Variational adiabatic transport of tensor networks

Abstract

We discuss a tensor network method for constructing the adiabatic gauge potential -- the generator of adiabatic transformations -- as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic evolution of tensor networks offers a wide range of applications, of which two are explored in this paper: improving tensor network optimization and scanning phase diagrams. By efficiently transporting eigenstates to quantum criticality and performing intermediary density matrix renormalization group (DMRG) optimizations along the way, we demonstrate that we can compute ground and low-lying excited states faster and more reliably than a standard DMRG method at or near quantum criticality. We demonstrate a simple automated step size adjustment and detection of the critical point based on the norm of the adiabatic gauge potential. Remarkably, we are able to reliably transport states through the critical point of the models we study.

arXiv comment11 pages, 7 figures; added note in discussion section and new references

References in corpus (67)

• The density-matrix renormalization group in the age of matrix product states
• Correlated Electrons in High Temperature Superconductors
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Continuous Quantum Phase Transitions
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Time-dependent variational principle for quantum lattices
• Ground state overlap and quantum phase transitions
• Unifying time evolution and optimization with matrix product states
• Towards Quantum Chemistry on a Quantum Computer
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Quantum critical scaling of the geometric tensors
• From density-matrix renormalization group to matrix product states
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Dynamical density-matrix renormalization-group method
• Matrix product operator representations
• Geometry and non-adiabatic response in quantum and classical systems
• Towards Quantum Machine Learning with Tensor Networks
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Alternating minimal energy methods for linear systems in higher dimensions. Part I: SPD systems
• Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems
• Fermionic Projected Entangled Pair States
• The mass spectrum of the Schwinger model with Matrix Product States
• Floquet-engineering counterdiabatic protocols in quantum many-body systems
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
• Classifying and measuring the geometry of the quantum ground state manifold
• Adiabatic tracking of quantum many-body dynamics
• Variational Quantum Eigensolver with Fewer Qubits
• Generic Construction of Efficient Matrix Product Operators
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
• Variational matrix product ansatz for dispersion relations
• First-Order Phase Transition in a Quantum Hall Ferromagnet
• Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing
• Digitized-counterdiabatic quantum approximate optimization algorithm
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• One-dimensional Continuum Electronic Structure with the Density Matrix Renormalization Group and Its Implications For Density Functional Theory
• Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
• High Temperature Superconductivity
• Counterdiabatic Optimised Local Driving
• Rapid adiabatic preparation of injective PEPS and Gibbs states
• Digitized-Counterdiabatic Quantum Algorithm for Protein Folding
• Towards adiabatic quantum computing using compressed quantum circuits
• Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field
• Entanglement renormalization in fermionic systems
• Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
• Preparing projected entangled pair states on a quantum computer
• Multigrid Algorithms for Tensor Network States
• Sliced Basis Density Matrix Renormalization Group for Electronic Structure
• Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory
• Tensor network representations of parton wave functions
• Fidelity susceptibility in Gaussian Random Ensembles
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
• Optimal steering of matrix product states and quantum many-body scars
• Matrix product state algorithms for Gaussian fermionic states
• Preparing topological PEPS on a quantum computer
• Adiabatic landscape and optimal paths in ergodic systems
• Surrogate models for quantum spin systems based on reduced order modeling
• Preparation and verification of tensor network states
• Implementation of rigorous renormalization group method for ground space and low-energy states of local Hamiltonians
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Numerical continuum tensor networks in two dimensions

Cited by in corpus (5)

• Quantum Dynamics in Krylov Space: Methods and Applications
• Towards adiabatic quantum computing using compressed quantum circuits
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Geometric Floquet theory
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra