Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

• URL: http://arxiv.org/abs/2108.02175v3
• Date: Fri, 23 Dec 2022 14:06:10 GMT
• Title: Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice
• Authors: Joris Kattem\"olle and Jasper van Wezel
• Abstract summary: We give a detailed proposal for a Vari Quantum Eigensolver (VQE) intending to solve a quantum problem on a quantum computer. We 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. 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 noise.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 (NISQ) 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.

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