Abstract
I describe how the number of abelian squares of given length relates to a certain problem in theoretical quantum computing, and I present a recursive formula for calculating the number of abelian squares of length t + t over an alphabet of size d. The presented formula is similar to a previously known formula but has substantially lower complexity for large d, a key improvement resulting in a practical solution to the original application.
| Original language | English |
|---|---|
| Pages (from-to) | 445-459 |
| Number of pages | 15 |
| Journal | Journal of Combinatorics |
| Volume | 14 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2023 |
Funding
This manuscript has been authored by UT-Battelle, LLC, under contract DE AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).This work was performed at Oak Ridge National Laboratory, operated by UT-Battelle, LLC under contract DE-AC05-00OR22725 for the US Department of Energy (DOE). Support for the work came from the DOE Advanced Scientific Computing Research (ASCR) Accelerated Research in Quantum Computing Program under field work proposal ERKJ354. This work was performed at Oak Ridge National Laboratory, operated by UT-Battelle, LLC under contract DE-AC05-00OR22725 for the US Department of Energy (DOE). Support for the work came from the DOE Advanced Scientific Computing Research (ASCR) Accelerated Research in Quantum Computing Program under field work proposal ERKJ354. arXiv: 2203.11886 arXiv: 2208.02360 \u2217This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Keywords
- Abelian squares
- quantum circuit expressiveness
- quantum computing
- variational methods