Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Abstract

Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a Variational Quantum Eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise-resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.

arXiv commentAdded noise effects, system-size scaling, decoherence-free subspace encoding. Published version, 19 pages, 13 figures

References in corpus (84)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Computation with Quantum Dots
• A variational eigenvalue solver on a quantum processor
• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Decoherence Free Subspaces for Quantum Computation
• Superconducting Qubits: Current State of Play
• Error mitigation for short-depth quantum circuits
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• 14-qubit entanglement: creation and coherence
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Multi-particle entanglement of hot trapped ions
• Quantum Computers and Dissipation
• Scalable Quantum Simulation of Molecular Energies
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Towards Practical Quantum Variational Algorithms
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Toward the first quantum simulation with quantum speedup
• Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Scalable Noise Estimation with Random Unitary Operators
• A Theory of Trotter Error
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• A four-qubit germanium quantum processor
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Repeated Quantum Error Detection in a Surface Code
• The Future of Quantum Computing with Superconducting Qubits
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
• Circuit QED lattices: towards quantum simulation with superconducting circuits
• Trading classical and quantum computational resources
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• A Crossbar Network for Silicon Quantum Dot Qubits
• Simulating Large Quantum Circuits on a Small Quantum Computer
• The General Quantum Interference Principle and the Duality Computer
• Reducing decoherence in quantum computer memory with all quantum bits coupling to the same environment
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Low-cost error mitigation by symmetry verification
• An introduction to integrable techniques for one-dimensional quantum systems
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Virtual Distillation for Quantum Error Mitigation
• Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Scalable quantum circuit and control for a superconducting surface code
• Efficient estimation of Pauli observables by derandomization
• Strategies for solving the Fermi-Hubbard model on near-term quantum computers
• Physics of low energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet
• Exponential Error Suppression for Near-Term Quantum Devices
• Efficient variational simulation of non-trivial quantum states
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Error Avoiding Quantum Codes
• Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
• Quantum computation with universal error mitigation on superconducting quantum processor
• Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Quantum NP - A Survey
• Low energy excitations of the kagome antiferromagnet and the spin gap issue
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Correlation functions of integrable models: a description of the ABACUS algorithm
• Evaluating the noise resilience of variational quantum algorithms
• Symmetry-adapted variational quantum eigensolver
• Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
• Penalty methods for variational quantum eigensolver
• Quantum simulation of antiferromagnetic Heisenberg chain with gate-defined quantum dots
• Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors
• Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems
• Perturbative quantum simulation
• Limitations of optimization algorithms on noisy quantum devices
• Parafermions in a Kagome lattice of qubits for topological quantum computation
• Scalable quantum computing model in the circuit-QED lattice with circulator function
• Dynamical fidelity susceptibility of decoherence-free subspaces
• Quantum simulation scheme of two-dimensional xy-model Hamiltonian with controllable coupling

Cited by in corpus (33)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Emerging quantum computing algorithms for quantum chemistry
• Hamiltonian variational ansatz without barren plateaus
• Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry
• Simulating large-size quantum spin chains on cloud-based superconducting quantum computers
• Calibrating the role of entanglement in variational quantum circuits
• Ability of error correlations to improve the performance of variational quantum algorithms
• EHA: Entanglement-variational Hardware-efficient Ansatz for Eigensolvers
• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
• Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
• Measurement-induced entanglement phase transitions in variational quantum circuits
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction
• Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Equivariant Variational Quantum Eigensolver to detect Phase Transitions through Energy Level Crossings
• Sketching phase diagrams using low-depth variational quantum algorithms
• All you need is spin: SU(2) equivariant variational quantum circuits based on spin networks
• Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Noise-aware variational eigensolvers: a dissipative route for lattice gauge theories
• From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons
• Compact Multi-Threshold Quantum Information Driven Ansatz For Strongly Interactive Lattice Spin Models
• Quantum simulation and ground state preparation for the honeycomb Kitaev model
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Tangent Space Excitation Ansatz for Quantum Circuits
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Role of Riemannian geometry in double-bracket quantum imaginary-time evolution
• Accelerated spin-adapted ground-state preparation with nonvariational quantum algorithms
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Preparation of the single-spinon wave function on a quantum computer
• Efficient quantum simulation for translationally invariant systems
• Quantum algorithm for one-quasiparticle excitations in the thermodynamic limit via cluster-additive block diagonalization