Efficient Tensor Network ansatz for high-dimensional quantum many-body problems

Abstract

We introduce a novel tensor network structure augmenting the well-established Tree Tensor Network representation of a quantum many-body wave function. The new structure satisfies the area law in high dimensions remaining efficiently manipulatable and scalable. We benchmark this novel approach against paradigmatic two-dimensional spin models demonstrating unprecedented precision and system sizes. Finally, we compute the ground state phase diagram of two-dimensional lattice Rydberg atoms in optical tweezers observing non-trivial phases and quantum phase transitions, providing realistic benchmarks for current and future two-dimensional quantum simulations.

11 pages, 9 figures

References in corpus (70)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• Probing many-body dynamics on a 51-atom quantum simulator
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Real time evolution using the density matrix renormalization group
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Entanglement renormalization
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
• Matrix product states represent ground states faithfully
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• The ALPS project release 1.3: open source software for strongly correlated systems
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Generation and manipulation of Schrödinger cat states in Rydberg atom arrays
• Parallel implementation of high-fidelity multi-qubit gates with neutral atoms
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Criticality, the area law, and the computational power of PEPS
• Classical simulation of quantum many-body systems with a tree tensor network
• Tensor networks for complex quantum systems
• Synthetic three-dimensional atomic structures assembled atom by atom
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Simulating Lattice Gauge Theories within Quantum Technologies
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Algorithms for entanglement renormalization
• Valence Bond Solids for Quantum Computation
• The computational complexity of PEPS
• Dynamical crystallization in a low-dimensional Rydberg gas
• A subradiant optical mirror formed by a single structured atomic layer
• Lattice gauge theories and string dynamics in Rydberg atom quantum simulators
• Lattice gauge theories simulations in the quantum information era
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Algorithms for finite Projected Entangled Pair States
• Applications of quantum Monte Carlo methods in condensed systems
• Review on novel methods for lattice gauge theories
• Time integration of tensor trains
• Lecture Notes of Tensor Network Contractions
• Observing the space- and time-dependent growth of correlations in dynamically tuned synthetic Ising antiferromagnets
• Entanglement renormalization in two spatial dimensions
• Cross-Platform Verification of Intermediate Scale Quantum Devices
• Three-dimensional trapping of individual Rydberg atoms in ponderomotive bottle beam traps
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• Emerging 2D Gauge theories in Rydberg configurable arrays
• Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Lattice Gauge Tensor Networks
• Finite-range interacting Ising quantum magnets with Rydberg atoms in optical lattices - From Rydberg superatoms to crystallization
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks
• Time Dependent Variational Principle for Tree Tensor Networks
• Simulation of time evolution with the MERA
• Critical properties of homogeneous binary trees
• Scalable and Parallel Tweezer Gates for Quantum Computing with Long Ion Strings
• Contracting projected entangled pair states is average-case hard
• Real-time-dynamics quantum simulation of (1+1)-D lattice QED with Rydberg atoms
• Variational Monte Carlo simulation with tensor networks of a pure ${\mathbb{Z}}_3$ gauge theory in (2+1)d
• Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
• The area law and real-space renormalization
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models
• Superfluid to Mott transition in a Bose-Hubbard ring: Persistent currents and defect formation
• Gradient optimization of fermionic projected entangled pair states on directed lattices
• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model
• Zero bias anomaly in a two dimensional granular insulator

Cited by in corpus (46)

• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Tensor Network Algorithms: a Route Map
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Entanglement generation in $(1+1)D$ QED scattering processes
• Emergent ${\mathbb{Z}}_2$ gauge theories and topological excitations in Rydberg atom arrays
• Emergent glassy behavior in a kagome Rydberg atom array
• Lattice Boltzmann-Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number
• Quantum Neuronal Sensing of Quantum Many-Body States on a 61-Qubit Programmable Superconducting Processor
• Digitising SU(2) Gauge Fields and the Freezing Transition
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Correlation-Enhanced Neural Networks as Interpretable Variational Quantum States
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Highly resolved spectral functions of two-dimensional systems with neural quantum states
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Stabilizer disentangling of conformal field theories
• Quantum-assisted Monte Carlo algorithms for fermions
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids
• Neural Projected Quantum Dynamics: a systematic study
• Loop-Free Tensor Networks for High-Energy Physics
• Matrix Product States with Backflow correlations
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Entanglement in the quantum phases of an unfrustrated Rydberg atom array
• Computing time-periodic steady-state currents via the time evolution of tensor network states
• Supervised learning of random quantum circuits via scalable neural networks
• Ideal flat and resolved SU(3) Landau levels in three dimensions
• Hybrid Tree Tensor Networks for quantum simulation
• Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
• Exploring Bosonic and Fermionic Link Models on $(3+1)-$d tubes
• Unsupervised Learning of Rydberg Atom Array Phase Diagram with Siamese Neural Networks
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Digital quantum simulation of lattice fermion theories with local encoding
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer
• Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Bulk and Boundary Quantum Phase Transitions in a Square Rydberg Atom Array
• Doped resonating-valence-bond states: Robustness of the spin-ice phases in three-dimensional Rydberg arrays
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method