Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids

Abstract

We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model, and use a trainable symmetry-guided ansatz for preparing its ground state. Applying the tools of quantum subspace expansion (QSE), Hamiltonian operator approximation, and overlap measurements, we simulate the QSL at zero temperature and finite magnetic field, thus moving outside of the symmetric subspace. Next, we implement a protocol for quantum subspace expansion-based measurement of spin-spin correlation functions. Finally, we perform QSE-based simulation of the dynamical structure factor obtained from Green's functions of the finite field Kitaev model. Our results show that quantum simulators offer an insight to quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.

8 pages, 6 figures

References in corpus (88)

• Anyons in an exactly solved model and beyond
• The density-matrix renormalization group in the age of matrix product states
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Barren plateaus in quantum neural network training landscapes
• Quantum Spin Liquids
• The Variational Quantum Eigensolver: a review of methods and best practices
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Proximate Kitaev Quantum Spin Liquid Behaviour in α-RuCl${}_3$
• Kitaev quantum spin liquid - concept and materialization
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Challenges and Opportunities in Quantum Machine Learning
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Herbertsmithite and the Search for the Quantum Spin Liquid
• Quantum Simulators: Architectures and Opportunities
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum computing with neutral atoms
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Renormalization and tensor product states in spin chains and lattices
• The randomized measurement toolbox
• Tensor Network Renormalization
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Strongly Correlated Materials
• Exploiting symmetry in variational quantum machine learning
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Theory of overparametrization in quantum neural networks
• Dynamics of Fractionalization in Quantum Spin Liquids
• Group-Invariant Quantum Machine Learning
• Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• A Non-Orthogonal Variational Quantum Eigensolver
• Methodology for replacing indirect measurements with direct measurements
• Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design
• Quantum Krylov subspace algorithms for ground and excited state energy estimation
• Quantum Power Method by a Superposition of Time-Evolved States
• Phase Diagram and Quantum Order by Disorder in the Kitaev $K_1$-$K_2$ Honeycomb Magnet
• Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
• Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
• Easing the Monte Carlo sign problem
• Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
• Matchgate Shadows for Fermionic Quantum Simulation
• Towards a Larger Molecular Simulation on the Quantum Computer: Up to 28 Qubits Systems Accelerated by Point Group Symmetry
• Hamiltonian variational ansatz without barren plateaus
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware
• A theory of quantum subspace diagonalization
• Krylov-projected quantum Monte Carlo
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Towards near-term quantum simulation of materials
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
• Quantum inverse iteration algorithm for programmable quantum simulators
• Contracting projected entangled pair states is average-case hard
• Constructions and Noise Threshold of Topological Subsystem Codes
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• Quantum simulation of the hexagonal Kitaev model with trapped ions
• Quantum Kernel Methods for Solving Differential Equations
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Chemistry on quantum computers with virtual quantum subspace expansion
• Floquet quantum simulation with superconducting qubits
• Quantum Virtual Cooling
• Kitaev honeycomb models in magnetic fields: Dynamical response and hidden symmetries
• Creating and controlling global Greenberger-Horne-Zeilinger entanglement on quantum processors
• Symmetry enhanced variational quantum spin eigensolver
• Magnetic field-induced evolution of intertwined orders in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$
• Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function
• Real-Time Krylov Theory for Quantum Computing Algorithms
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Hamiltonian operator approximation for energy measurement and ground state preparation
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Long-lived topological time-crystalline order on a quantum processor
• Variational Approach to Quantum Spin Liquid in a Rydberg Atom Simulator
• Topological quantum error correction in the Kitaev honeycomb model
• Variational quantum solver employing the PDS energy functional
• Analysis of quantum Krylov algorithms with errors
• Phase-Sensitive Quantum Measurement without Controlled Operations
• A blueprint for a Digital-Analog Variational Quantum Eigensolver using Rydberg atom arrays
• Measurement-based infused circuits for variational quantum eigensolvers
• Detection of long-range entanglement in gapped quantum spin liquids by local measurements
• Quantum subspace expansion in the presence of hardware noise
• Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method
• Hubbard physics with Rydberg atoms: using a quantum spin simulator to simulate strong fermionic correlations

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