QuantME4VQA: Modeling and Executing Variational Quantum

Algorithms Using Workﬂows

Martin Beisel

, Johanna Barzen

, Marvin Bechtold

, Frank Leymann

, Felix Truger

and Benjamin Weder

Institute of Architecture of Application Systems, University of Stuttgart, Germany

Keywords:

Quantum Workﬂows, Quantum Computing, Variational Quantum Algorithms, Modeling Extension.

Abstract:

The execution of quantum algorithms typically requires classical pre- and post-processing, making quantum

applications inherently hybrid. Classical resources are of particular importance for so-called variational quan-

tum algorithms, as they leverage classical computational power to overcome the limitations imposed by today’s

noisy quantum devices. However, the additional complex tasks required by these algorithms, complicate the

challenge of integrating quantum circuit executions with classical programs. To overcome this challenge, we

leverage the advantages and versatility of workﬂows, and introduce a workﬂow modeling extension for or-

chestrating variational quantum algorithms. The modeling extension comprises new task types, data objects,

and a comprehensible graphical notation. Furthermore, we ensure interoperability and portability by provid-

ing a method for transforming all new modeling constructs to native modeling constructs, and showcase the

practical feasibility of our modeling extension by presenting a system architecture, prototype, and case study.

1 INTRODUCTION

Quantum computing enables to solve various com-

plex problems, e.g., in machine learning (DeBene-

dictis, 2018) or chemistry (Cao et al., 2018), in a

faster, more precise, or energy-efﬁcient manner. The

computational advantage of quantum algorithms over

their classical counterparts is achieved by leverag-

ing quantum mechanical phenomena, such as su-

perposition and entanglement (Preskill, 2018). To-

day’s quantum devices are still error-prone and lim-

ited in their number of qubits (Leymann and Barzen,

2020). However, so-called Variational Quantum Al-

gorithms (VQAs) (Cerezo et al., 2021a) have emerged,

enabling meaningful computations on these devices

by combining classical and quantum resources.

In general, the execution of quantum algorithms

requires additional pre- and post-processing steps,

such as encoding classical data for quantum devices

or evaluating quantum execution results (Leymann

https://orcid.org/0000-0003-2617-751X

https://orcid.org/0000-0001-8397-7973

https://orcid.org/0000-0002-7770-7296

https://orcid.org/0000-0002-9123-259X

https://orcid.org/0000-0001-6587-6431

https://orcid.org/0000-0002-6761-6243

and Barzen, 2020). Hence, quantum applications are

inherently hybrid, comprising various classical and

quantum programs. Analogous to classical software

engineering, it is good practice to modularize the

functionalities of quantum programs (Beisel et al.,

2023). Therefore, developers can reuse existing, well-

tested components as building blocks for quantum ap-

plications, making their development and operation

less time-consuming, error-prone, and expensive.

As a result, the execution of a quantum applica-

tion requires the orchestration of various quantum and

classical programs, which often use different data for-

mats, interfaces, and programming languages (Ley-

mann and Barzen, 2021). A well-established tech-

nology for orchestrating heterogeneous processes are

workﬂows (Leymann and Roller, 1999). Workﬂows

provide many advantages, such as robustness, scala-

bility, and transactional processing. Hence, by inte-

grating quantum programs using workﬂows, they can

inherently beneﬁt from these advantages.

Although workﬂows enable the integration of ar-

bitrary tasks, many quantum-related tasks have spe-

ciﬁc characteristics and requirements, complicating

their modeling and conﬁguration. Therefore, deﬁn-

ing quantum workﬂows requires immense expertise

in quantum computing and workﬂow technologies, as

well as deep mathematical knowledge.

306

Beisel, M., Barzen, J., Bechtold, M., Leymann, F., Truger, F. and Weder, B.

QuantME4VQA: Modeling and Executing Variational Quantum Algorithms Using Workﬂows.

DOI: 10.5220/0011997500003488

In Proceedings of the 13th International Conference on Cloud Computing and Services Science (CLOSER 2023), pages 306-315

ISBN: 978-989-758-650-7; ISSN: 2184-5042

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

quantum

computation

task

quantum circuit

execution task

readout error

mitigation task

quantum circuit

loading task

oracle

expansion

task

quantum

circuit

object

data

preparation

task

result

object

quantum hardware

selection sub -process

Figure 1: Existing QuantME modeling constructs and their graphical notation (based on (Weder et al., 2020b, 2021)).

To facilitate the modeling of VQAs using work-

ﬂows, we (i) extend the Quantum Modeling Extension

(QUANTME) (Weder et al., 2020b) and introduce ex-

plicit modeling constructs for reoccurring tasks. Our

extension is called QUANTME4VQA and comprises

ﬁve new task types and three new data objects. To

improve the interoperability of QUANTME4VQA, we

(ii) present an approach for the transformation of

these modeling constructs into native workﬂow frag-

ments. Furthermore, we (iii) prove the practical fea-

sibility of our approach by providing a system ar-

chitecture and a prototypical implementation. Finally,

we (iv) demonstrate its suitability in a case study.

The remainder of this paper is structured as fol-

lows: In Section 2, fundamentals are described, and

the problems tackled in this work are stated. Section 3

introduces QUANTME4VQA and describes all new

modeling constructs. Section 4 shows their usage in a

case study. Section 5 explains how QUANTME4VQA

modeling constructs are transformed into native

workﬂow fragments. Section 6 presents a system ar-

chitecture for QUANTME4VQA and showcases its

functionality by a prototypical implementation. Fi-

nally, Section 7 discusses related work and Section 8

summarizes the paper and discusses future work.

2 FUNDAMENTALS & PROBLEM

STATEMENT

In this section, we establish fundamentals about the

structure and functionality of VQAs, quantum work-

ﬂows, and QUANTME. Afterward, we discuss exist-

ing problems and present our research questions.

2.1 VQAs

VQAs have emerged as a new class of quantum al-

gorithms to overcome the limitations imposed by to-

day’s quantum devices (Cerezo et al., 2021a). They

follow a learning-based approach, parameterizing

gates in quantum circuits and optimizing parameter

values in order to ﬁnd the optimal solution. To de-

termine good circuit parameters, VQAs alternate be-

tween executing a parameterized quantum circuit on a

quantum device, and classically optimizing its param-

eters based on the previous execution results. Hence,

they work well with shallow quantum circuits, i.e.,

circuits whose depth is independent of the input

size (Bravyi et al., 2020), and can take advantage of

the plethora of classical optimization methods. More-

over, promising techniques to further improve the per-

formance of VQAs are being developed, e.g., clas-

sical circuit parameter warm-starting (Galda et al.,

2021), initial state warm-starting (Egger et al., 2021),

or custom optimization techniques (Rad et al., 2022).

2.2 Quantum Workﬂows & QuantME

Quantum applications comprise a multitude of pro-

grams implementing different tasks whose control

and data ﬂow must be ensured (Leymann and Barzen,

2021). Workﬂows are used to orchestrate heteroge-

neous tasks in various domains, such as business pro-

cess management or e-Science (Ellis, 1999; Görlach

et al., 2011). Thereby, workﬂow technologies enable

the modeling of a set of activities, their partial or-

der, and the data ﬂow using workﬂow languages,

such as BPMN (OMG, 2011) or BPEL (OASIS,

2007). By modeling and executing quantum appli-

cations using workﬂows, they can beneﬁt from their

advantages, e.g., robustness, scalability, and moni-

toring. The complete workﬂow model, containing all

information required to orchestrate the quantum ap-

plication, can then automatically be executed using a

workﬂow engine (Leymann and Roller, 1999).

However, modeling quantum applications is a

complex task that requires knowledge about quantum

computing and workﬂow technologies (Vietz et al.,

2021; Weder et al., 2022). To facilitate the model-

ing process of quantum applications, Weder et al.

(2020b) have introduced the workﬂow modeling ex-

tension QUANTME, which is compatible with vari-

ous imperative workﬂow languages, such as BPMN

or BPEL. It comprises modeling constructs for com-

monly occurring tasks when orchestrating quantum

applications (Weder et al., 2020a, 2021). An overview

of all QUANTME modeling constructs is shown in

Figure 1. These modeling constructs are tailored

for the requirements of quantum-speciﬁc processing

QuantME4VQA: Modeling and Executing Variational Quantum Algorithms Using Workﬂows

307

steps and ease the understanding and conﬁguration

for workﬂow modelers. For example, the quantum

circuit execution task has properties deﬁning which

quantum provider and device shall be used. Further-

more, QUANTME improves the understandability of

the workﬂow by clearly visualizing task types and

endorses good software design by advocating well-

established concepts such as modularization.

Since existing workﬂow engines do not na-

tively support QUANTME modeling constructs, a

transformation step is necessary that converts all

QUANTME modeling constructs into native modeling

constructs. This transformation is done using reusable

workﬂow fragments. A description of the method can

be found in Section 5. Thus, no workﬂow engine ex-

tensions are needed, and QUANTME can be used to

integrate quantum tasks in existing workﬂows.

2.3 Problem Statement

Despite the availability of a custom-tailored quantum

modeling extension, the orchestration of VQAs re-

mains difﬁcult, as the original set of QUANTME mod-

eling constructs does not focus on VQAs and hence,

does not support crucial tasks of a VQA, e.g., pa-

rameter optimization. Typically, these tasks are com-

plex, requiring knowledge about quantum computing,

as well as a deep understanding of the used algo-

rithms and implementations. Hence, non-experts are

unable to exchange single constituents, e.g., an opti-

mization algorithm, to compare different implemen-

tations. Thus, additional modeling constructs are re-

quired to support workﬂow modelers in deﬁning and

conﬁguring all VQA steps in an easy-to-understand

manner. This leads us to our research question:

“What workﬂow modeling constructs are required

to facilitate the modeling of VQAs and what con-

ﬁguration options do they need to provide?”

3 MODELING VARIATIONAL

QUANTUM ALGORITHMS

In the following, we present QUANTME4VQA, an

extension to QUANTME facilitating the modeling

of VQAs in workﬂows. Since QUANTME4VQA is

meant to be used in combination with QUANTME,

and QUANTME modeling constructs are essential

building blocks of VQAs, we refer to all deﬁned mod-

eling constructs using QUANTME4VQA. For visual-

ization, we employ the widely used graphical notation

of the BPMN standard (OMG, 2011).

Warm-Starting Method: [warm-starting method to use]

Quantum Algorithm: [quantum algorithm to warm-start]

Classical Algorithm: [algorithm used for pre-computation]

Repetitions: [repetitions of classical approximation]

Rounded: [rounded or precise approximation]

| ⟩

𝜶

𝜷

Figure 2: Overview of the warm-starting task’s properties,

required input, and produced output.

3.1 Warm-Starting VQAs

To improve the performance of existing quantum al-

gorithms, so-called warm-starting methods were de-

veloped, which can be divided into two categories:

They either pre-compute (i) improved initial values

for the VQA’s parameters (Galda et al., 2021) or

(ii) an approximate solution of the targeted problem

instance that can be used to prepare a biased initial

state for the quantum circuit to start closer to the op-

timal solution (Egger et al., 2021).

To facilitate the integration of these methods, the

warm-starting task is introduced as a new task type.

Its semantics is the preparation of initial parameters

or approximate solutions to improve the performance

of a quantum algorithm. Figure 2 gives an overview

of the warm-starting task’s properties, required input,

and the produced output. It can be conﬁgured using

the following ﬁve properties: (i) the Warm-Starting

Method identiﬁes the technique that is applied to

warm-start the quantum algorithm, (ii) the Quantum

Algorithm identiﬁes which type of quantum algorithm

is warm-started, e.g., the Quantum Approximate Op-

timization Algorithm (Farhi et al., 2014), (iii) an op-

tional Classical Algorithm used for the approxima-

tion, (iv) an optional Repetitions property stating the

number of times the approximation algorithm shall be

executed, and (v) an optional Rounded property deﬁn-

ing whether the approximation returns a rounded or

precise result. The warm-starting task’s input data ob-

ject contains, e.g., the problem instance that shall be

solved by the algorithm, such as a speciﬁc graph. De-

pending on the type of warm-starting method, the

warm-starting task produces either an initial state ob-

ject containing information about the initial state that

shall be used by the quantum circuit, or a parame-

terization object that contains the pre-computed pa-

rameters to be used as starting points for the circuit

parameter optimization process, as its output.

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308

Cost Function: [problem-specific cost function to use]

Objective Function: [objective function to use]

Figure 3: Overview of the result evaluation task’s proper-

ties, required input, and produced output.

3.2 Evaluating Results

A quantum algorithm’s result is determined by mea-

suring the quantum device’s state once the exe-

cution of the algorithm is complete (Kaye et al.,

2006). When measuring a quantum state, it collapses

into a classical state, represented by a bit-string. How-

ever, due to the probabilistic nature of quantum me-

chanics, the measured bit-string does not necessar-

ily match the expected result (National Academies of

Sciences, Engineering, and Medicine, 2019). Hence,

quantum circuits are executed and measured multiple

times, such that accurate estimations of the probabil-

ity distributions are retrieved. To interpret these prob-

ability distributions, they need to be evaluated classi-

cally. For VQAs, an algorithm- and problem-speciﬁc

cost function understanding the bit-string’s semantics

is used to evaluate each measured bit-string (Cerezo

et al., 2021b). A bit-string representing a good solu-

tion is given a low cost value, whereas bad solutions

are rated with a high value. To compute a single value

describing the overall quality of the execution results

based on the measured bit-strings’ frequencies and

costs, an objective function, e.g., expectation value, is

used. Subsequently, this so-called objective value can

be used to optimize the circuit parameters of a VQA.

The quality of the quantum execution results is an-

alyzed by the result evaluation task. Figure 3 show-

cases the result evaluation task’s properties, as well

as the required input and produced output objects. It

has two properties: (i) the Cost Function identiﬁes the

problem-speciﬁc cost function for determining a bit-

string’s quality and (ii) the Objective Function iden-

tiﬁes the function for evaluating the overall quality

of the execution result, based on the bit-strings’ costs

and frequencies. Moreover, the result evaluation task

offers different objective function-speciﬁc properties,

for conﬁguring the hyperparameters of promising ob-

jective functions, e.g., for CVaR (Barkoutsos et al.,

2020) or Gibbs (Li et al., 2020). The result evalua-

tion task’s required input is a result object containing

the quantum circuit execution results. As an output,

it produces an evaluation result object, which com-

prises information about the overall quality retrieved

through the evaluation of the input.

𝜶

𝜷

Optimizer: [optimizer to use]

Maximum Iterations: [maximum number of iterations]

Tolerance Threshold: [termination threshold tolerance]

Learning Rate: [learning rate of the optimizer]

Figure 4: Overview of the parameter optimization task’s

properties, required input, and produced output.

3.3 Optimizing Parameters

The result quality achieved by a VQA heavily de-

pends on the chosen circuit parameters (Cerezo et al.,

2021a). Pre-computing suitable initial parameters can

lead to good solutions, however, ﬁnding optimal pa-

rameters is expected to be an NP-hard problem (Bit-

tel and Kliesch, 2021). Hence, VQAs use optimiza-

tion algorithms, commonly called optimizers, to iter-

atively ﬁnd better parameters such that a locally op-

timal solution is found once the optimization process

converges. However, the choice of the optimizer and

its conﬁguration can affect the convergence time and

the ﬁnal result quality (Pellow-Jarman et al., 2021).

To facilitate a ﬂexible integration and conﬁgura-

tion of different optimizers, the parameter optimiza-

tion task is introduced. An overview of its properties,

as well as the required input and produced output, are

shown in Figure 4. The semantics of the parameter

optimization task is the search for improved circuit

parameters based on the results achieved with previ-

ous parameter values. It has four properties: (i) the

Optimizer identifying the optimization algorithm that

shall be used, (ii) an optional Maximum Number of

Iterations limiting the duration of the optimization

process, (iii) an optional Tolerance Threshold used

by the optimization algorithm to determine conver-

gence, and (iv) an optional Learning Rate property,

which can be used to ﬁne-tune the learning rate of

the optimization algorithm. The parameter optimiza-

tion task’s required input is a result evaluation object

describing the quality achieved with the previous it-

eration’s parameters. As an output, it produces a pa-

rameterization object, which includes the parameters

that shall be used in the VQA’s next iteration.

3.4 Cutting Quantum Circuits

Quantum circuit cutting describes a set of techniques

used to break down a quantum circuit into smaller

sub-circuits requiring fewer qubits (Peng et al., 2019;

Mitarai and Fujii, 2021). Classical post-processing

QuantME4VQA: Modeling and Executing Variational Quantum Algorithms Using Workﬂows

309

Cutting Method: [cutting method to use]

Max Sub-Circuit Width: [max width of sub-circuits]

Max Number of Cuts: [max number of performed cuts]

Max Number of Sub-Circuits: [max number of sub-circuits]

Figure 5: Overview of the circuit cutting sub-process’s

properties, required input, and produced output.

is used to construct the outcome of the original cir-

cuit by using the execution results of the generated

sub-circuits. Thus, circuit cutting enables the execu-

tion of circuits whose width exceeds a quantum de-

vice’s number of physically available qubits. More-

over, even if a circuit ﬁts a quantum device, apply-

ing circuit cutting can reduce the effect of noise on

the result (Tang et al., 2021). To cut a circuit, there

are different cutting techniques (Lowe et al., 2022):

(i) A gate cut replaces a two-qubit gate with a set of

single-qubit gates, and (ii) wire cuts insert a set of

measurement and state-preparation operations. How-

ever, the number of sub-circuits grows exponentially

with the number of cuts needed to separate the orig-

inal circuit. Therefore, it is important to separate a

quantum circuit with as few cuts as possible.

To facilitate the usage and conﬁguration of differ-

ent circuit cutting techniques in workﬂows, we intro-

duce the circuit cutting sub-process. Its semantics is

the cutting of a quantum circuit into sub-circuits and

the combination of their execution result. This means

that all quantum circuit execution tasks deﬁned within

the sub-processes automatically operate on the cut cir-

cuits. Furthermore, all tasks using the execution re-

sults, use the probability distribution constructed from

the sub-circuit results. In Figure 5 an overview of the

circuit cutting sub-process’s properties, as well as its

required input and produced output, is shown. The

circuit cutting sub-process has four properties: (i) the

Cutting Method identiﬁes which technique should be

used to cut the original quantum circuit into smaller

sub-circuits, (ii) an optional Max Sub-Circuit Width

to deﬁne the maximum number of qubits used by the

resulting sub-circuits, (iii) an optional Max Number

of Cuts to limit the number of performed cuts, and

(iv) an optional Max Number of Sub-Circuits limit-

ing the number of sub-circuits the original quantum

circuit is cut into. The circuit cutting sub-process re-

quires a quantum circuit object containing the quan-

tum circuit that shall be cut and executed as its in-

put, and produces a generic data object containing the

problem-speciﬁc result of the sub-process as output.

Algorithmic Problem: [problem to solve]

Quantum Algorithm: [quantum algorithm to use]

Provider: [quantum provider to use]

Quantum Device: [quantum device to use]

Optimizer: [optimizer to use]

Objective Function: [objective function to use]

Warm-Starting Method: [warm-starting method to use]

Cutting Method: [cutting method to use]

Mitigation Method: [error mitigation method to use]

Figure 6: Overview of the variational quantum algorithm

task’s properties, required input, and produced output.

3.5 Executing Pre-Conﬁgured VQAs

Despite the previously introduced task types, orches-

trating a VQA is a challenging task for modelers that

lack experience with VQAs. To facilitate the integra-

tion of pre-conﬁgured VQAs, we provide the varia-

tional quantum algorithm task as a high-level model-

ing construct. It combines the previously introduced

QUANTME4VQA tasks in a single modeling con-

struct, using only their most crucial properties. Fig-

ure 6 gives an overview of the task’s properties, as

well as its input and output. As many properties of the

variational quantum algorithm task are part of the pre-

viously presented tasks, we only explain the remain-

ing properties here. The Algorithmic Problem iden-

tiﬁes the problem that shall be solved by the VQA,

e.g., the travelling salesman problem. It is used to

load a suitable quantum circuit and to select a match-

ing cost function. To execute the quantum circuits, a

Quantum Provider and a Quantum Device must be

selected. This can either be done manually or by us-

ing a quantum hardware selection sub-process (Weder

et al., 2021). The input and output of the task are

generic data objects, as they are problem-speciﬁc.

4 CASE STUDY

To demonstrate the suitability of the previously intro-

duced modeling constructs, we use them to specify

a typical VQA as a workﬂow. Exemplary, we solve

the Maximum Cut (MaxCut) problem, a graph par-

titioning problem with many application areas (Bar-

rett et al., 2020; Poland and Zeugmann, 2006), using

the Quantum Approximate Optimization Algorithm

(QAOA) (Farhi et al., 2014). Figure 7 (top) shows

a workﬂow model implementing QAOA for MaxCut

using QUANTME4VQA modeling constructs.

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310

Converged?

Yes

Optimized QAOA

Parameters

𝜶

𝜷

QAOA

Circuit

Execution Result

Evaluated

Results

Pre-computed

Initial State

| ⟩

Circuit Cutting Sub-Process

Approximate

MaxCut

Execute QAOA

Circuit

Optimize QAOA

Parameters

Evaluate

Results

Generate

QAOA Circuit

Converged?

Yes

Execute QAOA

Circuit

Evaluate

Results

Cut

Circuit

Combine

Results

…

QuantME4VQA Workflow

Workflow After First Transformation Step

Transform Circuit Cutting Sub-Process

Circuit Cutting Sub-Process

Optimize QAOA

Parameters

Generate

QAOA Circuit

Figure 7: QUANTME4VQA workﬂow solving MaxCut (top) and transformation of its circuit cutting sub-process (bottom).

The workﬂow is instantiated when a request mes-

sage containing a problem instance, i.e., the graph

that shall be solved, is received. First, a warm-starting

task is utilized to classically approximate a solution

by using the Goemans-Williamson algorithm (Goe-

mans and Williamson, 1995). Subsequently, the ap-

proximation is used as an initial state when generating

the QAOA circuit via a quantum circuit loading task,

facilitating the search for the optimal solution (Eg-

ger et al., 2021). To reduce the size of the quantum

circuit, a circuit cutting sub-process, containing all

tasks of the optimization loop, is used. Within the op-

timization loop, the quantum circuits are executed by

a quantum circuit execution task. Subsequently, the

quality of the execution results is assessed by a result

evaluation task. Next, the evaluated results are used to

optimize the QAOA circuit parameters by utilizing a

parameter optimization task, which initiates the next

iteration of the loop with a new set of QAOA parame-

ters. The optimization loop is stopped once no param-

eters that further improve the quality of the execution

results can be found. Last, the ﬁnal result is sent to the

process initiator via a message end event.

The discussed use-case and a step-by-step tuto-

rial showcasing its setup and execution using the

prototype presented in Section 6.2 can be found on

GitHub (University of Stuttgart, 2023).

5 TRANSFORMATION METHOD

To improve the portability of QUANTME4VQA mod-

eling constructs, we transform them into native work-

ﬂow fragments that can be executed on any workﬂow

engine supporting the used workﬂow language. To en-

sure compatibility between the existing QUANTME

modeling constructs and the ones introduced in this

work, we follow the same semi-automatic three-step

transformation method (Weder et al., 2020b).

First, the modeler speciﬁes a workﬂow using

native and QUANTME modeling constructs. Then,

all QUANTME modeling constructs contained in

the workﬂow are iteratively replaced using so-called

QuantME Replacement Models (QRM), which consist

of (i) a detector and (ii) a replacement fragment. The

detector determines, whether a modeled QUANTME

task can be substituted by the replacement fragment

of the QRM or not. In the last step of the transforma-

tion, modelers can manually reﬁne the transformed

workﬂow before deploying and executing it.

For the warm-starting, result evaluation, parame-

ter optimization, and variational quantum algorithm

tasks, the previously discussed method is applied.

However, the transformation of the circuit cutting

sub-process requires an extension of the method. Cir-

cuit cutting is a two-step process, consisting of a cir-

cuit cutting and a result combination step, which are

QuantME4VQA: Modeling and Executing Variational Quantum Algorithms Using Workﬂows

311

Workflow

Engine

Quantum Cloud

Offerings

Circuit

Execution

Objective

Evaluation

Circuit

Generation

Error

Mitigation

Optimi-

zation

Ecosystem

QuantME Transformation

Framework

QuantME Validator

QuantME Repository

QuantME Transformer

QRMs

Warm-

Starting

Circuit

Cutting

Quokka

Gateway

QuantME Modeler

Legend:

unchanged

extended

new

HTTP request

microservice

REST Api

Figure 8: System architecture for modeling and executing QUANTME4VQA workﬂows.

not performed in immediate succession. In an inter-

mediate step, the circuits need to be executed, and er-

ror mitigation can be used to improve result quality.

Figure 7 (bottom) shows the positioning of cir-

cuit cutting and result combination when transform-

ing the previously discussed workﬂow. As cutting the

circuit in each iteration of the loop leads to signiﬁcant

overhead, it is performed before the loop starts. Thus,

the transformation routine must determine the cor-

rect position of the circuit cutting and result combi-

nation modeling constructs, depending on the tasks

contained in the given circuit cutting sub-process.

To fulﬁll the requirements identiﬁed above, we de-

ﬁne the following transformation rules: (i) Replace-

ment fragments for the circuit cutting sub-process

must consist of two modeling constructs that are ei-

ther tasks or sub-processes, where the ﬁrst imple-

ments circuit cutting and the second implements re-

sult combination. (ii) The modeling construct imple-

menting circuit cutting is inserted directly after the

start event of the circuit cutting sub-process. (iii) The

modeling construct implementing result combination

is placed after each quantum circuit execution task

within the circuit cutting sub-process. If a quantum

circuit execution task is directly followed by an er-

ror mitigation task, it is instead inserted after this

task. (iv) All quantum circuit execution tasks within

the circuit cutting sub-process receive the sub-circuits

as their input. (v) Circuit cutting sub-processes must

be transformed before the other QUANTME model-

ing constructs contained in them. Subsequently, these

remaining modeling constructs must be transformed.

6 PROTOTYPICAL EVALUATION

In this section, we show the practical feasibility of our

approach by presenting a suitable system architecture

and providing a prototypical implementation for it.

6.1 System Architecture

To realize our approach, we propose a system ar-

chitecture comprising a workﬂow framework and a

quantum service ecosystem introduced in previous

works (Weder et al., 2020b; Beisel et al., 2023). Fig-

ure 8 gives an overview of all components.

The QuantME Transformation Framework sup-

ports the modeling and transformation of quantum

workﬂows. The QuantME Modeler, is a graphical

modeler, which was extended to support the mod-

eling of workﬂows using the new QUANTME4VQA

task types and their graphical notation. To ensure the

validity of these modeling constructs, the QuantME

Validator checks whether they satisfy all imposed

constraints, e.g., required properties and matching

data types. Hence, the QuantME Validator had to

be extended for the new modeling constructs. The

QuantME Transformer handles the transformation of

all QUANTME4VQA modeling constructs to native

BPMN. In this work, it has been extended to sup-

port the transformation process of the circuit cutting

sub-process as described in Section 5. The QuantME

Repository manages QUANTME-related data such as

QRMs. To support the new modeling constructs, we

extended the data storage by several QRMs. To en-

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312

able an automatic execution of the modeled quantum

workﬂows, they are uploaded to a Workﬂow Engine.

The Quokka Ecosystem (Beisel et al., 2023) is an

extensible open-source microservice ecosystem, pro-

viding a variety of functionalities for executing quan-

tum algorithms. To facilitate the request routing for

clients, the Quokka Gateway unites the endpoints

of all services in a single interface. The Optimiza-

tion Service, handles the parameter optimization for

VQAs. The Circuit Generation Service provides an

interface for generating quantum circuit implemen-

tations based on different algorithm-speciﬁc param-

eters. These can be executed using the Circuit Execu-

tion Service, which accesses different Quantum Cloud

Offerings to run the circuits. To improve the quality of

erroneous circuit execution results, the Error Mitiga-

tion Service can be used. The quality of the execution

results is assessed by the Objective Evaluation Ser-

vice. The new Circuit Cutting Service enables cutting

a quantum circuit into a set of smaller sub-circuits,

whose execution results can then be combined to con-

struct the result of the original circuit. The Warm-

Starting Service provides different methods for pre-

computing circuit parameters and approximate solu-

tions to warm-start quantum algorithms.

6.2 Prototype

In this section, we describe the implementation details

of our prototype, which implements the previously

shown system architecture. The QuantME Transfor-

mation Framework is built on the JavaScript-based

standalone version of the Camunda BPMN Mod-

eler (Camunda, 2023a) that can be extended via a plu-

gin system. In this work, we extended the plugins en-

abling the modeling and transformation of quantum

workﬂows, to additionally support all new modeling

constructs and transformation rules. To execute the

modeled workﬂows, we utilize the Camunda BPMN

Workﬂow Engine (Camunda, 2023b).

The Quokka Gateway is implemented as a Spring

Cloud Gateway providing a single REST API, which

forwards incoming requests to the respective ser-

vices. To facilitate the integration of code written with

mostly Python-based quantum SDKs, all Quokka mi-

croservices are implemented in Python. The Circuit

Cutting Service provides cutting functionalities, such

as the circuit cutting method by Tang et al. (2021),

whose implementation is publicly available as part

of the Circuit Knitting Toolbox (IBM, 2023). The

Warm-Starting Service enables the pre-computation

of circuit parameters and initial state approximations,

based on a given problem instance. For example,

it implements the ﬁxed angle conjecture for QAOA

on regular MaxCut graphs (Wurtz and Lykov, 2021)

and MaxCut approximation using the Goemans-

Williamson algorithm (Goemans and Williamson,

1995) for warm-started QAOA (Egger et al., 2021).

7 RELATED WORK

Agnostiq provides Covalent (Agnostiq, 2023), a

Pythonic open-source tool that specializes in orches-

trating heterogeneous computing tasks, such as quan-

tum or HPC tasks. To generate a workﬂow, develop-

ers annotate functions in their code with Covalent-

speciﬁc decorators. Workﬂows can be executed lo-

cally or deployed in the cloud and subsequently be

monitored via a user interface. Zapata Computing’s

workﬂow tool Orquestra (Zapata Computing, 2023)

focuses on orchestrating quantum applications. Sim-

ilar to Covalent, developers deﬁne workﬂows by us-

ing code decorators. Furthermore, Orquestra provides

functions that support users in generating and exe-

cuting quantum circuits. In contrast to our approach,

these two frameworks do not provide graphical mod-

eling capabilities or quantum task types to facilitate

the conﬁguration and integration of common quan-

tum tasks based on existing reusable implementa-

tions. Furthermore, our approach prevents a vendor

lock-in by supporting different workﬂow languages,

that enable features such as transactional processing.

Different works employ reusable workﬂow frag-

ments to reﬁne workﬂows. Sethi et al. (2012) demon-

strate the usability of reusable workﬂow fragments in

different domains and analyze how they affect devel-

opment time. Atkinson et al. (2017) highlight the ben-

eﬁts of reusable workﬂow fragments and predict their

growing importance. Belhajjame and Grigori (2021)

analyze the reusability of service-based workﬂow

fragments and discuss how it can be improved. Eberle

et al. (2009) introduce a workﬂow fragment reposi-

tory for composing new workﬂows by reusing exist-

ing workﬂow fragments. Képes et al. (2016) introduce

a method that enables a situation-aware adaptation of

workﬂows using workﬂow fragments.

Several works showcase similar workﬂow mod-

eling extensions for different domains. Falazi et al.

(2019) introduce BLOCKME, a modeling extension

for integrating blockchain operations in workﬂows,

and present an approach for transforming it into

standard-compliant BPMN. Graja et al. (2016) pro-

pose a BPMN modeling extension for the integra-

tion of cyber-physical systems. Breitenbücher et al.

(2015) introduce SITME, a modeling extension for

situational dependencies that introduces a new event

type and the concept of situational scopes.

QuantME4VQA: Modeling and Executing Variational Quantum Algorithms Using Workﬂows

313

8 CONCLUSION & OUTLOOK

VQAs enable meaningful computations on today’s

quantum devices. However, their high complexity

makes their orchestration complicated and error-

prone. To facilitate the orchestration of VQAs, we

introduced the language-independent workﬂow mod-

eling extension QUANTME4VQA, which provides

custom-tailored modeling constructs for different

tasks of a VQA. It comprises new task types and

data objects, as well as a graphical notation to ease

workﬂow modeling and understanding. To ensure the

interoperability and portability of workﬂow models

using our modeling extension, we presented an ap-

proach to transform them into native workﬂow mod-

els. Finally, we validated the practical feasibility of

QUANTME4VQA by presenting a case study as well

as a system architecture and prototype supporting it.

In future work, we plan to evaluate our approach

for additional use cases and analyze the achieved de-

gree of simpliﬁcation in a user study. To improve the

performance of circuit cutting in workﬂows, we plan

to evaluate what conditions need to be fulﬁlled to

make a parallelized quantum circuit execution using

different quantum devices more efﬁcient than the ex-

ecution on a single quantum device. Based on these

results, we want to analyze how parallelizing the exe-

cution of sub-circuits on different quantum devices af-

fects the performance of VQAs and how it can be ef-

ﬁciently integrated in the circuit cutting sub-process.

ACKNOWLEDGEMENTS

This work was funded by the BMWK projects

EniQmA (01MQ22007B), PlanQK (01MK20005N),

and SeQuenC (01MQ22009B).

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