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:2512.23009

Symmetry-Preserving Variational Quantum Simulation of the Heisenberg Spin Chain on Noisy Quantum Hardware

Rudraksh Sharma

quant-phSubmitted Dec 28, 2025• Announced Dec 30, 2025• 0 citations
arXivHTMLPDF

Abstract

Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.

Related papers

Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

George S. Barron, Bryan Gard, Orien J. Altman +3 more

One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE). We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other widely available ansatze. Through simulations of the ${\mathrm{H}}_{2}$ molecule and of a Heisenberg model on a two-dimensional lattice, we verify that these improvements persist in the presence of noise. This is done using both real IBM devices and classical simulations. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error-mitigation techniques to further improve the quality of our results.

arXiv:2003.00171•Physical Review Applied•Sep 1, 2021•32 citations

Entanglement-variational hardware-efficient ansatz for eigensolvers

Xin Wang, Bo Qi, Yabo Wang +1 more

Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are two main approaches for VQEs: problem-agnostic and problem-specific. For problem-agnostic methods, they often suffer from trainability issues. For problem-specific methods, their performance usually relies upon the choice of initial reference states, which are often hard to determine. In this paper, we propose an entanglement-variational hardware-efficient ansatz (EHA), and numerically compare it with some widely used ansatzes by solving benchmark problems in quantum many-body systems and quantum chemistry. Our EHA is problem-agnostic and hardware-efficient, is especially suitable for NISQ devices, and has potential for wide applications. Our EHA can achieve a higher level of accuracy in finding ground states and their energies in most cases, even compared with problem-specific methods. The performance of the EHA is robust to the choice of initial states and to parameter initialization, and it has the ability to quickly adjust the entanglement to the required amount, which is also the fundamental reason for its superiority.

arXiv:2311.01120•Physical Review Applied•Mar 27, 2024•14 citations

Designing Minimalistic Variational Quantum Ansatz Inspired by Algorithmic Cooling

Shin, Soyoung, Ha Eum Kim, Hyeonjun Yeo +3 more

This study introduces a novel minimalistic variational quantum ansatz inspired by algorithmic cooling principles. The proposed Heat Exchange algorithmic cooling ansatz (HE ansatz) facilitates efficient population redistribution without requiring bath resets, simplifying implementation on noisy intermediate-scale quantum (NISQ) devices. The HE ansatz achieves superior approximation ratios with the complete network \textsc{Maxcut} optimization problem compared to the conventional Hardware efficient and QAOA ansatz. We also proposed a new variational algorithm that utilize HE ansatz to compute the ground state of impure dissipative-system variational quantum eigensolver (dVQE) which achieved a sub-$1\%$ error in ground-state energy calculations of the 1D Heisenberg chain with impurity and successfully simulates the edge effect of impure spin chain, highlighting its potential for applications in quantum many-body physics. These results underscore the compatibility of the ansatz with hardware-efficient implementations, offering a scalable approach for solving complex quantum problems in disordered and open quantum systems.

arXiv:2501.16776•Jan 28, 2025•0 citations

Simulating the Antiferromagnetic Heisenberg Model on a Spin-Frustrated Kagome Lattice with the Contextual Subspace Variational Quantum Eigensolver

Tim Weaving, Alexis Ralli, Vinul Wimalaweera +2 more

In this work we investigate the ground state properties of a candidate quantum spin liquid using a superconducting Noisy Intermediate-Scale Quantum (NISQ) device. Specifically, we study the antiferromagnetic Heisenberg model on a Kagome lattice, a geometrically frustrated structure that gives rise to a highly degenerate energy spectrum. To successfully simulate this system, we employ a qubit reduction strategy leveraging the Contextual Subspace methodology, significantly reducing the problem size prior to execution on the quantum device. We improve the quality of these subspaces by using the wavefunctions obtained from low bond dimension Density Matrix Renormalization Group (DMRG) calculations to bias the subspace stabilizers through a symplectic approximate symmetry generator extraction algorithm. Reducing the Hamiltonian size allows us to implement tiled circuit ensembles and deploy the Variational Quantum Eigensolver (VQE) to estimate the ground state energy. We adopt a hybrid quantum error mitigation strategy combining Readout Error Mitigation (REM), Symmetry Verification (SV) and Zero Noise Extrapolation (ZNE). This approach yields high-accuracy energy estimates, achieving error rates on the order of 0.01% and thus demonstrating the potential of near-term quantum devices for probing frustrated quantum materials.

arXiv:2506.12391•Jun 14, 2025•0 citations

Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Joris Kattemölle, Jasper van Wezel

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 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:2108.02175•Physical review. B./Physical review. B•Dec 22, 2022•54 citations

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
Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.
One of the most promising applications of noisy intermediate-scale quantum computers is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE). We show that encoding symmetries of the simulated Hamiltonian in the VQE ansatz reduces both classical and quantum resources compared to other widely available ansatze. Through simulations of the H2{\mathrm{H}}_{2}H2​ molecule and of a Heisenberg model on a two-dimensional lattice, we verify that these improvements persist in the presence of noise. This is done using both real IBM devices and classical simulations. We also demonstrate how these techniques can be used to find molecular excited states of various symmetries using a noisy processor. We use error-mitigation techniques to further improve the quality of our results.
Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are two main approaches for VQEs: problem-agnostic and problem-specific. For problem-agnostic methods, they often suffer from trainability issues. For problem-specific methods, their performance usually relies upon the choice of initial reference states, which are often hard to determine. In this paper, we propose an entanglement-variational hardware-efficient ansatz (EHA), and numerically compare it with some widely used ansatzes by solving benchmark problems in quantum many-body systems and quantum chemistry. Our EHA is problem-agnostic and hardware-efficient, is especially suitable for NISQ devices, and has potential for wide applications. Our EHA can achieve a higher level of accuracy in finding ground states and their energies in most cases, even compared with problem-specific methods. The performance of the EHA is robust to the choice of initial states and to parameter initialization, and it has the ability to quickly adjust the entanglement to the required amount, which is also the fundamental reason for its superiority.
This study introduces a novel minimalistic variational quantum ansatz inspired by algorithmic cooling principles. The proposed Heat Exchange algorithmic cooling ansatz (HE ansatz) facilitates efficient population redistribution without requiring bath resets, simplifying implementation on noisy intermediate-scale quantum (NISQ) devices. The HE ansatz achieves superior approximation ratios with the complete network \textsc{Maxcut} optimization problem compared to the conventional Hardware efficient and QAOA ansatz. We also proposed a new variational algorithm that utilize HE ansatz to compute the ground state of impure dissipative-system variational quantum eigensolver (dVQE) which achieved a sub-1%1\%1% error in ground-state energy calculations of the 1D Heisenberg chain with impurity and successfully simulates the edge effect of impure spin chain, highlighting its potential for applications in quantum many-body physics. These results underscore the compatibility of the ansatz with hardware-efficient implementations, offering a scalable approach for solving complex quantum problems in disordered and open quantum systems.
In this work we investigate the ground state properties of a candidate quantum spin liquid using a superconducting Noisy Intermediate-Scale Quantum (NISQ) device. Specifically, we study the antiferromagnetic Heisenberg model on a Kagome lattice, a geometrically frustrated structure that gives rise to a highly degenerate energy spectrum. To successfully simulate this system, we employ a qubit reduction strategy leveraging the Contextual Subspace methodology, significantly reducing the problem size prior to execution on the quantum device. We improve the quality of these subspaces by using the wavefunctions obtained from low bond dimension Density Matrix Renormalization Group (DMRG) calculations to bias the subspace stabilizers through a symplectic approximate symmetry generator extraction algorithm. Reducing the Hamiltonian size allows us to implement tiled circuit ensembles and deploy the Variational Quantum Eigensolver (VQE) to estimate the ground state energy. We adopt a hybrid quantum error mitigation strategy combining Readout Error Mitigation (REM), Symmetry Verification (SV) and Zero Noise Extrapolation (ZNE). This approach yields high-accuracy energy estimates, achieving error rates on the order of 0.01% and thus demonstrating the potential of near-term quantum devices for probing frustrated quantum materials.
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 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.
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.