Structural stability of the quantum Fourier transform

Structural stability of the quantum Fourier transform While it is important to investigate the negative effects of decoherence on the performance of quantum information processors, Landauer was one of the first to point out that an equally basic problem, i.e., the effects of unavoidable hardware flaws in the real-world implementations of quantum gates, needs to be investigated as well. Following Landauer’s suggestion, we investigated the structural stability of the quantum Fourier transform (QFT) via significantly changing the analytical form of its controlled rotation gates, thus modeling structural flaws in the Hamiltonian of the QFT. Three types of modified rotation gates were investigated, numerically and analytically, changing the exact QFT rotation angles $$\pi /2^j$$ π / 2 j to (1) $$\pi /\alpha ^j$$ π / α j , (2) $$\pi /2 j^{\beta }$$ π / 2 j β , and (3) $$\pi /\log _{\gamma }(j+1)$$ π / log γ ( j + 1 ) , where $$\alpha $$ α , $$\beta $$ β , and $$\gamma $$ γ are constants and $$j$$ j is the integer distance between QFT qubits. Surprisingly good performance is observed in all the three cases for a wide range of $$\alpha $$ α , $$\beta $$ β , and $$\gamma $$ γ . This demonstrates the structural stability of the QFT Hamiltonian. Our results also demonstrate that the precise implementation of QFT rotation angles is not critical as long as the angles (roughly) observe a monotonic decrease in $$j$$ j (hierarchy). This result is important since it indicates that stringent tolerances do not need to be imposed in the actual manufacturing process of quantum information hardware components. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Structural stability of the quantum Fourier transform

Loading next page...
 
/lp/springer_journal/structural-stability-of-the-quantum-fourier-transform-Pau20dal3h
Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
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/s11128-015-0923-2
Publisher site
See Article on Publisher Site

Abstract

While it is important to investigate the negative effects of decoherence on the performance of quantum information processors, Landauer was one of the first to point out that an equally basic problem, i.e., the effects of unavoidable hardware flaws in the real-world implementations of quantum gates, needs to be investigated as well. Following Landauer’s suggestion, we investigated the structural stability of the quantum Fourier transform (QFT) via significantly changing the analytical form of its controlled rotation gates, thus modeling structural flaws in the Hamiltonian of the QFT. Three types of modified rotation gates were investigated, numerically and analytically, changing the exact QFT rotation angles $$\pi /2^j$$ π / 2 j to (1) $$\pi /\alpha ^j$$ π / α j , (2) $$\pi /2 j^{\beta }$$ π / 2 j β , and (3) $$\pi /\log _{\gamma }(j+1)$$ π / log γ ( j + 1 ) , where $$\alpha $$ α , $$\beta $$ β , and $$\gamma $$ γ are constants and $$j$$ j is the integer distance between QFT qubits. Surprisingly good performance is observed in all the three cases for a wide range of $$\alpha $$ α , $$\beta $$ β , and $$\gamma $$ γ . This demonstrates the structural stability of the QFT Hamiltonian. Our results also demonstrate that the precise implementation of QFT rotation angles is not critical as long as the angles (roughly) observe a monotonic decrease in $$j$$ j (hierarchy). This result is important since it indicates that stringent tolerances do not need to be imposed in the actual manufacturing process of quantum information hardware components.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 28, 2015

References

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
discover and read the research
that matters to you.

Enjoy affordable access to
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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off