Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

Abstract

We describe a hybrid quantum-classical approach to treat quantum many-body systems in the thermodynamic limit. This is done by combining numerical linked-cluster expansions (NLCE) with the variational quantum eigensolver (VQE). Here, the VQE algorithm is used as a cluster solver within the NLCE. We test our hybrid quantum-classical algorithm (NLCE$+$VQE) for the ferromagnetic transverse-field Ising model on the one-dimensional chain and the two-dimensional square lattice. The calculation of ground-state energies on each open cluster demands a modified Hamiltonian variational ansatz for the VQE. One major finding is convergence of NLCE$+$VQE to the conventional NLCE result in the thermodynamic limit when at least $N/2$ layers are used in the VQE ansatz for each cluster with $N$ sites. Our approach demonstrates the fruitful connection of techniques known from correlated quantum many-body systems with hybrid algorithms explored on existing quantum-computing devices.

14 pages, 7 figures

References in corpus (40)

• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Entanglement renormalization
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An Area Law for One Dimensional Quantum Systems
• The Variational Quantum Eigensolver: a review of methods and best practices
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Matrix product states represent ground states faithfully
• Towards Practical Quantum Variational Algorithms
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Training variational quantum algorithms is NP-hard
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• A Short Introduction to Numerical Linked-Cluster Expansions
• Magnetic Susceptibility of the Kagome Antiferromagnet ZnCu3(OH)6Cl2
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Entanglement at a Two-Dimensional Quantum Critical Point: a Numerical Linked Cluster Expansion Study
• Expressibility of the alternating layered ansatz for quantum computation
• Thermodynamics of strongly interacting fermions in two-dimensional optical lattices
• Thermal Ising transitions in the vicinity of two-dimensional quantum critical points
• Hamiltonian variational ansatz without barren plateaus
• Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz
• Corner contribution to the entanglement entropy of strongly-interacting O(2) quantum critical systems in 2+1 dimensions
• Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Effective models for gapped phases of strongly correlated quantum lattice models
• Disorder by disorder and flat bands in the kagome transverse field Ising model
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Thermodynamics of two-dimensional spin models with bimodal random-bond disorder
• Numerical study of the thermodynamics of clinoatacamite
• Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Numerical linked cluster expansions for inhomogeneous systems
• A generalized perspective on non-perturbative linked cluster expansions
• Numerical linked-cluster expansions for disordered lattice models
• Projective cluster-additive transformation for quantum lattice models
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• Bang-bang algorithms for quantum many-body ground states: a tensor network exploration

Cited by in corpus (5)

• A near-term quantum simulation of the transverse field Ising model hints at Glassy Dynamics
• Reinforcement learning with learned gadgets to tackle hard quantum problems on real hardware
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization
• Qubit encodings for lattices of dipolar planar rotors