Long-Distance Universality for the Berger Sphere and the Unicycle

Proofs of two claims of Brown, Freedman, Lin and Susskind on one-qubit complexity geometry: the Berger-sphere distance changes by at most pi/(2 sqrt I) as the penalty factor I tends to infinity, and the unicycle parking cost is z + 2 sqrt(1 - 1/I) + O(1/z).

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-11
DOI
https://doi.org/10.5281/zenodo.24126945
Primary Topic
Quantum Computing Algorithms and Architecture
Type
preprint
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preprint

Long-Distance Universality for the Berger Sphere and the Unicycle

Deep Bhattacharjee
Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
preprint

Long-Distance Universality for the Berger Sphere and the Unicycle

Deep Bhattacharjee
preprint en

Abstract

Proofs of two claims of Brown, Freedman, Lin and Susskind on one-qubit complexity geometry: the Berger-sphere distance changes by at most pi/(2 sqrt I) as the penalty factor I tends to infinity, and the unicycle parking cost is z + 2 sqrt(1 - 1/I) + O(1/z).

Zenodo (CERN European Organization for Nuclear Research)
Quantum Computing Algorithms and Architecture
DOIOpen Access PDFOpenAlex
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