Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2306.00467

Efficient VQE Approach for Accurate Simulations on the Kagome Lattice

S Jyothikamalesh, A. Kaarnika, Mohankumar. M, Sanjay Vishwakarma, Srinjoy Ganguly, P Yuvaraj

Published Jun 1, 2023• 1 citation
arXivHTMLPDF

Abstract

The Kagome lattice, a captivating lattice structure composed of interconnected triangles with frustrated magnetic properties, has garnered considerable interest in condensed matter physics, quantum magnetism, and quantum computing.The Ansatz optimization provided in this study along with extensive research on optimisation technique results us with high accuracy. This study focuses on using multiple ansatz models to create an effective Variational Quantum Eigensolver (VQE) on the Kagome lattice. By comparing various optimisation methods and optimising the VQE ansatz models, the main goal is to estimate ground state attributes with high accuracy. This study advances quantum computing and advances our knowledge of quantum materials with complex lattice structures by taking advantage of the distinctive geometric configuration and features of the Kagome lattice. Aiming to improve the effectiveness and accuracy of VQE implementations, the study examines how Ansatz Modelling, quantum effects, and optimization techniques interact in VQE algorithm. The findings and understandings from this study provide useful direction for upcoming improvements in quantum algorithms,quantum machine learning and the investigation of quantum materials on the Kagome Lattice.

DOI
10.48550/arxiv.2306.00467

Related papers

Probing ground-state properties of the kagome antiferromagnetic Heisenberg model using the variational quantum eigensolver

Jan Lukas Bosse, Ashley Montanaro

Finding and probing the ground states of spin lattices, such as the antiferromagnetic Heisenberg model on the kagome lattice (KAFH), is a very challenging problem on classical computers and only possible for relatively small systems. We propose using the variational quantum eigensolver (VQE) to find the ground state of the KAFH on a quantum computer. We find efficient ansatz circuits and show how physically interesting observables can be measured efficiently. To investigate the expressiveness and scaling of our ansatz circuits we used classical, exact simulations of VQE for the KAFH for different lattices ranging from 8 to 24 qubits. We find that the fidelity with the ground state approaches one exponentially in the circuit depth for all lattices considered, except for a 24-qubit lattice with an almost degenerate ground state. We conclude that VQE circuits that are able to represent the ground state of the KAFH on lattices inaccessible to exact diagonalization techniques may be achievable on near-term quantum hardware. However, for large systems, circuits with many variational parameters are needed to achieve high fidelity with the ground state.

arXiv:2108.08086•Physical review. B./Physical review. B•Mar 7, 2022•32 citations

Scalable Quantum Ground State Preparation of the Heisenberg Model: A Variational Quantum Eigensolver Approach

Wang, Jinao, Rimika Jaiswal

Quantum systems have historically been formidable to simulate using classical computational methods, particularly as the system size grows. In recent years, advancements in quantum computing technology have offered new opportunities for tackling complex quantum systems, potentially enabling the study and preparation of quantum states directly on quantum processors themselves. The Variational Quantum Eigensolver (VQE) algorithm is a system composed of a quantum circuit as well as a classical optimizer that can be used to efficiently prepare interesting many-body states on the current noisy intermediate-scale quantum (NISQ) devices. We assess the efficacy and scalability of VQE by preparing the ground states of the 1D generalized Heisenberg model, a pivotal model in understanding magnetic materials. We present an ansatz capable of preparing the ground states for all possible values of the coupling, including the critical states for the anisotropic XXZ model. This paper also aims to provide insights into the precision and time consumption involved in classical and optimized sampling approaches in the calculation of expectation values. In preparing the ground state for the Heisenberg models, this paper paves the way for more efficient quantum algorithms and contributes to the broader field of condensed matter physics.

arXiv:2308.12020•Aug 23, 2023•1 citation

Probing the ground state of the antiferromagnetic Heisenberg model on the kagome lattice using geometrically informed variational quantum eigensolver

Anonymous, Nacer Eddine Belaloui, Abdelmouheymen Rabah Khamadja +4 more

This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver algorithm on real quantum hardware. We demonstrate that the ground-state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation. We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubitwise readout-error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.

arXiv:2509.18029•Physical Review Research•Sep 8, 2026•0 citations

Prepare Ground States of Highly Frustrated Magnetic Clusters on Quantum Computers

Yan Wang

Solving challenging problems in physical, chemical, and materials sciences is one of the most promising applications of quantum utility that can be realized on current noisy hardware, considering (i) the direct map (encoding) from the quantum particles and their interactions to the qubits and their entangling gates and (ii) the rapidly improved quantum hardware and advanced error-mitigation techniques. Understanding quantum spin liquid in frustrated magnetic materials is a longstanding challenge in condensed matter physics and the nature of the ground-state phases is highly debated among researchers. Using IBM quantum computers with superconducting qubits, we implemented a variational quantum eigensolver (VQE) algorithm to prepare the ground states of two 12-site cluster approximations of these highly frustrated magnetic materials. The interaction graphs of the two corresponding Hamiltonians are (a) the six-pointed star graph (a unit cell of the kagome lattice) and (b) the cuboctahedral graph (the kagome on a sphere). These are also two instances of Quantum Max Cut problem. With the VQE based on the Hamiltonian variational ansatz acting on a valence bond solid initial trial state, we prepared the ground states and obtained the exact ground energy on simulator and high accuracy on noisy hardware. The deep ansatz necessary to reach the ground state of the cuboctahedral graph indicates that it is a hard instance of Quantum Max Cut.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•2 citations

Utility-Scale Quantum Computation of Ground-State Energy in a 100+ Site Planar Kagome Antiferromagnet via Hamiltonian Engineering

Ahsan, Muhammad

We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is $-0.417\,J$, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., $-0.4386\,J$. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.

arXiv:2507.06361•Jul 8, 2025•0 citations

Application of Variational Quantum Eigensolver for Ground State Energies Calculation in Hydrogen and Helium Atomic Sequences

Difa Farhani Hakim, Teguh Budi Prayitno, Yanoar Pribadi Sarwono

Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.

SPEKTRA Jurnal Fisika dan Aplikasinya•Dec 14, 2024•2 citations
The Kagome lattice, a captivating lattice structure composed of interconnected triangles with frustrated magnetic properties, has garnered considerable interest in condensed matter physics, quantum magnetism, and quantum computing.The Ansatz optimization provided in this study along with extensive research on optimisation technique results us with high accuracy. This study focuses on using multiple ansatz models to create an effective Variational Quantum Eigensolver (VQE) on the Kagome lattice. By comparing various optimisation methods and optimising the VQE ansatz models, the main goal is to estimate ground state attributes with high accuracy. This study advances quantum computing and advances our knowledge of quantum materials with complex lattice structures by taking advantage of the distinctive geometric configuration and features of the Kagome lattice. Aiming to improve the effectiveness and accuracy of VQE implementations, the study examines how Ansatz Modelling, quantum effects, and optimization techniques interact in VQE algorithm. The findings and understandings from this study provide useful direction for upcoming improvements in quantum algorithms,quantum machine learning and the investigation of quantum materials on the Kagome Lattice.
Finding and probing the ground states of spin lattices, such as the antiferromagnetic Heisenberg model on the kagome lattice (KAFH), is a very challenging problem on classical computers and only possible for relatively small systems. We propose using the variational quantum eigensolver (VQE) to find the ground state of the KAFH on a quantum computer. We find efficient ansatz circuits and show how physically interesting observables can be measured efficiently. To investigate the expressiveness and scaling of our ansatz circuits we used classical, exact simulations of VQE for the KAFH for different lattices ranging from 8 to 24 qubits. We find that the fidelity with the ground state approaches one exponentially in the circuit depth for all lattices considered, except for a 24-qubit lattice with an almost degenerate ground state. We conclude that VQE circuits that are able to represent the ground state of the KAFH on lattices inaccessible to exact diagonalization techniques may be achievable on near-term quantum hardware. However, for large systems, circuits with many variational parameters are needed to achieve high fidelity with the ground state.
Quantum systems have historically been formidable to simulate using classical computational methods, particularly as the system size grows. In recent years, advancements in quantum computing technology have offered new opportunities for tackling complex quantum systems, potentially enabling the study and preparation of quantum states directly on quantum processors themselves. The Variational Quantum Eigensolver (VQE) algorithm is a system composed of a quantum circuit as well as a classical optimizer that can be used to efficiently prepare interesting many-body states on the current noisy intermediate-scale quantum (NISQ) devices. We assess the efficacy and scalability of VQE by preparing the ground states of the 1D generalized Heisenberg model, a pivotal model in understanding magnetic materials. We present an ansatz capable of preparing the ground states for all possible values of the coupling, including the critical states for the anisotropic XXZ model. This paper also aims to provide insights into the precision and time consumption involved in classical and optimized sampling approaches in the calculation of expectation values. In preparing the ground state for the Heisenberg models, this paper paves the way for more efficient quantum algorithms and contributes to the broader field of condensed matter physics.
This work investigates the nature of the ground state of the antiferromagnetic Heisenberg model on fundamental kagome cells, a triangle and a star, using the variational quantum eigensolver algorithm on real quantum hardware. We demonstrate that the ground-state preparation is achievable using a shallow hardware-efficient quantum circuit with a naturally Euclidean parameter space. Our custom ansatz is capable of accurately recovering meaningful properties of the ground state such as the spin-spin correlation terms and static structure factor without explicit error mitigation. These features are found to be resilient to noise. We exploited the Fubini-Study metric in constructing the ansatz, ensuring a singularity-free parameter space. With this ansatz design, the adaptive gradient descent optimizer achieves a faster convergence in terms of the number of iterations compared to simultaneous perturbation stochastic approximation. We further apply error mitigation techniques, including zero-noise extrapolation (ZNE) and qubitwise readout-error mitigation (REM). While ZNE does not obey the Rayleigh-Ritz variational principle, the conditions under which REM preserves it are discussed.
Solving challenging problems in physical, chemical, and materials sciences is one of the most promising applications of quantum utility that can be realized on current noisy hardware, considering (i) the direct map (encoding) from the quantum particles and their interactions to the qubits and their entangling gates and (ii) the rapidly improved quantum hardware and advanced error-mitigation techniques. Understanding quantum spin liquid in frustrated magnetic materials is a longstanding challenge in condensed matter physics and the nature of the ground-state phases is highly debated among researchers. Using IBM quantum computers with superconducting qubits, we implemented a variational quantum eigensolver (VQE) algorithm to prepare the ground states of two 12-site cluster approximations of these highly frustrated magnetic materials. The interaction graphs of the two corresponding Hamiltonians are (a) the six-pointed star graph (a unit cell of the kagome lattice) and (b) the cuboctahedral graph (the kagome on a sphere). These are also two instances of Quantum Max Cut problem. With the VQE based on the Hamiltonian variational ansatz acting on a valence bond solid initial trial state, we prepared the ground states and obtained the exact ground energy on simulator and high accuracy on noisy hardware. The deep ansatz necessary to reach the ground state of the cuboctahedral graph indicates that it is a hard instance of Quantum Max Cut.
We present experimental quantum computation of the ground-state energy in a 103-site flat Kagome lattice under the antiferromagnetic Heisenberg model (KAFH), with IBM's Heron r1 and Heron r2 quantum processors. For spin-1/2 KAFH, our per-site ground-state energy estimate is −0.417 J-0.417\,J−0.417J, which, under open-boundary corrections, matches the energy in the thermodynamic limit, i.e., −0.4386 J-0.4386\,J−0.4386J. To achieve this, we used a hybrid approach that splits the conventional Variational Quantum Eigensolver (VQE) into local (classical) and global (quantum) components for efficient hardware utilization. More importantly, we introduce a Hamiltonian engineering strategy that increases coupling on defect triangles to mimic loop-flip dynamics, allowing us to simplify the ansatz while retaining computational accuracy. Using a single-repetition, hardware-efficient ansatz, we entangle up to 103 qubits with high fidelity to determine the Hamiltonian's lowest eigenvalue. This work demonstrates the scalability of VQE for frustrated 2D systems and lays the foundation for future studies using deeper ansatz circuits and larger lattices on utility quantum processors.
Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.