Optimal synthesis into fixed XX interactions

Eric C. Peterson; Lev S. Bishop; Ali Javadi-Abhari

doi:10.22331/q-2022-04-27-696

Optimal synthesis into fixed XX interactions

Eric C. Peterson¹, Lev S. Bishop², and Ali Javadi-Abhari²

¹IBM Quantum, San Jose, CA, USA
²IBM Quantum, Yorktown Heights, NY, USA

Published:	2022-04-27, volume 6, page 696
Eprint:	arXiv:2111.02535v3
Doi:	https://doi.org/10.22331/q-2022-04-27-696
Citation:	Quantum 6, 696 (2022).

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Abstract

We describe an optimal procedure, as well as its efficient software implementation, for exact and approximate synthesis of two-qubit unitary operations into any prescribed discrete family of XX-type interactions and local gates. This arises from the analysis and manipulation of certain polyhedral subsets of the space of canonical gates. Using this, we analyze which small sets of XX-type interactions cause the greatest improvement in expected infidelity under experimentally-motivated error models. For the exact circuit synthesis of Haar-randomly selected two-qubit operations, we find an improvement in estimated infidelity by 31.4% when including alongside CX its square- and cube-roots, near to the optimal limit of 36.9% obtained by including all fractional applications of CX.

Featured image: Path of compilation steps through the space of canonical coordinates for a random two-qubit unitary decomposing into CX, its square root, and its cube root.

► BibTeX data

@article{Peterson2022optimalsynthesis,
  doi = {10.22331/q-2022-04-27-696},
  url = {https://doi.org/10.22331/q-2022-04-27-696},
  title = {Optimal synthesis into fixed {XX} interactions},
  author = {Peterson, Eric C. and Bishop, Lev S. and Javadi-Abhari, Ali},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {696},
  month = apr,
  year = {2022}
}

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