# Optimal length of decomposition sequences composed of imperfect gates

Optimal length of decomposition sequences composed of imperfect gates Quantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length $$L_{\text {opt}}$$ L opt of the length L of the decomposition sequence. The existence of $$L_{\text {opt}}$$ L opt is due to the competition between the increase in gate accuracy with increasing L, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of L that is in satisfactory agreement with the results of our simulations and allows the determination of $$L_{\text {opt}}$$ L opt via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Optimal length of decomposition sequences composed of imperfect gates

, Volume 16 (5) – Mar 24, 2017
33 pages

/lp/springer_journal/optimal-length-of-decomposition-sequences-composed-of-imperfect-gates-3BFpIZyXF0
Publisher
Springer US
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/s11128-017-1571-5
Publisher site
See Article on Publisher Site

### Abstract

Quantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length $$L_{\text {opt}}$$ L opt of the length L of the decomposition sequence. The existence of $$L_{\text {opt}}$$ L opt is due to the competition between the increase in gate accuracy with increasing L, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of L that is in satisfactory agreement with the results of our simulations and allows the determination of $$L_{\text {opt}}$$ L opt via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 24, 2017

## 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