Unifying variational methods for simulating quantum many-body systems

Abstract

We introduce a unified formulation of variational methods for simulating ground state properties of quantum many-body systems. The key feature is a novel variational method over quantum circuits via infinitesimal unitary transformations, inspired by flow equation methods. Variational classes are represented as efficiently contractible unitary networks, including the matrix-product states of density matrix renormalization, multiscale entanglement renormalization (MERA) states, weighted graph states, and quantum cellular automata. In particular, this provides a tool for varying over classes of states, such as MERA, for which so far no efficient way of variation has been known. The scheme is flexible when it comes to hybridizing methods or formulating new ones. We demonstrate the functioning by numerical implementations of MERA, matrix-product states, and a new variational set on benchmarks.

5 pages, 3 figures, replaced with published version

References in corpus (18)

• The density-matrix renormalization group
• Entanglement in quantum critical phenomena
• Efficient classical simulation of slightly entangled quantum computations
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Matrix product states represent ground states faithfully
• DMRG and periodic boundary conditions: a quantum information perspective
• Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture
• Entanglement Properties of the Harmonic Chain
• The computational complexity of PEPS
• Optimal Control-Based Efficient Synthesis of Building Blocks of Quantum Algorithms Seen in Perspective from Network Complexity towards Time Complexity
• Correlations, spectral gap, and entanglement in harmonic quantum systems on generic lattices
• CORE Technology and Exact Hamiltonian Real-Space Renormalization Group Transformations
• Ground state approximation for strongly interacting systems in arbitrary dimension
• Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model
• Computational Difficulty of Global Variations in the Density Matrix Renormalization Group

Cited by in corpus (40)

• Area laws for the entanglement entropy - a review
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Towards Practical Quantum Variational Algorithms
• Algorithms for entanglement renormalization
• A positive tensor network approach for simulating open quantum many-body systems
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Multi-scale Entanglement Renormalization Ansatz in Two Dimensions: Quantum Ising Model
• Unitary circuits for strongly correlated fermions
• Quantum MERA Channels
• Riemannian optimization of isometric tensor networks
• Causal structure of the entanglement renormalization ansatz
• Simulation of time evolution with the MERA
• Computations in Quantum Tensor Networks
• Critical properties of homogeneous binary trees
• Sequentially generated states for the study of two dimensional systems
• Gradient Flows for Optimisation and Quantum Control: Foundations and Applications
• Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime
• Spontaneous symmetry breaking in a generalized orbital compass model
• The Thirring quantum cellular automaton
• Optimizing quantum circuits with Riemannian gradient flow
• Renormalization algorithm with graph enhancement
• Entangled and sequential quantum protocols with dephasing
• Homogeneous MERA states: an information theoretical analysis
• Local optimization on pure Gaussian state manifolds
• Derivation of the t-J model for finite doping
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Conformal Properties of Hyperinvariant Tensor Networks
• Boundary theories of critical matchgate tensor networks
• Entanglement renormalization and boundary critical phenomena
• Tensor network methods with graph enhancement
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Unraveling long-time quantum dynamics using flow equations
• Entanglement Continuous Unitary Transformations
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Large-scale stochastic simulation of open quantum systems
• Symmetries of the Dirac quantum walk and emergence of the de Sitter group
• Entanglement renormalization for chiral topological phases
• Entanglement renormalization of fractonic anisotropic ${\mathbb{Z}}_N$ Laplacian models
• Tensor network states for the description of quantum many-body systems