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Paper 1
A Quantum Complexity Lowerbound from Differential Geometry
Adam R. Brown
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2112.05724
- arXiv
- 2112.05724
The Bishop-Gromov bound -- a cousin of the focusing lemmas that Hawking and Penrose used to prove their black hole singularity theorems -- is a differential geometry result that upperbounds the rate of growth of volume of geodesic balls in terms of the Ricci curvature. In this paper, I apply the Bishop-Gromov bound to Nielsen's complexity geometry to prove lowerbounds on the quantum complexity of a typical unitary. For a broad class of penalty schedules, the typical complexity is shown to be exponentially large in the number of qubits. This technique gives results that are tighter than all known lowerbounds in the literature, as well as establishing lowerbounds for a much broader class of complexity geometry metrics than has hitherto been bounded. For some metrics, I prove these lowerbounds are tight. This method realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity.
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Anomalous Lifetimes of Ultracold Complexes Decaying into a Single Channel: What's Taking So Long in There?
James F. E. Croft, John L. Bohn, Goulven Quéméner
- Year
- 2021
- Journal
- arXiv preprint
- DOI
- arXiv:2111.09956
- arXiv
- 2111.09956
We investigate the lifetimes of complexes formed in ultracold molecule collisions. Employing both transition-state-theory and an optical model approach we examine processes that can extend the lifetime of complexes beyond that predicted by Rice-Ramsperger-Kassel-Marcus theory. We focus on complexes that possess only one open channel, and find that the extreme distribution of widths for this case favors low decay rates. Thus decay from a complex into a single energetically available channel can be anomalously slow, and moreover nonexponential in time. We apply the theory to two systems of current experimental interest, RbCs and NaRb, finding qualitatively that the empirical time scales can be accounted for in the theory.
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