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PreprintCC BY 4.0arXiv

A remark on the Brown-Susskind conjecture

  • Jean-Luc Brylinski
  • Ranee Brylinski
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Abstract

In the spirit of the Brown-Susskind conjecture, proven in \cite{haf} and \cite{li}, we study the growth of the dimension of the set of n-qubit unitaries which can be obtained as a product of a fixed number of $2$-qubit gates from a fixed set of pairs of qubits. We show that this dimension increases strictly when one more pair is added, for at least some choice of the $2$-qubit pairs at each step.

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Cite

BibTeXRIS
BibTeX
@misc{brylinski2026remark,
  title = {{A remark on the Brown-Susskind conjecture}},
  author = {Jean-Luc Brylinski and Ranee Brylinski},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23221},
  eprint = {2609.23221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23221},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A remark on the Brown-Susskind conjecture
AU  - Jean-Luc Brylinski
AU  - Ranee Brylinski
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2609.23221
UR  - https://arxiv.org/abs/2609.23221
AB  - In the spirit of the Brown-Susskind conjecture, proven in \cite{haf} and \cite{li}, we study the growth of the dimension of the set of n-qubit unitaries which can be obtained as a product of a fixed number of $2$-qubit gates from a fixed set of pairs of qubits. We show that this dimension increases strictly when one more pair is added, for at least some choice of the $2$-qubit pairs at each step.
ER  -