Optimization schemes for unitary tensor-network circuit

Abstract

We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also the conjugate-gradient method with an effective line search. We present the benchmarking calculations for different network structures by studying the Heisenberg model in a strongly disordered magnetic field and a tensor-network $QR$-decomposition.

arXiv comment9 pages, 6 figures, sample source codes are available at https://github.com/rezah/unitary-tensor-network-operator

References in corpus (50)

• Entanglement Entropy and Quantum Field Theory
• Chaos and Quantum Thermalization
• Entanglement in quantum critical phenomena
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The many-body localization phase transition
• Entanglement spectrum of a topological phase in one dimension
• Entanglement renormalization
• An Area Law for One Dimensional Quantum Systems
• Many-body localization edge in the random-field Heisenberg chain
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classifying quantum phases using Matrix Product States and PEPS
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Many-body localization in a disordered quantum Ising chain
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Variational ansatz-based quantum simulation of imaginary time evolution
• Area laws in a many-body localized state and its implications for topological order
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Algorithms for entanglement renormalization
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Continuous Matrix Product States for Quantum Fields
• Tensor network states and geometry
• Entanglement renormalization for quantum fields
• Real- and imaginary-time evolution with compressed quantum circuits
• Tensor network study of the Shastry-Sutherland model in zero magnetic field
• Hyper-optimized tensor network contraction
• Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
• Ground State and Finite Temperature Lanczos Methods
• Isometric Tensor Network States in Two Dimensions
• Unifying Projected Entangled Pair States contractions
• Finding matrix product state representations of highly-excited eigenstates of many-body localized Hamiltonians
• Many-body localisation implies that eigenvectors are matrix-product states
• Power-Law Entanglement Spectrum in Many-Body Localized Phases
• A tensor product state approach to spin-1/2 square $J_1$-$J_2$ antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
• Efficient variational diagonalization of fully many-body localized Hamiltonians
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Quantum critical phase with infinite projected entangled paired states
• Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations
• Efficient representation of fully many-body localized systems using tensor networks
• Applying the variational principle to (1+1)-dimensional quantum field theories
• Conversion of projected entangled pair states into a canonical form
• A ground state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Quantum phase diagram of spin-$1$ $J_1-J_2$ Heisenberg model on the square lattice: an infinite projected entangled-pair state and density matrix renormalization group study
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain

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