Cost-efficient design of a quantum multiplier–accumulator unit

Cost-efficient design of a quantum multiplier–accumulator unit This paper proposes a cost-efficient quantum multiplier–accumulator unit. The paper also presents a fast multiplication algorithm and designs a novel quantum multiplier device based on the proposed algorithm with the optimum time complexity as multiplier is the major device of a multiplier–accumulator unit. We show that the proposed multiplication technique has time complexity $$O((3 {\hbox {log}}_{2}n)+1)$$ O ( ( 3 log 2 n ) + 1 ) , whereas the best known existing technique has $$O(n{\hbox {log}}_{2} n)$$ O ( n log 2 n ) , where n is the number of qubits. In addition, our design proposes three new quantum circuits: a circuit representing a quantum full-adder, a circuit known as quantum ANDing circuit, which performs the ANDing operation and a circuit presenting quantum accumulator. Moreover, the proposed quantum multiplier–accumulator unit is the first ever quantum multiplier–accumulator circuit in the literature till now, which has reduced garbage outputs and ancillary inputs to a great extent. The comparative study shows that the proposed quantum multiplier performs better than the existing multipliers in terms of depth, quantum gates, delays, area and power with the increasing number of qubits. Moreover, we design the proposed quantum multiplier–accumulator unit, which performs better than the existing ones in terms of hardware and delay complexities, e.g., the proposed ( $$n\times n$$ n × n )—qubit quantum multiplier–accumulator unit requires $$O(n^{2})$$ O ( n 2 ) hardware and $$O({\hbox {log}}_{2}n)$$ O ( log 2 n ) delay complexities, whereas the best known existing quantum multiplier–accumulator unit requires $$O(n^{3})$$ O ( n 3 ) hardware and $$O((n-1)^{2} +1+n)$$ O ( ( n - 1 ) 2 + 1 + n ) delay complexities. In addition, the proposed design achieves an improvement of 13.04, 60.08 and 27.2% for $$4\times 4$$ 4 × 4 , 7.87, 51.8 and 27.1% for $$8\times 8$$ 8 × 8 , 4.24, 52.14 and 27% for $$16\times 16$$ 16 × 16 , 2.19, 52.15 and 27.26% for $$32 \times 32$$ 32 × 32 and 0.78, 52.18 and 27.28% for $$128 \times 128$$ 128 × 128 -qubit multiplications over the best known existing approach in terms of number of quantum gates, ancillary inputs and garbage outputs, respectively. Moreover, on average, the proposed design gains an improvement of 5.62% in terms of area and power consumptions over the best known existing approach. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Cost-efficient design of a quantum multiplier–accumulator unit

Loading next page...
 
/lp/springer_journal/cost-efficient-design-of-a-quantum-multiplier-accumulator-unit-m0eaDHP52r
Publisher
Springer US
Copyright
Copyright © 2016 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/s11128-016-1455-0
Publisher site
See Article on Publisher Site

Abstract

This paper proposes a cost-efficient quantum multiplier–accumulator unit. The paper also presents a fast multiplication algorithm and designs a novel quantum multiplier device based on the proposed algorithm with the optimum time complexity as multiplier is the major device of a multiplier–accumulator unit. We show that the proposed multiplication technique has time complexity $$O((3 {\hbox {log}}_{2}n)+1)$$ O ( ( 3 log 2 n ) + 1 ) , whereas the best known existing technique has $$O(n{\hbox {log}}_{2} n)$$ O ( n log 2 n ) , where n is the number of qubits. In addition, our design proposes three new quantum circuits: a circuit representing a quantum full-adder, a circuit known as quantum ANDing circuit, which performs the ANDing operation and a circuit presenting quantum accumulator. Moreover, the proposed quantum multiplier–accumulator unit is the first ever quantum multiplier–accumulator circuit in the literature till now, which has reduced garbage outputs and ancillary inputs to a great extent. The comparative study shows that the proposed quantum multiplier performs better than the existing multipliers in terms of depth, quantum gates, delays, area and power with the increasing number of qubits. Moreover, we design the proposed quantum multiplier–accumulator unit, which performs better than the existing ones in terms of hardware and delay complexities, e.g., the proposed ( $$n\times n$$ n × n )—qubit quantum multiplier–accumulator unit requires $$O(n^{2})$$ O ( n 2 ) hardware and $$O({\hbox {log}}_{2}n)$$ O ( log 2 n ) delay complexities, whereas the best known existing quantum multiplier–accumulator unit requires $$O(n^{3})$$ O ( n 3 ) hardware and $$O((n-1)^{2} +1+n)$$ O ( ( n - 1 ) 2 + 1 + n ) delay complexities. In addition, the proposed design achieves an improvement of 13.04, 60.08 and 27.2% for $$4\times 4$$ 4 × 4 , 7.87, 51.8 and 27.1% for $$8\times 8$$ 8 × 8 , 4.24, 52.14 and 27% for $$16\times 16$$ 16 × 16 , 2.19, 52.15 and 27.26% for $$32 \times 32$$ 32 × 32 and 0.78, 52.18 and 27.28% for $$128 \times 128$$ 128 × 128 -qubit multiplications over the best known existing approach in terms of number of quantum gates, ancillary inputs and garbage outputs, respectively. Moreover, on average, the proposed design gains an improvement of 5.62% in terms of area and power consumptions over the best known existing approach.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 21, 2016

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 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

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