# Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design

Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design In Choi (Quantum Inf Process, 7:193–209, 2008), we introduced the notion of minor-embedding in adiabatic quantum optimization. A minor-embedding of a graph G in a quantum hardware graph U is a subgraph of U such that G can be obtained from it by contracting edges. In this paper, we describe the intertwined adiabatic quantum architecture design problem, which is to construct a hardware graph U that satisfies all known physical constraints and, at the same time, permits an efficient minor-embedding algorithm. We illustrate an optimal complete-graph-minor hardware graph. Given a family $${\mathcal{F}}$$ of graphs, a (host) graph U is called $${\mathcal{F}}$$ -minor-universal if for each graph G in $${\mathcal{F}, U}$$ contains a minor-embedding of G. The problem for designing a $${{\mathcal{F}}}$$ -minor-universal hardware graph U sparse in which $${{\mathcal{F}}}$$ consists of a family of sparse graphs (e.g., bounded degree graphs) is open. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design

, Volume 10 (3) – Oct 13, 2010
11 pages

Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0200-3
Publisher site
See Article on Publisher Site

### Abstract

In Choi (Quantum Inf Process, 7:193–209, 2008), we introduced the notion of minor-embedding in adiabatic quantum optimization. A minor-embedding of a graph G in a quantum hardware graph U is a subgraph of U such that G can be obtained from it by contracting edges. In this paper, we describe the intertwined adiabatic quantum architecture design problem, which is to construct a hardware graph U that satisfies all known physical constraints and, at the same time, permits an efficient minor-embedding algorithm. We illustrate an optimal complete-graph-minor hardware graph. Given a family $${\mathcal{F}}$$ of graphs, a (host) graph U is called $${\mathcal{F}}$$ -minor-universal if for each graph G in $${\mathcal{F}, U}$$ contains a minor-embedding of G. The problem for designing a $${{\mathcal{F}}}$$ -minor-universal hardware graph U sparse in which $${{\mathcal{F}}}$$ consists of a family of sparse graphs (e.g., bounded degree graphs) is open.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 13, 2010

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations

Abstract access only

18 million full-text articles

Print

20 pages / month

PDF Discount

20% off