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Showing 1 to 11 of 11 for “"Matrix Product State"”.
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Local Hamiltonians in quantum computation
… with local Hamiltonians and finding their ground state properties. I give a numerical method for finding the ground state of translationally invariant Hamiltonians on an infinite tree. This method is based on imaginary time evolution within the Matrix Product State ansatz, and uses a new method …
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Many-body localization and tensor networks
… systems. Chapter 3 studies the shift-and-invert matrix product state method for obtaining highly excited states of MBL systems. Chapter 4 studies an efficient full diagonalization method using Wegner unitary gates. Chapter 5 studies the distribution of the entanglement entropy in the MBL-ergodic …
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Dynamics of quantum many-body systems with long-range interactions
… topic we address is a new method of quantum state estimation, certified Matrix Product State (MPS) tomography, which has potential applications in regimes unreachable by full quantum state tomography. The investigation of quantum many-body systems often goes beyond analytically solvable …
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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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Efficiently Learning, Testing, and Simulating Quantum Many-Body Systems
… of entanglement in a pure many-body quantum state. This algorithm tests whether a quantum state is a matrix product state of certain bond dimension in the property testing model. We provide both upper and lower bounds on the number of identical copies of the quantum state required by this …
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Numerical analysis for quantum electrodynamics in the ultrastrong coupling regime
In the race towards achieving true quantum advantage, the development of a scalable and reliable quantum computer demands lower gate error rates, longer qubit coherence times, increased qubit connectivity, and enhanced controllability of qubit couplings. Addressing these challenges necessitates …
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Dynamics of Chiral Fermions
… renormalization group flows. Finally, we present matrix product state simulations of the 3450 lattice chiral fermion model in two dimensions. We consider a lattice setup introduced by Wang and Wen which realises two left and two right-moving fermions on one edge of a thin Chern insulator. The …
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Exotic vortices in superfluids and matrix product states for quantum optimization and machine learning
… between the two components. We study the ground state of an infinite system of vortex molecules in two dimensions, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of intercomponent interactions …
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Numerical studies on many-body localization
… systems, which relies on the idea of the eigenstate thermalization hypothesis (ETH). I then present localization as a phenomenon that breaks ETH, both in its single-particle as in its many-body versions. I discuss some of the main aspects that are known about MBL, as well as some of its open …
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TENSOR NETWORKS FOR OPEN QUANTUM SYSTEMS
… resources needed to manipulate quantum many-body states typically scale exponentially in the number of their constituents, making the simulation very difficult or outright impossible even at modest sizes. Tensor networks provide a powerful mathematical tool to address this issue: by efficiently …