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

@article{Bosse2022ProbingGP, title={Probing ground-state properties of the kagome antiferromagnetic Heisenberg model using the variational quantum eigensolver}, author={Jan Lukas Bosse and Ashley Montanaro}, journal={Physical Review B}, year={2022} }

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…

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## References

SHOWING 1-10 OF 43 REFERENCES

### Data from "Probing ground state properties of the kagome antiferromagnetic Heisenberg model using the Variational Quantum Eigensolver"/wf_cost_fun_2x6_gradlog_ansatz_comparison

- Physics
- 2021

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…

### Strategies for solving the Fermi-Hubbard model on near-term quantum computers

- Physics
- 2019

If the numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimising over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalisation.

### Variational Quantum Eigensolver for Frustrated Quantum Systems

- PhysicsArXiv
- 2020

This work considers the performance of the VQE technique for a Hubbard-like model describing a one-dimensional chain of fermions with competing nearest- and next-nearest-neighbor interactions and studies the barren plateau phenomenon for the Hamiltonian in question.

### Properties of an algebraic spin liquid on the kagome lattice

- Physics
- 2008

In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the S = 1/2 kagome lattice Heisenberg antiferromagnet. This state, which lacks a spin gap, is…

### Gapped spin liquid with Z 2 topological order for the kagome Heisenberg model

- Physics
- 2017

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in…

### Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet

- PhysicsScience
- 2015

O oxygen-17 single-crystal nuclear magnetic resonance measurements of the spin-1/2 kagome lattice in herbertsmithite suggest that herberTSmithite is indeed a QSL, and imply that the k Kagome Heisenberg antiferromagnet has a spin-liquid ground state with a finite gap.

### Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2

- PhysicsNature Physics
- 2020

Spin liquids are exotic phases of quantum matter that challenge Landau’s paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to…

### Resource Estimation for Quantum Variational Simulations of the Hubbard Model

- Physics
- 2019

This Article outlines the details about the gate sequence, the measurement scheme and the relevant error mitigation techniques for the implementation of the Hubbard VQE on a NISQ platform, and performs resource estimation on Hubbard VZE using silicon spin qubits as an example platform.

### Ground state of the spin-1/2 kagome-lattice Heisenberg antiferromagnet

- Physics
- 2007

Using series expansions around the dimer limit, we show that the ground state of the Heisenberg Antiferromagnet on the Kagome Lattice appears to be a Valence Bond Crystal (VBC) with a 36-site unit…

### Physics of low-energy singlet states of the Kagome lattice quantum Heisenberg antiferromagnet

- Physics
- 2003

This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight…