Quick Navigation
Topics
Trapped Ion Quantum Computing
Unstructured Randomness, Small Gaps and Localization
arXiv
Authors: Edward Farhi, Jeffrey Goldstone, David Gosset, Sam Gutmann, Peter Shor
Year
2010
Paper ID
11049
Status
Preprint
Abstract Read
~2 min
Abstract Words
107
Citations
N/A
Abstract
We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function. Because the cost function lacks structure we can prove results about the ground state. We find the ground state energy as the number of bits goes to infinity, show that the minimum gap goes to zero exponentially quickly, and we see a localization transition. We prove that there are no levels approaching the ground state near the end of the evolution. We do not know which features of this model are shared by a quantum adiabatic algorithm applied to random instances of satisfiability since despite being random they do have bit structure.
Why This Paper Matters
- This paper contributes to the Trapped-Ion Quantum Computing research area in the Quantum Articles archive.
- It adds a 2010 reference point for readers tracking recent quantum research.
- We study the Hamiltonian associated with the quantum adiabatic algorithm with a random cost function.
Paper Tools
Become a member to use research tools
Sign in to open papers, visit source links, share, cite, compare, copy DOI links, request category corrections, and build your reading list.
Show Paper arXiv Publisher Share
Cite This Paper
Copy URL
Compare
Copy DOI Add to Reading List
Category Correction Request
Category Correction Request
Help us improve classification quality by proposing a better category. Every request is reviewed by an admin.
Sign in to submit a category correction request for this paper.
Log In to SubmitReferences & Citation Signals
Community Reactions
Quick sentiment from readers on this paper.
Score:
0
Likes: 0
Dislikes: 0
Sign in to react to this paper.
Discussion & Reviews (Moderated)
Average Rating: 0.0 / 5 (0 ratings)
No written reviews yet.