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PreprintarXiv licencearXiv

Encoded reversible addition in constant Toffoli depth

  • Aidan Epperly
  • Isaac H. Kim
  • Mingyu Lee
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Abstract

We show that reversible in-place quantum addition modulo 2n−1 can be implemented in constant Toffoli depth using O(n) space, provided that the variables are encoded in a certain non-standard form. Using measurement-based uncomputation, the Toffoli depth can be reduced to one. We also present space-depth tradeoffs and an application to programmable rotations.

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Cite

BibTeXRIS
BibTeX
@misc{epperly2026encoded,
  title = {{Encoded reversible addition in constant Toffoli depth}},
  author = {Aidan Epperly and Isaac H. Kim and Mingyu Lee},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41142},
  eprint = {2610.41142},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41142},
}
RIS
TY  - UNPB
TI  - Encoded reversible addition in constant Toffoli depth
AU  - Aidan Epperly
AU  - Isaac H. Kim
AU  - Mingyu Lee
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41142
UR  - https://arxiv.org/abs/2610.41142
AB  - We show that reversible in-place quantum addition modulo 2^n−1 can be implemented in constant Toffoli depth using O(n) space, provided that the variables are encoded in a certain non-standard form. Using measurement-based uncomputation, the Toffoli depth can be reduced to one. We also present space-depth tradeoffs and an application to programmable rotations.
ER  -