Uniﬁed Framework for Implementing Inaccurate Knowledge in

Quantum Symbolic Artiﬁcial Intelligence Models

Eduardo Mosqueira-Rey

, Samuel Magaz-Romero

and Vicente Moret-Bonillo

Department of Computer Science and Information Technologies,

University of Coru

na (CITIC), Campus de Elvi

na s/n, A Coru

na, Spain

{eduardo, s.magazr, vicente.moret}@udc.es

Keywords:

Quantum Symbolic AI, Quantum Inaccurate Knowledge, Certainty Factors, Bayesian Networks, Fuzzy

Models.

Abstract:

Symbolic models of Artiﬁcial Intelligence are based on deﬁning declarative knowledge that is connected

through procedural knowledge forming symbolic graphs through which reasoning ﬂows. Both declarative and

procedural knowledge can be inaccurate, which has led to the deﬁnition of different models to represent this

inaccuracy. Since the functioning of quantum computers is inherently probabilistic, it has been proposed to

take advantage of this nature to implement inaccurate knowledge more effectively. In this paper, we present

different models for implementing inaccurate knowledge in quantum computers and propose a uniﬁed frame-

work to represent and implement the common features of all of them.

1 INTRODUCTION

Symbolic AI builds computational models of intelli-

gent behavior, focusing on a symbolic representation

of the world and then using logic and search to solve

problems. These AI models are composed of declar-

ative knowledge, a set of facts that describe the real

world and procedural knowledge that speciﬁes how

different elements of declarative knowledge relate.

The reasoning in these symbolic models is built

by establishing knowledge graphs that are formed

by declarative knowledge (the nodes) connected

through procedural knowledge (the connections be-

tween nodes). These knowledge graphs are then im-

plemented as logic rules or, more popularly, as rule-

based systems (RBS).

One of the problems that arises when working

with symbolic AI models is that knowledge in the real

world rarely is completely accurate.

In this paper, we assume that inaccuracy can be

present in two different ways: (1) Imprecision when

it is associated with declarative knowledge, i.e. how

accurate is the description of a given fact. (2) Uncer-

tainty when it is associated with procedural knowl-

edge, i.e. the uncertainty related to the evidential

https://orcid.org/0000-0002-4894-1067

https://orcid.org/0000-0001-6438-5569

https://orcid.org/0000-0002-9435-3151

strength of the causal relationship.

Over the past years, there have been several pro-

posals to solve the issue of reasoning under inac-

curacy with Quantum Computing (QC). One of the

reasons behind these approaches is the probabilis-

tic nature of QC, which aligns quite seamlessly with

the preexisting models for reasoning with inaccuracy.

However, there are certain drawbacks to develop-

ing practical applications with QC because nowadays

quantum computations are very sensitive to noise in

the currently available hardware.

In this paper, we present a brief state-of-the-art

of how inaccurate knowledge can be represented in

a quantum computer. We extract the common char-

acteristics of these inaccuracy models and their corre-

sponding quantum implementations to build a uniﬁed

software framework that allows for easy implementa-

tion of a knowledge graph with inaccurate knowledge

in a quantum circuit. We also carry on a study on how

these models are affected by noise, given its relevance

to the current viability of QC applications.

The paper is structured as follows: section 2

brieﬂy describes classical inaccurate knowledge mod-

els and presents quantum implementations that have

been proposed for these models, section 3 proposes to

build a uniﬁed framework for dealing with the quan-

tum implementation of inaccuracy, section 4 applies

our uniﬁed model to a synthetic problem (basketball)

and, ﬁnally, section 5 include the conclusions.

Mosqueira-Rey, E., Magaz-Romero, S. and Moret-Bonillo, V.

Uniﬁed Framework for Implementing Inaccurate Knowledge in Quantum Symbolic Artiﬁcial Intelligence Models.

DOI: 10.5220/0013400200003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 1, pages 839-846

ISBN: 978-989-758-737-5; ISSN: 2184-433X

839

2 QUANTUM INACCURATE

KNOWLEDGE MODELS

IMPLEMENTATION

In this section, we present some of the most promi-

nent models to manage inaccurate knowledge in clas-

sical systems (Certainty Factors, Bayesian Networks,

and Fuzzy Models) and we discuss hoy to to use the

probabilistic nature of QC to represent the impreci-

sion and uncertainty inherent to these models.

2.1 Certainty Factors

Proposed by (Shortliffe and Buchanan, 1975), this

model was one of the ﬁrst to propose a way of deal-

ing with inaccurate knowledge. The certainty factors

(CF) model is ad hoc in nature and therefore lacks

a solid theoretical basis. However, this model was

immediately accepted because of its ease of under-

standing and the quality of the results obtained after

its application. In any case, it seems that, despite its

ad hoc nature, probabilities are at the core of these

certainty factors. In the CF model, the imprecision

is represented by the certainty factors associated with

facts, whereas the uncertainty is represented by cer-

tainty factors associated with rules.

We implemented CFs model in quantum com-

puters using quantum rule-based systems, which are

quantum circuits that implement knowledge in the

form of production rules (Moret-Bonillo et al., 2022).

We propose that inaccuracy can be obtained from a

unitary matrix that operates on a speciﬁc state of the

quantum system. In this context, we introduce matrix

M(δ) (eq. 1), deﬁned as follows in which the δ an-

gle represents the inaccuracy associated with a given

state (if δ = 0, the statement is completely false, and

when δ = π/2, the statement is completely true):

M(δ) =



cos(δ) sin(δ)

sin(δ) −cos(δ)



(1)

For example, suppose the following RBS with two

rules: R1 : A AND B ⇒ X, R2 : X OR C ⇒ Y . These

rules can be represented in a quantum computer as

shown in Fig. 1. The circuit uses one qubit for each

fact and each rule and some ancilla qubits for imple-

menting the AND and OR operators. M gates are ap-

plied to fact qubits for representing imprecision and

to rule qubits to represent uncertainty.

2.2 Bayesian Networks

A Bayesian network is a probabilistic graphical model

that represents a set of variables and their conditional

M(δ

)

•

M(δ

)

•

M(δ

)

•

• •

M(δ

)

• •

•

M(δ

)

•

c :

Figure 1: Quantum inferential circuit.

dependencies via a directed acyclic graph that rep-

resents the joint probability distribution over those

variables. Bayesian networks reduce the space com-

plexity by exploiting conditional dependencies in the

distribution, associating with each graph node a con-

ditional probability table for each random variable,

with directed edges representing conditional depen-

dencies. Here, the imprecision is represented by the

marginal probabilities of the root nodes of the net-

work, whereas the uncertainty is represented by the

conditional probabilities that connect the non-root

nodes of the network.

There are several implementations of Bayesian

networks in quantum computers. Low et al. (Low

et al., 2014) proposed a quantum circuit that ef-

ﬁciently represents the full joint distribution of a

Bayesian network in which the edges in the network

are mapped to conditioning nodes in the circuit. Boru-

jeni et al. (Borujeni et al., 2021) proposed a model in

which the marginal probabilities associated with root

nodes (nodes without any parent nodes) are repre-

sented using rotation gates, and the conditional proba-

bility tables associated with non-root nodes are repre-

sented using controlled rotation gates. The controlled

rotation gates with more than one control qubit are

represented using ancilla qubits.

Let’s see an example using the Titanic dataset, that

lists the complete passengers and crew members on

the RMS Titanic with a variable indicating whether a

person did survive the sinking. Following the “Women

and children ﬁrst” rule, one can easily guess that sex

and being a child have an impact on the probabilities

of survival. Therefore we can represent the following

Bayesian network: (Sex) → (Survival) ← (isChild)

Since the nodes Sex and isChild are binary, we can

represent them using a single qubit. By applying an

RY gate with an appropriate angle, the probabilities

of the root node can be mapped to the probabilities

(and thus probability amplitudes) of the basis states,

|0⟩ and |1⟩. We use a third qubit with controlled RY

QAIO 2025 - Workshop on Quantum Artiﬁcial Intelligence and Optimization 2025

840

gates to represent the conditional probability tables

associated with the Survival node (see Fig. 2).

2.3 Fuzzy Models

Fuzzy logic is a form of many-valued logic in which

the truth value of the variables can be any real number

between 0 and 1. The term was introduced with the

1965 proposal of fuzzy set theory by scientist Lotﬁ

A. Zadeh (Zadeh, 1965). In these models, impreci-

sion is represented by a fuzziﬁcation process in which

a numeric input is assigned to a given fuzzy set with

some degree of membership. Uncertainty is propa-

gated through the system using a fuzzy implication

function that triggers partially, and in parallel, several

rules that include those fuzzy sets with some degree

of membership different from zero. The ﬁnal step is

the defuzziﬁcation process, in which the fuzzy results

are converted back into crisp results.

It is easy to see the parallelism between fuzzy

models and quantum computing. The fuzziﬁcation

process puts a given crisp value in a sort of “super-

position” of several fuzzy variables (a person can be

considered tall and short at the same time with dif-

ferent degrees of membership). The defuzziﬁcation

process is the counterpart to the measure in quantum

computers, the superposition disappears but affects

how a new crisp value is obtained.

But the similarities end there, quantum mechan-

ics is based on the Hilbert space formalism and has a

probabilistic nature. On the other hand, fuzzy logic

takes the concept of intersection, union, and implica-

tion of classic logic and converts them to t-norms, t-

conorms, and fuzzy implications that can have several

different implementations.

There are several attempts to implement fuzzy

logic in a quantum computer, among the early works

we can highlight (Mannucci, 2006) and (Schmitt

et al., 2009), and among the more recent ones

(Pykacz, 2015), (Nadaban, 2021) and (Gentili, 2021).

The differences rely on how to implement the dif-

ferent fuzzy connectives as a composition of quan-

tum operations (using unitary and controlled quantum

gates) applied to quantum registers.

3 A UNIFIED VIEW OF

QUANTUM INACCURATE

KNOWLEDGE

We can see that the classical models of inaccurate

reasoning present similarities: Heckerman proposed

a probabilistic interpretation for Certainty Factors

(Heckerman, 1986) and Gentili stated that “the terms

of Bayes’ formula are describable as degrees of mem-

bership to fuzzy sets, and the Bayesian inference is

conceivable as a fuzzy inference” (Gentili, 2021).

This allows us to suggest the possibility of estab-

lishing a uniﬁed framework of these models to imple-

ment them in QC. In Table 1 we summarize the sim-

ilarities of the models when dealing with inaccuracy

and implementing them in a quantum computer.

The idea is to deﬁne of a knowledge graph and

then facilitate different of this graph as different inac-

curacy models on a quantum computer. Our ﬁrst step

was the development of software (Magaz-Romero

et al., 2023) for implementing quantum rule-based

systems (QRBS) deﬁning a classical RBS.

3.1 QRBS Software

We present a software library for the implementation

of QRBSs whose source code is available at (Consor-

tium, 2024) under an open-source license.

This software library is structured in two pack-

ages, one for encoding knowledge and one for man-

aging the quantum tasks (Moret-Bonillo et al., 2024).

The ﬁrst package contains all the required ele-

ments for modeling RBSs, as illustrated in Fig. 3.

In this package we can ﬁnd the following classes:

• Fact: the building block of RBSs, as it is used to

encode the declarative knowledge of the system.

• {Not,And,Or}Operator: these classes allow for

the composition of the system’s facts, each estab-

lishing a different relationship among them.

• Rule: encodes the procedural knowledge of the

system, as it relates a composition of facts (the

precedent) with a single fact (the consequent).

• KnowledgeIsland: this class aggregates different

sets of rules. The rules of a knowledge island are

those that aim at the same consequent.

The second package contains all the elements to

deﬁne a QRBS, as well as the tools to evaluate and

execute it. These components (Fig. 4) are:

• WorkingMemory, InferenceEngine: store the

declarative and procedural knowledge.

• QRBS: used to initialize the system and populate

it with the corresponding knowledge elements.

• QPU: interface deﬁning how the QRBSs are op-

erated, with regards to evaluation and execution.

The library provides the following functionalities:

• RBS modeling: users can model a rule-based

system by encoding declarative and procedural

knowledge into a system, establishing different

Uniﬁed Framework for Implementing Inaccurate Knowledge in Quantum Symbolic Artiﬁcial Intelligence Models

841

Figure 2: Quantum Bayesian network circuit.

Table 1: Summary on representing the imprecision and uncertainty of different models in classical and quantum computers.

Classical Quantum

Model Imprecision Uncertainty Imprecision Uncertainty

Certainty Factors CFs in facts CFs in rules M gate in facts M gate in rules

Bayesian

Networks

Marginal

probabilities

Conditional

probabilities

RY gates in root

nodes

CRY gates in

non-root nodes

Fuzzy models

Fuzziﬁcation of

facts

Fuzzy implication

Superposition of

quantum states

Controlled

quantum gates

consequent

Fact

+ attribute: String

+ precision: float

NotOperator

+ child: LeftHandSide

AndOperator

+ leftChild: LeftHandSide

+ rightChild: LeftHandSide

OrOperator

+ leftChild: LeftHandSide

+ rightChild: LeftHandSide

<<Abstrac>>

LeftHandSide

child

leftChild,

rightChild

leftChild,

rightChild

precedent

Rule

+ precedent: LeftHandSide

+ consequent: Fact

KnowledgeIsland

+ rules: List<Rule>

Figure 3: Class diagram of the knowledge rep. package.

QRBS

+ memory: WorkingMemory

+ engine: InferenceEngine

WorkingMemory

+ facts: List<Fact>

InferenceEngine

+ rules: List<Rule>

+ islands: List<KnowledgeIsland>

<<Interface>>

QPU

+ evaluate(QRBS)

+ execute(QRBS)

"use"

Figure 4: Class diagram of the QRBS package

facts with their respecting imprecision, and relat-

ing them through rules with uncertainty.

• Automated QRBS implementation in different

models: after deﬁning an RBS, users can auto-

matically obtain the corresponding QRBS in the

different models available without providing any

additional information.

• Evaluate and execute QRBS: users can evaluate

their QRBS to analyze their viability , and if fa-

vorable execute it to obtain the corresponding re-

sults. These are encoded as the certainty values of

the rules’ consequents, which users can consult.

The general QRBS workﬂow would be as follows:

1. The user deﬁnes the elements of a classical rule-

based system (facts, rules, etc.)

2. The user establishes the level of inaccuracy in the

elements of the system.

3. An implementation of the QPU interface uses this

information to build the corresponding quantum

routine for a given quantum computer.

4. This implementation is executed, yielding the re-

sults for the consequents of the different rules.

5. The values of the consequents are updated so the

user can consult them.

With this library, we allow for an easy manage-

ment of the knowledge elements of RBSs, indepen-

dently from a speciﬁc model of uncertainty. Once the

declarative and procedural knowledge of the system

is identiﬁed, it is trivial to encode it with the library.

Furthermore, it enables a fast workﬂow for exper-

imenting with these systems. Once its structure has

QAIO 2025 - Workshop on Quantum Artiﬁcial Intelligence and Optimization 2025

842

been deﬁned, the user can easily tweak small aspects

directly (e.g., the accuracy values of each of the el-

ements) and automatically obtain the corresponding

quantum routines for each of the models available.

3.2 On the Subject of Noisy Quantum

Computations

Quantum Computing has gained enormous momen-

tum in recent years thanks to the development of the

ﬁrst publicly available quantum computers, although

these machines are still far from being comparable

with classical computers. While classical computers

have enough capacity for error correction , for quan-

tum computers it is a luxury (Wolfowicz et al., 2021).

Nevertheless, current quantum computers are

worth using and researching . This is where NISQ al-

gorithms come into play, as they are designed to work

under these circumstances. Their goal is to leverage

the available resources to perform classically chal-

lenging tasks (Bharti et al., 2022).

We have developed our approach within this con-

text. While the quantum routines that result from

the different models are themselves limited by the

number of qubits, the framework itself is ready to

scale when quantum computers with more capacity

are made available. However, we must test the frame-

work’s robustness against noise.

4 SYNTHETIC CASE:

BASKETBALL PROBLEM

To illustrate the framework and the use of the QRBS

software, we propose to study the following case,

which we name the basketball problem.

4.1 Description of the Problem

This problem is based on a simulated case, where a

basketball coach has to make a new team from the

players available. He decides to compare them by

evaluating two statistics: the scored shots out of 20 as

a measurement of skill, and the height of the player.

Each stat is split into ﬁve categories: Worst, Bad,

Regular, Good and Best. Therefore, we have 10 in-

put facts for the system, with a level of inaccuracy

assigned depending on the input of the stat.

For the evaluation of the player, we consider four

categories: Bad (which is discarded directly), Regu-

lar, Good, and Excellent. In this case, we obtain the

precision levels for each category from the inference

process of executing the system.

Once we have deﬁned the facts of the system, we

deﬁne the rules that relate the stats to the evaluations.

We consider those in Table 2.

To evaluate the system, we generate a batch of

synthetic players, i.e. a pair of shots/height, and input

this data into the system to analyze the results. Table

3 shows the generated data for the synthetic players.

We have implemented the problem classically to ob-

tain an expected value for each synthetic player, so we

can later validate the output.

For each of these players, we initialize the pre-

cision of the facts according to their pair of statistics.

For the sake of briefness, we assume that the certainty

for the rules is always 1.00.

We have deﬁned this set of players with values

spread across the range of evaluation so we can later

evaluate the effect of noise in them.

4.2 Implementation of the Problem

We test the three models available in the QRBS soft-

ware,as each should yield similar results to the other

two.As stated in Table 1, each model has a differ-

ent quantum implementation. To illustrate them, we

present the quantum routines corresponding for Rule

5 (see Table 2). The same procedure is applied for the

rest of the rules to compose the corresponding entire

quantum circuit.

For Certainty Factors, the quantum routine is the

one shown in Fig. 5. M(θ) is used to initialize the

facts’ qubits for their imprecision and the rules’ qubits

for their uncertainty. We apply the quantum opera-

tors according to the logical associations between the

facts, as well as the ones for the inference of the rules.

⟩

M(θ

h Good

)

⟩

M(θ

s Good

)

⟩

M(θ

h Best

)

⟩

M(θ

s Good

)

⟩

M(θ

)

⟩

Figure 5: Quantum routine for Rule 5 with CF model.

For Bayesian networks, we obtain the quantum

routine from Fig. 6. We use RY (θ) for the declara-

Uniﬁed Framework for Implementing Inaccurate Knowledge in Quantum Symbolic Artiﬁcial Intelligence Models

843

Table 2: Rules for the basketball problem.

ID Precedent Output

1 IF shots is Worst OR shots is Bad Bad

2 IF height is Worst OR height is Bad Bad

3 IF height is Regular OR shots is Regular Bad

4 IF (height is Regular AND shots is Good) OR (height is Regular AND shots is Best)

OR (height is Good AND shots is Regular) OR (height is Best AND shots is Regular)

Regular

5 IF (height is Good AND shots is Good) OR (height is Best AND shots is Good) Good

6 IF (height is Good AND shots is Best) OR (height is Best AND shots is Best) Excellent

Table 3: Generated data for the basketball problem.

ID Scored shots Height Expected value

P1 15 203 50.00

P2 16 198 64.60

P3 17 188 16.90

P4 17 193 56.10

P5 18 176 0.00

P6 18 186 17.60

P7 18 200 83.70

⟩

(θ

h Good

)

⟩

(θ

s Good

)

⟩

X X

⟩

(θ

h Best

)

⟩

(θ

s Good

)

⟩

X X

⟩

(θ

) R

(θ

) R

(θ

)

Figure 6: Quantum routine for Rule 5 with Bayes model.

tive knowledge (root nodes), and CRY (θ) for the pro-

cedural knowledge (non-root nodes). We apply the

quantum operators to model the relationship between

nodes, following the rules of the system.

For Fuzzy models, the resulting quantum routine

is illustrated in Fig. 7. For this model, we apply R

(θ)

gates for the inaccuracy of both the facts and the rules.

We implement the AND with a CCNOT and the OR

with a composition of X and CCNOT .

With these quantum routines, we show how each

of the models is implemented with slight differences.

It is worth mentioning that the routines have been ob-

tained from the same classical inferential circuit.

Regarding the noise models, we follow the error

model based on thermal relaxation with the qubit en-

vironment. Table 4 illustrates the parameters applied

for each noise model, as we introduce noise in U1,

U2, and U3 quantum gates, in the CX controlled op-

erator, and in the measuring process. The ﬁrst model

is noiseless and validates the values from the quantum

⟩

(θ

h Good

)

⟩

(θ

s Good

)

⟩

X X

⟩

(θ

h Best

)

⟩

(θ

s Good

)

⟩

X X

⟩

(θ

)

⟩

Figure 7: Quantum routine for Rule 5 with Fuzzy model.

Table 4: Parameters (in nanoseconds) for the noise models.

Noise U1 U2 U3 CX Measure

0 0 0 0 0 0

1 71 142 428 1428 1428

2 142 285 857 2857 2857

3 214 428 1285 4285 4285

4 285 571 1714 5714 5714

5 357 714 2142 7142 7142

6 428 857 2571 8571 8571

7 500 1000 3000 10000 10000

routines against the classical expected values.

4.3 Results

In the ﬁrst place, we must validate that the quantum

routines’ outputs match with the expected ones. For

that, we evaluate the quantum routine of each model

with the noiseless model, shown in Fig. 8.

It can be observed how the obtained values cor-

respond to the expected values from the classical im-

plementation, therefore validating our framework. As

expected, the results obtained for each model are sim-

ilar to the ones from the other two, with some of them

QAIO 2025 - Workshop on Quantum Artiﬁcial Intelligence and Optimization 2025

844

even being identical.

We continue with the results of the experiments

with the different noise levels, shown in Fig. 9.

These results showcase how noise affects the val-

ues returned by the quantum routines. The output

value tends to 50 as the noise becomes more ag-

gressive. As more noise is introduced in a reason-

ing process, the conclusions provide less information,

which is reﬂected as an evaluation of 50: the player is

equally “good” and “bad”.

However, for the proposed framework, the in-

ﬂuence of noise does not affect the problem’s goal.

Since noise affects all cases equally, the players’ or-

der is preserved. There are some points where this

proportion does not hold up as strongly as one would

prefer, due to the probabilistic nature of QC.

We have calculated the error for each noise level

output for the noiseless model, which can be seen in

Fig. 10. In general, the CF model presents the highest

error value, yet it could be argued that also preserves

the proportion of the players’ values the best.

In general, the models developed in this work

present enough robustness against the noise models

that have been experimented with. This makes them

appropriate to be used during the NISQ era of QC.

5 CONCLUSIONS

AI has classically been divided into two worlds, the

symbolic world and the connectionist world. Today

we can say that the latter has surpassed the former in

terms of results. However, many researchers believe

that an exclusively connectionist model is not enough

to achieve Artiﬁcial General Intelligence (AGI), i.e.

human-level AI, and that a mixed approach is needed.

Similarly, quantum AI has tended to machine

learning (ML) developments because such mod-

Figure 8: Scores for the synthetic players without noise.

els deal with massive parallel processing of high-

dimensional data, it seems that quantum computers

can be an advantage when designing ML algorithms.

However, we think that there is room in the quan-

tum world for symbolic AI. Since QC is inherently

probabilistic, we can take advantage of this nature to

implement inaccurate knowledge more effectively.

This idea has taken form in the QRBS software

presented here. With this framework, users can model

their knowledge classically and implement it automat-

ically in a given quantum computer.

On top of that, the results obtained prove both that

the framework presented is valid for the implemen-

tation of symbolic AI models in a QC, and that it

manages inaccurate knowledge successfully. We also

have demonstrated how our framework is suitable for

NISQ quantum computers, making it viable before

noise-correcting quantum computers are available.

This development presents a ﬁrst step towards

a quantum symbolic AI library that can implement

generically classical symbolic AI models in a quan-

tum computer, and that allows us to take advantage of

the probabilistic nature of quantum computers to ﬁnd

a quantum advantage in such implementation.

ACKNOWLEDGEMENTS

This work has been supported by the EU’s Horizon

2020 under project NEASQC (grant No 951821), the

State Research Agency of the Spanish Government

(Grant PID2023-147422OB-I00) and by the Xunta de

Galicia (Grant ED431C 2022/44), supported by the

EU European Regional Development Fund (ERDF).

CITIC, as a center accredited for excellence within

the Galician University System and a member of the

CIGUS Network, receives subsidies from the De-

partment of Education, Science, Universities, and

Vocational Training of the Xunta de Galicia. Ad-

ditionally, it is co-ﬁnanced by the EU through the

FEDER Galicia 2021-27 operational program (Ref.

ED431G 2023/01). We thank the support from Min-

istry for Digital Transformation and Civil Service

and Next-GenerationEU/RRF (TSI-100925-2023-1).

SMR has received funding from Xunta de Galicia

(grant ED481A 2023/008).

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