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

Bosse, Jan Lukas; Montanaro, Ashley

doi:10.1103/physrevb.105.094409

Cited by 16 publications

(9 citation statements)

References 42 publications

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“…Instead of the z-magnetisation m z one can also use the x-magnetisation m x = 1 N sites i X i and its (discrete) derivative ∆⟨mx⟩ ∆hx to detect the phase transitions in the 1D and 2D TFIM. Calculating them from the VQE groundstates used to produce figures 2 and 3 and published in [28] yields almost the same results as in the bottom panes of figures 2 and 3.…”

Section: The Tfimmentioning

confidence: 62%

“…the 3D TFIM out of reach. Nevertheless, extrapolating from figures 2 and 3 and the data we have for smaller systems for the 1D and 2D TFIM in [28] indicates that also for the 3D TFIM low depth circuits will be enough to locate the phase transition but that the effort minimisation to find good VQE groundstates will be even larger than for the 2D TFIM.…”

Section: Discussion and Outlookmentioning

confidence: 79%

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Sketching phase diagrams using low-depth variational quantum algorithms

Lukas Bosse,

Santos,

Montanaro

2024

Quantum Sci. Technol.

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Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the Variational Quantum Eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low ﬁdelity approximations to the ground state may be enough to correctly identify diﬀerent phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We ﬁnd that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and ﬁnd that in some cases this is also able to predict phase transitions.

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Section: The Tfimmentioning

confidence: 62%

Section: Discussion and Outlookmentioning

confidence: 79%

Sketching phase diagrams using low-depth variational quantum algorithms

Lukas Bosse,

Santos,

Montanaro

2024

Quantum Sci. Technol.

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“…13. It is seen that the PRH-QAOA can improve the performance of the VQE for 2D target Hamiltonians with triangular geometry, which may enlightens further works aiming to improve the performance of the VQE for frustrated quantum systems [75][76][77].…”

Section: Appendix B: Additional Numerics Of Ising Modelsmentioning

confidence: 81%

Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

Sun¹,

Wang²,

Cui³

et al. 2022

Preprint

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The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: Without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressing atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.

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“…The results are plotted in figure11. It is seen that the PRH-QAOA can improve the performance of the VQE for 2D target Hamiltonians with triangular geometry, which may enlightens further works aiming to improve the performance of VQEs for frustrated quantum systems[93][94][95].…”

mentioning

confidence: 80%

Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

Sun

Wang²,

Cui³

et al. 2023

New J. Phys.

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The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: Without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.

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

Cited by 16 publications

References 42 publications

Sketching phase diagrams using low-depth variational quantum algorithms

Sketching phase diagrams using low-depth variational quantum algorithms

Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

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