Probing ground state properties of the kagome antiferromagnetic Heisenberg model using the Variational Quantum Eigensolver

Bosse, Jan Lukas; Montanaro, Ashley

doi:10.48550/arxiv.2108.08086

Cited by 6 publications

(12 citation statements)

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“…[269] shows that VQE approaches the true ground of the lattice exponentially as a function of circuit depth on a noiseless simulation of up to 20 sites. Bosse and Montanaro [268] find a similar result ton a simulation of 24 sites, though point out to the large number of variational parameters needed.…”

Section: The Hamiltonian Variational Ansatz and Extensionssupporting

confidence: 53%

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The Variational Quantum Eigensolver: a review of methods and best practices

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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Section: The Hamiltonian Variational Ansatz and Extensionssupporting

confidence: 53%

“…The ansatz was also adapted to solve the Heisenberg antiferromagnetic model on the Kagome lattice in Refs. [268,269], both study showing promising results. In particular, Ref.…”

Section: The Hamiltonian Variational Ansatz and Extensionsmentioning

confidence: 89%

The Variational Quantum Eigensolver: a review of methods and best practices

Tilly¹,

Chen²,

Cao³

et al. 2021

Preprint

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“…In the instances shown here, there was no clear difference between the performance of BayesMGD and MGD. However, in simulated tests of VQE for the antiferromagnetic Heisenberg model on the kagome lattice 64 with 12 qubits and 18 parameters we found that for η := p (nc+1)(nc+2)/2 ≥ 1 the performance of BayesMGD and MGD is comparable, while for η < 1 BayesMGD often outperforms MGD. As in Appendix D, η is defined as the ratio between the number p of evaluation points taken in each iteration and the number (n c +1)(n c +2)/2 of evaluation points necessary for a fully determined quadratic fit.…”

Section: Experimental Comparison Of Optimisation Algorithmsmentioning

confidence: 84%

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Stanisic¹,

Bosse²,

Gambetta³

et al. 2021

Preprint

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The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model. We address 1 × 8 and 2 × 4 instances on 16 qubits on a superconducting quantum processor, substantially larger than previous work based on less scalable compression techniques, and going beyond the family of 1D Fermi-Hubbard instances, which are solvable classically. Consistent with predictions for the ground state, we observe the onset of the metal-insulator transition and Friedel oscillations in 1D, and antiferromagnetic order in both 1D and 2D. We use a variety of errormitigation techniques, including symmetries of the Fermi-Hubbard model and a recently developed technique tailored to simulating fermionic systems. We also introduce a new variational optimisation algorithm based on iterative Bayesian updates of a local surrogate model. Our scalable approach is a first step to using near-term quantum computers to determine low-energy properties of stronglycorrelated electronic systems that cannot be solved exactly by classical computers.

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“…Note added.-While completing this work several independent variational protocols of kagome Heisenberg models and square-octagon-lattice Kitaev model appeared in [124], [125], and [126]. While having the same spirit and pushing NISQ boundaries, our work highlights the importance of stabilization and adds dynamical aspects.…”

Section: Kαmentioning

confidence: 88%

Quantum simulation and ground state preparation for the honeycomb Kitaev model

Bespalova,

Kyriienko

2021

Preprint

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We propose a quantum protocol that allows preparing a ground state (GS) of the honeycomb Kitaev model. Our approach efficiently uses underlying symmetries and techniques from topological error correction. It is based on the stabilization procedure, the developed centralizer ansatz, and utilizes the vortex basis description as the most advantageous for qubit-based simulations. We demonstrate the high fidelity preparation of spin liquid ground states for the original Kitaev model, getting the exact GS for N = 24 spins using 230 two-qubit operations. We then extend the variational procedure to non-zero magnetic fields, studying observables and correlations that reveal the phase transition. Finally, we perform dynamical simulation, where the ground state preparation opens a route towards studies of strongly-correlated dynamics, and a potential quantum advantage.

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Probing ground state properties of the kagome antiferromagnetic Heisenberg model using the Variational Quantum Eigensolver

Cited by 6 publications

References 0 publications

The Variational Quantum Eigensolver: a review of methods and best practices

The Variational Quantum Eigensolver: a review of methods and best practices

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer

Quantum simulation and ground state preparation for the honeycomb Kitaev model

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