) parameters. The MPS representation is exponentially smaller than the exact representation, which involves 0(2n) parameters. …
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Interrogating the void : the difficulty of extracting information from many-body systems
… the dynamics of the Iizuka-Polchinksi model, a matrix model of a black hole whose response functions can be calculated exactly. Second, I will study the average information content of subsystems of a larger system. In particular, I will improve a result of Page giving the average entanglement …
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Eigenvalues and low energy eigenvectors of quantum many-body systems
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin systems on a line with an improvement on the notation. The rest of this thesis is divided into two parts. The first part is devoted to eigenvalues of quantum many-body systems (QMBS). I introduce …
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Variational Algorithms and Resources for Near-Term Quantum Simulation
… to the case of degenerate Hamiltonians. Using matrix product states we evaluate the non-stabilizer quantum resources needed to represent thermalized subregions of a chaotic Potts model, which we use to address the feasibility for classical simulation of quantum hydrodynamics.
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Studies in: entanglement entropy of two dimensional quasi-topological quantum field theory and geometry of the exact renormalization group and higher spin holography
… network representation, or more precisely, matrix product state (MPS) representation, of the quantum states of QTFT. We demonstrate that the two calculations are in agreement. Part II: Geometry of the Exact Renormalization Group and Higher Spin Holography We consider the Wilson-Polchinski …
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Many-body entangled dynamics of closed and open systems for quantum simulators
… available in our open source package Open Source Matrix Product States. The algorithms contain a selection of state-of-the-art methods for closed and open quantum system, e.g., matrix product density operators as tensor network type and the time-dependent variational principle as time evolution …
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Tensor network states simulations of exciton-phonon quantum dynamics for applications in artifcial light-harvesting
… I developed a powerful tree tensor network states (TTNS) method that finds an optimally compressed explicit representation of the combined electronic and vibrational quantum state. With TTNS it is possible to simulate exciton-phonon quantum dynamics from small molecules to larger complexes, …