Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

Guoming Wang; Daniel Stilck França; Ruizhe Zhang; Shuchen Zhu; Peter D. Johnson

doi:10.22331/q-2023-11-06-1167

Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

Guoming Wang¹, Daniel Stilck França², Ruizhe Zhang^1,3, Shuchen Zhu^1,4, and Peter D. Johnson⁵

¹Zapata Computing Canada Inc., Toronto, ON M5V 2Y1, Canada
²Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France
³Department of Computer Science, University of Texas at Austin, Austin, TX 78712, USA
⁴Department of Computer Science, Georgetown University, Washington, DC 20057, USA
⁵Zapata Computing Inc., Boston, MA 02110 USA

Published:	2023-11-06, volume 7, page 1167
Eprint:	arXiv:2209.06811v3
Doi:	https://doi.org/10.22331/q-2023-11-06-1167
Citation:	Quantum 7, 1167 (2023).

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Abstract

A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will require some degree of fault tolerance. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation are costly in that they require a number of gates per circuit that grows exponentially with the desired number of bits in precision. We reduce this cost exponentially, by developing a ground state energy estimation algorithm for which this cost grows linearly in the number of bits of precision. Relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethylene-carbonate and PF$_6^-$, the estimated gate count and circuit depth is reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can use additional circuit depth to reduce the total runtime. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing.

► BibTeX data

@article{Wang2023quantumalgorithm,
  doi = {10.22331/q-2023-11-06-1167},
  url = {https://doi.org/10.22331/q-2023-11-06-1167},
  title = {Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision},
  author = {Wang, Guoming and Fran{\c{c}}a, Daniel Stilck and Zhang, Ruizhe and Zhu, Shuchen and Johnson, Peter D.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1167},
  month = nov,
  year = {2023}
}

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