Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution

Tianqi Chen; Tim Byrnes

doi:10.22331/q-2024-12-10-1557

Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution

Tianqi Chen^1,2,3,4 and Tim Byrnes^1,5,6,7

¹New York University Shanghai; NYU-ECNU Institute of Physics at NYU Shanghai, 567 West Yangsi Road, Pudong New District, Shanghai 200126, China
²Department of Physics, National University of Singapore, Singapore 117551
³Centre for Quantum Technologies, National University of Singapore, Singapore 117543
⁴School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798
⁵State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China
⁶Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, New York University Abu Dhabi, UAE
⁷Department of Physics, New York University, New York, NY 10003, USA

Published:	2024-12-10, volume 8, page 1557
Eprint:	arXiv:2310.06031v3
Doi:	https://doi.org/10.22331/q-2024-12-10-1557
Citation:	Quantum 8, 1557 (2024).

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Abstract

Quantum state preparation plays a crucial role in several areas of quantum information science, in applications such as quantum simulation, quantum metrology and quantum computing. However, typically state preparation requires resources that scale exponentially with the problem size, due to their probabilistic nature or otherwise, making studying such models challenging. In this article, we propose a method to prepare the ground state of the Affleck-Lieb-Kennedy-Tasaki (AKLT) model deterministically using a measurement-based imaginary time evolution (MITE) approach. By taking advantage of the special properties of the AKLT state, we show that it can be prepared efficiently using the MITE approach. Estimates based on the convergence of a sequence of local projections, as well as direct evolution of the MITE algorithm suggest a constant scaling with respect to the number of AKLT sites, which is an exponential improvement over the naive estimate for convergence. We show that the procedure is compatible with qubit-based simulators, and show that using a variational quantum algorithm for circuit recompilation, the measurement operator required for MITE can be well approximated by a circuit with a much shallower circuit depth compared with the one obtained using the default Qiskit method.

Featured image: State preparation of the AKLT state using MITE for $N = 6$.

Popular summary

Preparing the Affleck, Kennedy, Lieb, and Tasaki (AKLT) state — a key many-body state in quantum physics— on a quantum device has been an outstanding challenge in the field of quantum simulations. Traditional approaches require transforming the projective operations into a unitary form, often demanding additional resources that make the method slow and impractical for larger systems.

In this study, we apply the Measurement-Based Imaginary Time Evolution (MITE) approach to overcome these challenges. By leveraging unique properties of the AKLT state, our method eliminates the need for resource-intensive transformations and reduces preparation time to a constant, independent of the system size of the AKLT state. This represents an exponential improvement over conventional methods.

We demonstrate its compatibility with qubit-based platforms like IBM Q Qiskit and Google Cirq, mapping the AKLT model onto qubit Hamiltonians and using advanced optimization techniques for implementation. This breakthrough opens the door to more practical and scalable quantum simulations on existing hardware, marking a significant step forward for the field.

► BibTeX data

@article{Chen2024efficient,
  doi = {10.22331/q-2024-12-10-1557},
  url = {https://doi.org/10.22331/q-2024-12-10-1557},
  title = {Efficient preparation of the {AKLT} {S}tate with {M}easurement-based {I}maginary {T}ime {E}volution},
  author = {Chen, Tianqi and Byrnes, Tim},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1557},
  month = dec,
  year = {2024}
}

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