Composite Quantum Simulations

Matthew Hagan; Nathan Wiebe

doi:10.22331/q-2023-11-14-1181

Composite Quantum Simulations

Matthew Hagan¹ and Nathan Wiebe^2,3,4

¹Department of Physics, University of Toronto, Toronto ON, Canada
²Department of Computer Science, University of Toronto, Toronto ON, Canada
³Pacific Northwest National Laboratory, Richland Wa, USA
⁴Canadian Institute for Advanced Study, Toronto ON, Canada

Published:	2023-11-14, volume 7, page 1181
Eprint:	arXiv:2206.06409v3
Doi:	https://doi.org/10.22331/q-2023-11-14-1181
Citation:	Quantum 7, 1181 (2023).

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Abstract

In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the Composite channel and the ideal simulation channel and show under what conditions the cost of implementing the Composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.

► BibTeX data

@article{Hagan2023compositequantum,
  doi = {10.22331/q-2023-11-14-1181},
  url = {https://doi.org/10.22331/q-2023-11-14-1181},
  title = {Composite {Q}uantum {S}imulations},
  author = {Hagan, Matthew and Wiebe, Nathan},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {7},
  pages = {1181},
  month = nov,
  year = {2023}
}

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