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PreprintCC BY 4.0arXiv

A VQE simulation of the transverse field Ising model

  • Luke Bennett
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Abstract

One of the most promising applications of quantum computing is the ability to simulate quantum systems. A quantity of particular importance in condensed matter physics is the ground-state energy of a system. Here, we present an implementation of a hybrid quantum-classical algorithm known as the variational quantum eigensolver (VQE) to estimate the ground state energy of a prototypical quantum spin system. For this spin system, we use the transverse field Ising model (TFIM) which is known to exhibit a quantum phase transition (QPT) at a critical point. We apply the VQE to a $4$-spin TFIM and evaluate its performance using both a local noise model and IBM quantum hardware to estimate the ground-state energy and reproduce the QPT. The resulting ground-state energy estimates and QPT behaviour are compared with exact-diagonalisation benchmarks.

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Cite

BibTeXRIS
BibTeX
@misc{bennett2026simulation,
  title = {{A VQE simulation of the transverse field Ising model}},
  author = {Luke Bennett},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05379},
  eprint = {2611.05379},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05379},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A VQE simulation of the transverse field Ising model
AU  - Luke Bennett
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.05379
UR  - https://arxiv.org/abs/2611.05379
AB  - One of the most promising applications of quantum computing is the ability to simulate quantum systems. A quantity of particular importance in condensed matter physics is the ground-state energy of a system. Here, we present an implementation of a hybrid quantum-classical algorithm known as the variational quantum eigensolver (VQE) to estimate the ground state energy of a prototypical quantum spin system. For this spin system, we use the transverse field Ising model (TFIM) which is known to exhibit a quantum phase transition (QPT) at a critical point. We apply the VQE to a $4$-spin TFIM and evaluate its performance using both a local noise model and IBM quantum hardware to estimate the ground-state energy and reproduce the QPT. The resulting ground-state energy estimates and QPT behaviour are compared with exact-diagonalisation benchmarks.
ER  -