Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Xiao Xiao; J. K. Freericks; A. F. Kemper

doi:10.22331/q-2021-09-28-553

Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware

Xiao Xiao¹, J. K. Freericks², and A. F. Kemper¹

¹Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
²Department of Physics, Georgetown University, 37th and O Sts. NW, Washington, DC 20057 USA

Published:	2021-09-28, volume 5, page 553
Eprint:	arXiv:2006.05524v3
Doi:	https://doi.org/10.22331/q-2021-09-28-553
Citation:	Quantum 5, 553 (2021).

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Abstract

Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection $\textit{intrinsic to models being simulated}$, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundaries. We show how maintaining particle-hole symmetry when sampling through the Brillouin zone is critical to obtaining high accuracy. This work illustrates how topological protection intrinsic to a quantum model can be employed to perform robust calculations on NISQ hardware, when one measures the appropriate protected quantum properties. It opens the door for further simulation of topological quantum models on quantum hardware available today.

Featured image: Left panel: the quantum circuits to perform braiding operations on a conventional quantum hardware; right panels: the phase diagram of the Kitaev honeycomb model determined by NISQ quantum hardware; the details of entanglement entropy along the dashed line in the lower right panel is shown in the upper right one.

Popular summary

It is challenging to achieve high accuracy for programs run on current noisy intermediate-scale quantum (NISQ) hardware. Topological quantum computing has long been thought to be a remedy for handling noise and decoherence, because topological qubits are intrinsically protected from environment. However, the creation of topological qubits is so difficult that we are yet to see topological quantum computers available for use. Here we demonstrate that performing calculations of the topological properties of quantum systems is also intrinsically robust, even if we do so on a conventional quantum computer. We do this in two steps. First, we construct nontrivial topological states by braiding non-Abelian quasi-particles with conventional qubits. Second, we use symmetry-enforced quantum circuits to perform calculations with small numbers of qubits. This study provides a paradigm for applying NISQ hardware to study nontrivial topological quantum states.

► BibTeX data

@article{Xiao2021determiningquantum,
  doi = {10.22331/q-2021-09-28-553},
  url = {https://doi.org/10.22331/q-2021-09-28-553},
  title = {Determining quantum phase diagrams of topological {K}itaev-inspired models on {NISQ} quantum hardware},
  author = {Xiao, Xiao and Freericks, J. K. and Kemper, A. F.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {553},
  month = sep,
  year = {2021}
}

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[3] Ammar Jahin, Andy C. Y. Li, Thomas Iadecola, Peter P. Orth, Gabriel N. Perdue, Alexandru Macridin, M. Sohaib Alam, and Norm M. Tubman, "Fermionic approach to variational quantum simulation of Kitaev spin models", Physical Review A 106 2, 022434 (2022).

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