A Systematic Mapping Study on Quantum Circuits Design Patterns

Sergio Jim

enez-Fern

andez

, Jos

e A. Cruz-Lemus

and Mario Piattini

Institute of Technologies and Information Systems & Escuela Superior de Inform

atica, University of Castilla-La Mancha,

13071, Ciudad Real, Spain

Keywords:

Quantum Circuits, Patterns, SMS.

Abstract:

Introduction. In order to study quantum software’s quality, the use of patterns for designing quantum circuits

is quite an unexplored ﬁeld whereas a promising one too. Method. This work aims to discover the current

state of the art of quantum circuits design patterns by searching the literature via a Systematic Mapping Study.

Results. The search space was formed by 1327 studies in three different databases for a ﬁnal result of 15

primary studies. Conclusions. These studies include a taxonomy for different design patterns over quantum

circuits.

1 INTRODUCTION

A quantum circuit is normally deﬁned as a set of

quantum gates to be applied to a set of qubits. Ac-

cording to (Ozols and Walter, 2021) a quantum circuit

has three main parts:

1. An initial state, usually starting with every qubit

in state

⟩

2. A sequence of quantum gates acting over a set

of qubits (normally from one qubit up to three or

even more).

3. A set of measurements to extract the information

after applying all the quantum gates.

Design patterns (DP) have traditionally been used

at the design phase of the development of classic

software systems (Budgen, 2013)(Gray, 1996)(Rosal,

2014). The use of DP in classic computing has meant

a huge advance in the design phase of every software

development life cycle, as it helps leading to better de-

signs so that higher quality software solutions can be

achieved. DP allow us to focus on an speciﬁc Object-

Oriented challenge by naming, abstracting and iden-

tifying the main aspects of the class design used for

solving that problem. For that, DP identify the dif-

ferent classes designed and gives each class a role for

solving the problem (Gamma et al., 1994).

Considering the rise of Quantum Computing

(QC), we consider that there is a gap in QC ﬁnding

https://orcid.org/0000-0002-8548-0597

https://orcid.org/0000-0002-0470-609X

https://orcid.org/0000-0002-7212-8279

and using DP when designing quantum circuits, so

that the quality of these is improved. This is cer-

tainly a relevant subject to be taken into account in

order to follow many of the principles of the Talav-

era Manifesto for quantum software engineering and

programming (Piattini et al., 2020) and thus, it might

be helpful for improving different quality aspects of

quantum circuits which will affect the quality of the

quantum software programmed from them, including

several well-known quality characteristics such as the

understandability (Cruz-Lemus et al., 2021) or even

the maintenance of quantum/hybrid software systems

(Piattini et al., 2021).

In this Manifesto, several principles and commit-

ments are exposed for the sake of reaching a correct

and formal growth of the Quantum Software Engi-

neering (QSE) so that a high quality quantum soft-

ware development process can be achieved. Keep-

ing this in mind, we consider that DP may contribute

to increase the quality of quantum circuits, as they

have traditionally done with models in classic soft-

ware (Budgen, 2013)(Gray, 1996)(Rosal, 2014).

Within this context, we have performed a System-

atic Mapping Study (SMS) based on the methodology

by Petersen et al. (Petersen et al., 2008). A SMS is

a secondary study with a wide scope aiming to pro-

vide a global view about certain topic (design pat-

terns for quantum circuits in our case) and identify

the amount and kind of research already performed.

A total of 1327 studies were analyzed, resulting in 41

potential candidates, leading to a primary studies list

(PSL) with 15 items. We think that the obtained re-

Jiménez-Fernández, S., Cruz-Lemus, J. and Piattini, M.

A Systematic Mapping Study on Quantum Circuits Design Patterns.

DOI: 10.5220/0011744000003467

In Proceedings of the 25th International Conference on Enterprise Information Systems (ICEIS 2023) - Volume 2, pages 109-116

ISBN: 978-989-758-648-4; ISSN: 2184-4992

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

109

sults could beneﬁt: (i) future researchers studying the

quantum DP ﬁeld and (ii) quantum software develop-

ment companies interested in improving the quality of

their systems by means of QSE principles.

The remainder of the paper is organized as fol-

lows: Section 2 deﬁnes the methodology followed

for developing the SMS. The answers to the research

questions expressed in the previous section are de-

tailed in Section 3. Also, the different potential threats

to validity are explained in Section 4. To conclude, in

Section 5 some ideas for future works and some con-

clusion are proposed.

2 SMS METHODOLOGY

2.1 Planning the Review

As aforementioned, we performed a SMS based on

the proposed process by Petersen et al. (Petersen

et al., 2008) combined with the backward snowballing

technique

. The mapping was performed by the ﬁrst

author and was constantly supervised by the other

two authors. The methodology and its stages are ex-

plained throughout this section.

2.1.1 Protocol Deﬁnition

Three different stages were performed (see Figure 1):

1. Planning the Review: Deﬁne the protocol, the se-

lection criteria and the research questions among

other items.

2. Performing the Review: Process all the search

space and obtain the PSL as well as classifying

all the studies found.

3. Reporting the Review: Answer the research ques-

tions and obtain the conclusions.

2.1.2 Research Questions

Bearing the goal of the study in mind, the following

research questions have been deﬁned:

• RQ1: Which kind of publications have been done

about DP in QC?

• RQ2: Which are the core research topics about

DP in QC?

• RQ3: Which are the main advances regarding the

deﬁnition and/or detection of DP in quantum cir-

cuits?

Process consisting on performing the selection strategy

over each study in the references section from an article and,

if applicable, add it to the PSL (Wohlin, 2014).

2.1.3 Selection Criteria

In order to minimize the threats to validity of the

study, a set of inclusion and exclusion criteria (IC

and EC

) were deﬁned. The inclusion criteria (IC

)

used were:

• IC

: Studies expressing explicitly its aim of con-

tributing in the DP in quantum circuits in the ab-

stract and/or title.

• IC

: Studies dated between 1980 and 2022.

• IC

: Studies labeled in any of these ﬁelds: Com-

puter Science, Mathematics, and Engineering.

The start date was 1980 since that is the year when

Paul Benioff proposed his “Quantum Model of the

Turing Machine” (Benioff, 1980), which was consid-

ered as a seminal work.

On the other hand, the applied exclusion criteria

were:

• EC

: Studies not written in English.

• EC

: Studies mentioning patterns but not being

proper DP (e.g., light patterns, encoding-based

patterns, etcetera).

• EC

: Studies related to Quantum Annealing

(QA). QA presents a series of differences with re-

spect to quantum circuits such as:

1. Atomic information level is considered differ-

ently, in other words, a qubit in a gate-based

circuit behaves differently to a qubit within a

QA algorithm, and so, the way of manipulating

the information is not the same.

2. The types of problems to be solved within each

model are different. More speciﬁcally, QA

focuses on optimization problems while gate-

based has a wider problems scope.

For this purpose, in the second phase of the SMS,

the appropriate queries were launched to three scien-

tiﬁc databases: SCOPUS, arXiv, and Google Scholar.

Consequently, all the resulting studies passed through

two ﬁltering stages by applying all the aforemen-

tioned exclusion and inclusion criteria. All those ar-

ticles passing the ﬁrst ﬁltering stage were considered

as potential candidates. Finally, all the potential can-

didates went through the last riddling stage. Those

studies (primary studies) passing this stage became

part of the PSL and were classiﬁed and processed for

answering the research questions.

2.1.4 Search String

The search string used, bearing in mind the selection

criteria was:

(design pattern) AND

(quantum AND (circuit OR computing))

ICEIS 2023 - 25th International Conference on Enterprise Information Systems

110

Figure 1: SMS methodology steps.

2.2 Data Extraction

To acquire quantitative and qualitative information for

answering our research questions, the following data

were extracted from each primary study:

1. Document title.

2. Authors.

3. Publication date/year.

4. Type of publication (RQ1).

5. Research subject (RQ2 & RQ3).

3 RESULTS

After applying the explained strategy, we found 904

articles matching the search string on SCOPUS. From

those, 30 were considered possible candidates but

only eight of them were selected as primary studies.

In arXiv, 122 publications were initially found

plus one more due to snowballing. From them,

seven were considered possible candidates and three

of them were ﬁnally included as a primary studies.

For Google Scholar, we analyzed the ﬁrst 300 re-

sults that appeared in the search result. The vast ma-

jority of the results were far from matching the se-

lection criteria or had already been found in SCO-

PUS or arXiv. Also one more citation was obtained

from Scholar proposed in later reviews. However,

four more publications were tagged as potential can-

didates and later as primary studies.

This way, the ﬁnal PSL contained 15 primary

studies. The complete list with the references can be

found in an Appendix at the end of the document. Fig-

ure 2 graphically summarizes all this process.

The ﬁrst remarkable fact to highlight is the low

number of publications found (see Figure 3). Despite

the quick evolution experienced in the recent years,

QC is an area still in it infancy, especially in some spe-

ciﬁc ﬁelds such the use of design patterns for quantum

circuits. Anyhow, in the recent years it seems to be a

increasing interest in the topic.

Additionally, Table 1 shows a ranking of the most

contributing authors in DP for quantum circuits.

Table 1: Most contributing authors ranking.

Name # publications

Houshmand, M. 4

Sedighi M. 4

Zamani, M.S. 4

Eslamy, M. 2

Leymann, F. 2

Samavatian, M.H. 2

3.1 RQ1: Types of Publications

According to the results found in Table 2, there is not

a predominant type of publication related to DP in

QC. The number of works published in journals (5),

conferences (5) and pre-prints included in arXiv (5)

-labelled as Other in Table 2- is quite similar. It is

interesting to highlight that there are no books pub-

lished about this topic yet. Once again, we consider

that the topic is still in its early development stages

and these numbers will grow in the future.

Table 2: RQ1 results.

Category # publications Percentage

Journal 5 33.33%

Conferences 5 33.33%

Books 0 0.00%

Other 5 33.33%

A Systematic Mapping Study on Quantum Circuits Design Patterns

111

Figure 2: Search protocol summary.

Figure 3: Publications per year.

3.2 RQ2: Core Research Topics

Table 3 provides information about the different top-

ics on which the works in the PSL were based. Most

of them (8 out of 15) were focused on 1WQC

mea-

surement patterns. This approach uses only mea-

surements as operational units applied over a set of

qubits by establishing “measurement patterns”. Be-

sides, three publications are focused on pattern lan-

guages and models for quantum circuits, two are fo-

cused on pattern matching and, ﬁnally, two on pat-

terns in hybrid quantum/classic algorithms.

These numbers seem to show how the 1WQC

Measurement Patterns trend the search space on

quantum patterns. Later in Sections 3.3 and 5 some

differences between the concepts of DP and measure-

ment patterns will be dealt with.

One Way Quantum Computing

3.3 RQ3: Main Advances in DP for

Quantum Circuits

In spite of being such an unexplored subject, several

promising results and research topics were found.

In the previous sub-section, we already intro-

duced the 1WQC. It describes a model within the

Measurement-Based Quantum Computing (MBQC).

The MBQC proposes performing quantum computa-

tions using only measurement as computational steps

(Jozsa, 2005). Knowing this, 1WQC proposes a quan-

tum computing model that works by only performing

a sequence of one-qubit measurements (also known

as “measurement patterns”) on a particular entangled

multi-qubit state, the cluster state (Raussendorf et al.,

2002).

Another noteworthy study is (P

erez-Castillo and

Piattini, 2022), which proposes a continuous UML

ﬂow for designing hybrid systems. Within all the pre-

sented UML abstractions, we can highlight a poten-

tial pattern presented in subsection 4.3 for designing

a hybrid behaviour involving a request from a classi-

cal system to the “Quantum Driver”, named Quantum

Request. Nevertheless, we do not consider it as a DP

for quantum circuits since it is deﬁning a behaviour in

a higher abstraction level (hybrid system).

Moreover, we found quite an interesting piece of

work, actually and directly related with DP for quan-

tum circuits (Leymann, 2019). In this article, it is

explained what is a DP in classic Software Engi-

ICEIS 2023 - 25th International Conference on Enterprise Information Systems

112

Table 3: Core research topics and RQ2 results.

Main Subject # publications Percentage

1WQC measurement patterns 8 53.33%

Patterns in hybrid algorithms 2 13.33%

Pattern languages/models 3 20%

Pattern mining over quantum circuits 2 13.33%

neering and its importance when designing software

systems. Furthermore, the work states the different

points that any pattern description should have and,

later, deﬁnes a set of patterns for quantum circuits.

For the design of those patterns, the same strategy

than in classic Software Engineering was followed:

ﬁrst ﬁnding recurring problems when designing quan-

tum circuits and then composing an optimal solution

for them. The complete description of these patterns

can be found in (Leymann, 2019), but in short, they

could be stated as:

1. Initialization: a set of state preparation or ini-

tialization operations are described.

2. Uniform Superposition: an uniform superposi-

tion can be achieved by initializing all the n qubits

as the unit vector

0...0

⟩

and applying a Hadamard

gate afterwards.

3. Creating Entanglement: it is a commonly used

yet powerful mechanism in QC.

4. Function Table: used for optimizing computa-

tion time.

5. Oracle: it is another commonly used concept in

quantum algorithms.

6. Uncompute: this patterns manages the “undo”

computations needed to be performed over aux-

iliary or ancillae qubits.

7. Phase Shift: used to encode the ﬁtness of a solu-

tion to an algorithm.

8. Amplitude Ampliﬁcation: used to increase the

probability of measuring an speciﬁc value by am-

plifying the amplitude of a state.

9. Speedup Via Verifying: an approach for reach-

ing different solutions in an algorithm.

10. Quantum-Classic Split: used for distributing the

computational work between classic and quantum

computers in hybrid systems.

It is important to highlight that this list is nor

closed neither ﬁnished, as it is clariﬁed on the article,

but means quite a solid basis to start from in future

works. Besides, we think that more than one of these

patterns can be found within the same quantum cir-

cuit. This work also provides several considerations

on the use of DP in classic software engineering and

the marriage between the abstract concept of a pat-

tern, i.e., the abstraction technology-agnostic that a

pattern proposes and how it is implemented actually

in real software systems.

Furthermore, we consider important to highlight

the Quantum Computing Patterns

web. This web-

site collects the deﬁnitions of several patterns, quan-

tum circuit entities and even quantum algorithms. The

last category of patterns in this website is based on

the previously commented article (Leymann, 2019).

We also analyzed the rest of article references in the

web page but we believe that the concepts and enti-

ties exposed do not exactly ﬁt with the deﬁnition of

DP explained in Section 1. Due to this reason, neither

those articles nor the quantum circuit entities exposed

in them were considered for their inclusion as part of

the results. These articles are: (Weigold et al., 2020),

(Weigold et al., 2021a), and (Weigold et al., 2021b).

In order to check how these DP apply on a

Quantum Circuit, Figure 4 presents an example by

analysing Grover’s Algorithm (Grover, 1996). Basi-

cally, this well-known algorithm is capable of ﬁnd-

ing an element within an unsorted search space with a

complexity of O(

√

N), being N the size of the search

space.

We can ﬁnd four out of the ten patterns provided

in the previous list on this example:

• Initialization, quantum algorithms usually re-

quire the initialization of the qubits involved. In

this case, Grover’s Algorithm needs to initialize

all of them to the

⟩

state (see the left-most part

of the circuit in Figure 4).

• Uniform Superposition, highlighted in blue in

Figure 4. All the qubits involved in the algo-

rithm are initialized in a

0...0

⟩

state and, later, a

Hadamard gate is applied to them. This way, the

search space created is equiprobable.

• Oracle, highlighted in red in Figure 4. In this al-

gorithm, an oracle is used to revert the amplitude

of the intended solution.

• Amplitude Ampliﬁcation, highlighted in green

in Figure 4. The last step of the algorithm re-

quires to increase the probability of the previously

reversed solution.

https://www.quantumcomputingpatterns.org/

A Systematic Mapping Study on Quantum Circuits Design Patterns

113

uniform superposition

oracle

amplitude ampliﬁcation

... ... ...

⟩

⟩⟨

−I

⟩

H H H

Figure 4: Design patterns in Grover’s Algorithm.

4 THREATS TO VALIDITY

The ﬁrst threat to validity is the power and accuracy

of the search string. Prior to starting the review, we

familiarized with the ﬁeld of DP for quantum cir-

cuits and used several synonyms and key concepts

for the search strategy. After several iterations, all

the authors agreed on the ﬁnal search string. Further-

more, in the literature search strategy, we aimed to

retrieve as many relevant studies as possible. To do

so, the main scientiﬁc databases in QC research with

the most extensive coverage were chosen: SCOPUS,

arXiv, and Google Scholar. The use of arXiv is es-

pecially important in the ﬁeld of Quantum Comput-

ing as, being it a novel discipline, there is a certain

number of publications in pre-print phase which are

shared in the repository.

Regarding the data extraction and selection pro-

cess, the ﬁltering and classiﬁcation stages were per-

formed manually by only one researcher to ensure

that all studies were reviewed with the same criteria.

The inexperience of the ﬁrst author could be also con-

sidered as a thread to validity. Despite this, continu-

ous reviews and corrections have been done through-

out the whole process.

5 CONCLUSIONS AND FUTURE

WORK

Once we have performed the qualitative and quanti-

tative synthesis of the extracted data, we can present

the main conclusions obtained.

The number of primary studies found is small, but

in the recent years the number of studies is increas-

ing. This might imply a growing interest in this novel

topic, once researchers are becoming aware of the im-

portance of using these kind of elements for establish-

ing the foundations of the QSE (Piattini et al., 2020).

We have discovered that the most published topic

in the ﬁeld are the One-Way Quantum Computing

Measurement Patterns (Raussendorf et al., 2002).

But, as we remarked in Section 3 deﬁnition, these

measurement patterns are not properly DP as we de-

scribed them in Section 1.

We have identiﬁed a list of authors holding the

current knowledge about DP for quantum circuits, es-

pecially the main contribution provided by (Leymann,

2019). This works offers an interesting seminal tax-

onomy for different DP for quantum circuits.

As future work, we believe that there exists several

possibilities for research inside this subject, mainly:

• Increase the patterns list proposed in (Leymann,

2019).

• Pondering to start using those patterns in actual

quantum software systems.

From a more practical point of view, a strongly vi-

able project implementing all these ideas could be the

development of a tool for detecting quantum patterns

in quantum circuits. It should be able to detect which

(sub-)problems a quantum circuit is solving and so:

(i) warn the developer to use the adequate pattern(s)

when designing a suitable solution; (ii) match some

patterns used in classic software engineering which

might show beneﬁts in quantum circuits design; (iii)

if needed, register and formalize it as a new pattern

establishing a constant line of feedback.

ACKNOWLEDGEMENTS

The authors would like to thank all the aQuan-

tum members, especially Guido Peterssen and Pepe

Hevia, for their continuous and valuable help and sup-

port.

This work was partially funded by the “QHealth:

Quantum Pharmacogenomics Applied to Aging”

project (EXP 00135977 / MIG-20201059), part

ICEIS 2023 - 25th International Conference on Enterprise Information Systems

114

of the 2020 CDTI Missions Program (Center

for the Development of Industrial Technology

of the Ministry of Science and Innovation of

Spain), the R+D+d project PID2020-112540RB-

C42, AETHER-UCLM (A smart data holistic ap-

proach for context-aware data analytics), funded by

MCIN/AEI/10.13039/501100011033/, and the QU-

ASAP project “QUAntum Software modernizA-

tions Prototype” (PDC2022-133051-I00), funded by

MCIN/ AEI/10.13039/501100011033/ and the Euro-

pean Union NextGenerationEU.

REFERENCES

Benioff, P. (1980). The computer as a physical system: A

microscopic quantum mechanical hamiltonian model

of computers as represented by turing machines. Jour-

nal of Statistical Physics, 22:563–591.

Budgen, D. (2013). Design patterns: Magic or myth? IEEE

Software, 30(2):87 – 90. Cited by: 6.

Cruz-Lemus, J. A., Marcelo, L. A., and Piattini, M. (2021).

Towards a set of metrics for quantum circuits under-

standability. In Paiva, A. C. R., Cavalli, A. R., Ven-

tura Martins, P., and P

erez-Castillo, R., editors, Qual-

ity of Information and Communications Technology,

pages 239–249, Cham. Springer International Pub-

lishing.

Duncan, R. and Perdrix, S. (2010). Rewriting measurement-

based quantum computations with generalised ﬂow.

Lecture Notes in Computer Science (including sub-

series Lecture Notes in Artiﬁcial Intelligence and

Lecture Notes in Bioinformatics), 6199 LNCS(PART

2):285 – 296. Cited by: 61; All Open Access, Green

Open Access.

Eslamy, M., Houshmand, M., Zamani, M. S., and Sedighi,

M. (2016). Geometry-based signal shifting of one-

way quantum computation measurement patterns. In

2016 24th Iranian Conference on Electrical Engineer-

ing (ICEE), page 356 – 361, Piscataway, NJ. Institute

of Electrical and Electronic Engineers. Cited by: 2.

Eslamy, M., Houshmand, M., Zamani, M. S., and Sedighi,

M. (2018). Optimization of one-way quantum com-

putation measurement patterns. International Journal

of Theoretical Physics, 57(11):3296 – 3317. Cited by:

2; All Open Access, Green Open Access.

Gamma, E., Helm, R., Johnson, R., and Vlissides, J.

(1994). Design Patterns: Elements of Reusable

Object-Oriented Software. Addison-Wesley Profes-

sional, Indianapolis, IN, 1 edition.

Gilliam, A., Venci, C., Muralidharan, S., Dorum, V., May,

E., Narasimhan, R., and Gonciulea, C. (2019). Foun-

dational patterns for efﬁcient quantum computing.

Gray, N. (1996). Teaching object orientation: Patterns and

reuse. In Proceedings of 1996 Australian Software En-

gineering Conference, page 72 – 80. Cited by: 1.

Grover, L. K. (1996). A fast quantum mechanical algorithm

for database search. volume Part F129452, page 212

– 219. Cited by: 3963.

Houshmand, M., Zamani, M. S., Samavatian, M. H., and

Sedighi, M. (2012). Extracting one-way quantum

computation patterns from quantum circuits. In The

16th CSI International Symposium on Computer Ar-

chitecture and Digital Systems (CADS 2012), page 64

– 69, Piscataway, NJ. Institute of Electrical and Elec-

tronic Engineers. Cited by: 3.

Houshmand, M., Zamani, M. S., Samavatian, M. H., and

Sedighi, M. (2015). Automatic translation of quantum

circuits to optimized one-way quantum computation

patterns. Quantum Information Processing, 13:2463

– 2482.

Iten, R., Moyard, R., Metger, T., Sutter, D., and Woerner,

S. (2022). Exact and practical pattern matching for

quantum circuit optimization. ACM Transactions on

Quantum Computing, 3(1).

Jang, W., Terashi, K., Saito, M., Bauer, C. W., Nachman,

B., Iiyama, Y., Kishimoto, T., Okubo, R., Sawada, R.,

and Tanaka, J. (2021). Quantum gate pattern recog-

nition and circuit optimization for scientiﬁc applica-

tions. EPJ Web of Conferences, 251:03023.

Jozsa, R. (2005). An introduction to measurement based

quantum computation.

Leymann, F. (2019). Towards a pattern language for quan-

tum algorithms. Lecture Notes in Computer Science

(including subseries Lecture Notes in Artiﬁcial Intel-

ligence and Lecture Notes in Bioinformatics), 11413

LNCS:218 – 230. Cited by: 10; All Open Access,

Green Open Access.

Lomont, C. (2003). Quantum circuit identities.

Maslov, D., Young, C., Miller, D. M., and Dueck, G. (2005).

Quantum circuit simpliﬁcation using templates. In

Design, Automation and Test in Europe, pages 1208–

1213 Vol. 2, Piscataway, NJ. Institute of Electrical and

Electronic Engineers.

Ozols, M. and Walter, M. (2021). The quantum quest.

erez-Castillo, R. and Piattini, M. (2022). Design of

classical-quantum systems with uml. Computing,

104:2374–2403.

Petersen, K., Feldt, R., Mujtaba, S., and Mattsson, M.

(2008). Systematic mapping studies in software en-

gineering. In Proceedings of the 12th International

Conference on Evaluation and Assessment in Software

Engineering, EASE’08, page 68–77, Swindon, GBR.

BCS Learning & Development Ltd.

Piattini, M., Peterssen, G., P

erez-Castillo, R., Hevia, J. L.,

Serrano, M. A., Hern

andez, G., de Guzm

an, I. G.-R.,

Paradela, C. A., Polo, M., Murina, E., Jim

enez, L.,

Marque

no, J. C., Gallego, R., Tura, J., Phillipson, F.,

Murillo, J. M., Ni

no, A., and Rodr

ıguez, M. (2020).

The talavera manifesto for quantum software engi-

neering and programming. 1st International Work-

shop on Quantum Software Engineering and Pro-

gramming (QANSWER 2020), n/a(n/a):11–12.

Piattini, M., Serrano, M. A., P

erez-Castillo, R., Petersen,

G., and Hevia, J. L. (2021). Toward a quantum soft-

ware engineering. IT Professional, 23(1):62–66.

Pius, E. and Silva, E. K. R. D. D. (2015). Optimising

the information ﬂow of one-way quantum computa-

A Systematic Mapping Study on Quantum Circuits Design Patterns

115

tions. Quantum Information and Computation, 15(9-

10):853 – 884. Cited by: 1.

Raussendorf, R., Browne, D., and Briegel, H. (2002). The

one-way quantum computer–a non-network model of

quantum computation. Journal of Modern Optics,

49(8):1299–1306.

Rosal, S. (2014). Design patterns in object oriented pro-

gramming. Cited by: 0.

Simmons, W. (2021). Relating measurement patterns to cir-

cuits via pauli ﬂow. Electronic Proceedings in The-

oretical Computer Science, EPTCS, 343:50 – 101.

Cited by: 0; All Open Access, Gold Open Access,

Green Open Access.

Weigold, M., Barzen, J., Leymann, F., and Salm, M. (2020).

Data encoding patterns for quantum computing. In

Proceedings of the 27th Conference on Pattern Lan-

guages of Programs, PLoP ’20, USA. The Hillside

Group.

Weigold, M., Barzen, J., Leymann, F., and Salm, M.

(2021a). Expanding data encoding patterns for

quantum algorithms. In 2021 IEEE 18th Interna-

tional Conference on Software Architecture Compan-

ion (ICSA-C), pages 95–101.

Weigold, M., Barzen, J., Leymann, F., and Vietz, D.

(2021b). Patterns for Hybrid Quantum Algorithms.

In Proceedings of the 15

Symposium and Summer

School on Service-Oriented Computing (SummerSOC

2021), pages 34–51. Springer International Publish-

ing.

Weigold, M., Barzen, J., Leymann, F., and Vietz, D.

(2021c). Patterns for hybrid quantum algorithms.

Communications in Computer and Information Sci-

ence, 1429 CCIS:34 – 51. Cited by: 1.

Wohlin, C. (2014). Guidelines for snowballing in system-

atic literature studies and a replication in software en-

gineering. In Proceedings of the 18th International

Conference on Evaluation and Assessment in Software

Engineering, EASE ’14, New York, NY, USA. Asso-

ciation for Computing Machinery.

APPENDIX

The studies in the PSL correspond to the following

items in the references section:

• (Duncan and Perdrix, 2010)

• (Eslamy et al., 2016)

• (Eslamy et al., 2018)

• (Gilliam et al., 2019)

• (Houshmand et al., 2012)

• (Houshmand et al., 2015)

• (Iten et al., 2022)

• (Jang et al., 2021)

• (Leymann, 2019)

• (Lomont, 2003)

• (Maslov et al., 2005)

• (P

erez-Castillo and Piattini, 2022)

• (Pius and Silva, 2015)

• (Simmons, 2021)

• (Weigold et al., 2021c)

ICEIS 2023 - 25th International Conference on Enterprise Information Systems

116