Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
arXiv:2401.02355 · doi:10.1063/5.0215573
Abstract
The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.
References in corpus (45)
- Quantum Computing in the NISQ era and beyond
- Double-slit photoelectron interference in strong-field ionization of the neon dimer
- A variational eigenvalue solver on a quantum processor
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Barren plateaus in quantum neural network training landscapes
- The theory of variational hybrid quantum-classical algorithms
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Dynamical Decoupling of Open Quantum Systems
- Quantum Chemistry in the Age of Quantum Computing
- Quantum principal component analysis
- Error mitigation for short-depth quantum circuits
- 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
- Hamiltonian Simulation by Qubitization
- Scalable Quantum Simulation of Molecular Energies
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
- Matrix product states represent ground states faithfully
- Efficient variational quantum simulator incorporating active error minimisation
- A Theory of Trotter Error
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Efficient Simulation of Quantum Systems by Quantum Computers
- Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
- A random compiler for fast Hamiltonian simulation
- Minimal Universal Two-qubit Quantum Circuits
- A practical scheme for quantum computation with any two-qubit entangling gate
- Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
- Real- and imaginary-time evolution with compressed quantum circuits
- Fundamental limits of quantum error mitigation
- Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
- Sequential Generation of Matrix-Product States in Cavity QED
- Barren plateaus in quantum tensor network optimization
- Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing Hamiltonians to Compute Controlled-Not Gates
- Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
- Tensor networks for quantum machine learning
- On the complexity of implementing Trotter steps
- Dequantizing quantum machine learning models using tensor networks
- Tensor-network-assisted variational quantum algorithm
- Time Evolution of Uniform Sequential Circuits
- MindSpore Quantum: A User-Friendly, High-Performance, and AI-Compatible Quantum Computing Framework
- Pre-optimizing variational quantum eigensolvers with tensor networks
- Efficient VQE Approach for Accurate Simulations on the Kagome Lattice