QuantME4VQA: Modeling and Executing Variational Quantum
Algorithms Using Workflows
Martin Beisel
a
, Johanna Barzen
b
, Marvin Bechtold
c
, Frank Leymann
d
, Felix Truger
e
and Benjamin Weder
f
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
a
https://orcid.org/0000-0003-2617-751X
b
https://orcid.org/0000-0001-8397-7973
c
https://orcid.org/0000-0002-7770-7296
d
https://orcid.org/0000-0002-9123-259X
e
https://orcid.org/0000-0001-6587-6431
f
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
Copyright
c
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]
0
|
1
|
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 VQAs 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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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 VQAs 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?
No
Yes
Optimized QAOA
Parameters
𝜶
𝜷
QAOA
Circuit
Execution Result
Evaluated
Results
Pre-computed
Initial State
0
|
1
|
Circuit Cutting Sub-Process
Approximate
MaxCut
Execute QAOA
Circuit
Optimize QAOA
Parameters
Evaluate
Results
Generate
QAOA Circuit
Converged?
No
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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