Introduction

Wireless sensor networks (WSN), which correspond to sensing nodes connected to each other and deployed for performing a task, are among the solutions offered for systems being capable of quickly and reliably transmitting information from the edge of a network to the monitoring/control center [1]. The sensor data are shared with each other and used as input to a distributed estimation system for extracting the relevant information.

For the information used for decision-making in the mining industry to be effective, which works under extreme conditions in the operations, it is necessary to perform a fault diagnosis to avoid errors in the processing and output of data from the system [2].

On the other hand, Networks having a Long Range (LoRa) communication protocol, managed by a local server in the field or by an online cloud server over the internet [3], are capable of offering safe solution without a substantial increase in the energy consumption and using a wireless frequency spectrum without paying a license fee [4]. The network layer for LoRa may vary depending on the kind of topology with which the communications network is built. Long Range Wide Area Network (LoRaWAN) and Long Range Mesh network (LoRa Mesh) are some common topologies [5, 6].

The features of LoRa make it a relevant technology for use in Internet of Things (IoT) applications to exchange information at an acceptable speed with the cloud, for uploading and downloading data. IoT allows systems to be remotely detected and controlled, providing a greater integration between the physical world and computer-based systems, which in the long term provides greater efficiency, accuracy, and economic benefits. However, IoT has some limitations since the information is not encrypted, lacks security, and shows a low data transfer rate and a high latency time [7].

If the network is vulnerable, it can lead to cyber-attacks in which communication systems are corrupted and false information can be transmitted that changes the real data [8].

In wireless communication networks of smart industries in the primary sector, quantum-inspired optimization is increasingly used for solving complex problems. Quantum-inspired optimization is based on quantum mechanics and comprises the analysis, processing, and transmission of data in real-time [9, 10]. Quantum-inspired optimization is a concept of quantum computing and has the qubit as the minimal unit and the superposition of states (for example, an electron exists in all its possible states at the same time and simultaneously) [10]. The quantum provides a greater availability, scalability, and operativity to the balancing of the data loading in the cloud of the computing network working with IoT [11].

By means of quantum computing it is possible to solve problems that can not be solved using classical computing. It also allows the combination of quantum algorithms with databases and with more efficient querying algorithms for large amounts of data [12, 13]. Quantum systems are based on the postulates of quantum mechanics related to the Hilbert space, in which multiple target states may be superpositioned and more rapidly analyzed, since there is a probability vector showing the probability distribution among multiple states and the evolution of the transition matrix between states [12].

Quantum Genetic Algorithms (QGA) have been used to solve complex optimization problems in engineering, due to their great capacity for global computing in a shorter execution time, due to the search for their implicit parallel, and due to the smaller size of the population [14].

Quantum systems have advantages in the industry since they can minimize energy costs due to lower network traffic, improve performance with less delay latency, reduce the risks of failures in the information security field, and allow distributed use and analysis of IoT data in offline or limited connectivity environments [15]. It is possible to use the concepts of eigenvectors and eigenvalues of a Hilbert space together with an information system with multi-agents to improve decision-making, wherein robustness helps to capture a large amount of data in an environment that operates with disturbances from different sources with a dynamic and evolving environment [16].

Motivation

Underground mining is an important productive sector in Chile, in which productive activities are carried out daily in tunnels that require Ventilation on Demand (VoD) with sensors and actuators. These devices transmit data through the rocks, which usually generates losses in communication due to frequent cuts of optical fiber and the shortcomings that wireless systems present due to the lack of robustness of the configuration [17]. The loss of connectivity in mining tunnels is risky since, for example, forces workers to evacuate so that they do not get intoxicated by gases. It can also cause fatal accidents, silicosis, etc.

If communications fail and the current legal regulations related to the protection of life, physical integrity of people, facilities and infrastructure in which operational activities are carried out are not complied with, sanctions are applied to the mining company that generate economic costs in production. [18].

As a solution, it is necessary to find communication methods that are more secure and capable of transmitting information in a ventilation system in which data are captured with sensors, optimized with a hybrid quantum algorithm, monitored and controlled with a more robust communication support. If mining has resilient networks that can withstand failures and attacks, decisions can be made in real time to prevent risks and accidents in the workplace. It is required to look for technologies that improve communication and algorithms that provide advantages due to their accuracy, speed, effectiveness, and efficiency.

To determine which algorithm is more robust for a tunnel in underground mining, in the present work a bibliographic review of the methods, algorithms, and metrics is exposed in the next section. A communication method best matching the requirements of the underground mining environment is selected. With the selected method, in the subsequent section, an experimental case will be developed followed by which experimental results of the quantum genetic algorithm are given. Key aspects will be discussed next. Conclusions and future lines of research will be given in the final section.

Scope

The research is focused on determining a quantum algorithm that can be used experimentally to communicate a VoD system inside the tunnel. The work includes the design of the ventilation system with sensors and the optimisation of the quantum genetic algorithm (see “Conceptual design” in steps (1) and (2). It should be noted that future research will address the computer and software development that builds a monitoring and control system (see “Conceptual design” in step (3).

Literature review

To know in which areas quantum algorithms are applied and what are the parameters that could build metrics that can be used in communications with IoT, the literature review was performed on October 3, 2022, using the keywords ‘quantum’ AND ‘optimization’ AND ‘IOT’. Among the 54 results found, the sample presented in Table 1 was selected due to the close relation with the experimental case as developed in “Experiment”.

Table 1 Industrial areas with IoT quantum algorithm applications
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Most repeated features in the quantum algorithms shown in Table 1 are classified in Table 2. The results show that in the Telecommunications field, most of the publications are related to data transmission networks and quantum heuristic algorithms.

Table 2 Characterístics of quantum algorithms
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A search with the Scripts in the Main Collection of Web of Science: TS=(quantum AND IoT AND communication) was performed on August 11, 2022, 2022, to determine which technologies have been studied in the area of communications with IoT. The results obtained in the in Table 3 show that the compatibility of the different technologies with the algorithms needs to be further studied and that, in general, IoT systems are considered as means to optimize resources.

Table 3 Quantum-inspired communication and IoT methods
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Table 4 compares which metaheuristic method with and without quantum is more efficient. A search was carried out in the Web of Science, IEEE, and Scopus databases on October 20, 2022, with the keywords ‘Quantum Algorithms’ AND ‘Metaheuristic Algorithm’. Results were obtained for Metaheuristic Algorithms (10,463 on the Web of Science, 5257 on IEEE, and 19,049 on Scopus), and for Quantum Algorithms (27,139 on the Web of Science, 38,736 on Scopus, and 10,483 on IEEE).

Table 4 Criteria of quantum and non-quantum metaheuristic algorithms
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Table 5 Classification of the key attributes of each quantum and metaheuristic algorithm
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The obtained results in Table 1 were used to create Table 5, in which the algorithms were classified according to the following criteria: complexity (efficiency), effectiveness, processing, and accuracy. It was observed that the algorithm that presented the greatest number of attributes is the quantum bee colony with 21.4%, followed by the quantum firefly colony algorithm with 19.6%. In third place appeared the quantum genetics and the firefly colony algorithm with 17.9%. It should be noted that the choice of the algorithm also depends on the field of the optimization problem being studied, as can be seen in Table 1.

As explained in “Experiment”, the experiment was performed with the quantum genetic algorithm since it included the following criteria: data processing, mathematical modeling, and object detection.

Materials and methods

Basic representations

Unlike classical computing, quantum computing uses superposition and entanglement, in which the quantum states of two or more objects are to be described by a single state involving all objects in the system even when the objects are spatially separated; since the electron may be in any of the infinitely many intermediate quantum states between classical states 0 and 1 [62, 63]. In quantum computing, it is possible to prepare a system cold enough for the electron not being able to escape from the two levels with the lowest energy. As shown in Fig. 1 an atom can have two orbitals that simulate the behavior of a qubit. When the energy is not enough to change its orbit, the electron remains in an intermediate state, the superposition is broken (collapse or decoherence), and it is likely to pass to state 0 or 1.

Quantum computing has the advantage that it benefits from superposition or parallelism by considering all the paths at the same time, thus increasing its processing capacity. It can be represented by the qubit, which is the smallest unit of the Information Theory [64].

Fig. 1
figure 1

Atom with 2 orbitals simulating 1 qubit

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Fig. 2
figure 2

Parallelism [66,67,68]

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For representing the superposition for 1, 2 and n qubits, it is proposed [65]:

  • Example \((n=1).\) For 1 qubit it is obtained the dimension \(2^{1}\).

  • Example \((n=2).\) In the case of 2 qubits, \(2^{2}\) dimensions are obtained, corresponding to simultaneously having the combinations 00, 01, 10 y 11 [62].

    In the Bloch sphere shown in Fig. 2, the \(\psi \) state describing the linear combination of ket 0 and ket 1, given an orthonormal basis, is represented

    Regarding the mathematical formulation, the following linear combination is proposed [69].

    $$\begin{aligned} \mid \psi \rangle = \alpha \mid 0\rangle +\beta \mid 1 \rangle = \left( {\begin{array}{c}\alpha \\ 0\end{array}}\right) +\left( {\begin{array}{c}0\\ \beta \end{array}}\right) =\left( {\begin{array}{c}\alpha \\ \beta \end{array}}\right) \end{aligned}$$
    (1)

    With \(\alpha \in {\mathbb {C}}\) and \({\beta \in {\mathbb {C}}}\)

    It is worth mentioning the probabilistic condition for the normed complex magnitudes \(\alpha \) and \(\beta \):

    $$\begin{aligned} \mid \alpha \mid ^{2} + \mid \beta \mid ^{2} =1. \end{aligned}$$
    (2)

    Wherein \(\mid \alpha \mid ^{2} \) is the probability of the qubit being in ket 0 y \( \mid \beta \mid ^{2}\) is the probability of the qubit being in ket 1 [61].

  • Example for n. It is possible to have multiple qubits with \(2^{n}\) dimensions. It is a quantum entanglement state with a higher correlation than classical systems.

Quantum systems

The evolution or dynamic of the qubits is determined by a unitary operator U, over the Hilbert vector space with finite or infinite dimension. The Hilbert space is based on the postulates of quantum mechanics [70,71,72].

It follows the following steps:

Step 1 Choose the system to be described. There is a system described by a unitary state vector \(\mid \psi (t_{i})\rangle \) belonging to a Hilbert vector space.

Step 2 Choose the possible system configurations. The system \(\psi \left( t _{i} \right) \) changes of state U in time, and there is a linear transformation in which the quadratic sum of probabilities is maintained equal to 1

$$\begin{aligned} S_{1}:\mid \psi (t _{i}) \rangle ~ \overset{U}{\longrightarrow }~ S_{2}:\mid \psi (t_{i+1})\rangle . \end{aligned}$$
(3)

With \(S_{1}\) = system 1 and \(S_{2}\) = system 2; \(i=1,2,\ldots n\), \(i\in {\mathbb {N}}.\)

Equation (3) may be expressed as a dynamic matrix of the system.

Step 3 Propose the dynamic of the system for explaining why it moves. For example, 3 hermitian or self-adjoint matrixes may be provided in a complex vector space V with a sesquilinear form \(h:V\otimes V\rightarrow {\mathbb {C}}\), wherein h is antilinear (or conjugate linear). A hermitian form requires:

$$\begin{aligned} h(x,y)= \overline{h(y,x)};\quad x,y\in V. \end{aligned}$$
(4)
Fig. 3
figure 3

General diagram of the experiment

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Then, \(E_{i}=V^H_{i}; i=1,2,3\) is a real vector space with hermitian forms of \(V^H\).

In a quantum system, an observable may be defined if the sum of the probabilities equals 1, that is, if it is known how many possible results there are in the observation, as shown in Eq. (5):

$$\begin{aligned} E_{1}+E_{2}+E_{3}=1. \end{aligned}$$
(5)

It is possible to define the superposition and create two stable states A and B [73]:

$$\begin{aligned} E^{A}\rightarrow \mid A \rangle = \frac{\mid 0 \rangle + \mid 1 \rangle }{\sqrt{2}}; E^{B}\rightarrow \mid A \rangle = \frac{\mid 0 \rangle - \mid 1 \rangle }{\sqrt{2}}. \end{aligned}$$
(6)

Step 4 Performing measurements.

With R the observable is measured and U shows the change in the state from system 1 to system 2:

$$\begin{aligned} S_{1}\overset{U}{\rightarrow }S_{2}\overset{R}{\rightarrow } P_{i}=\langle \psi \mid \widehat{E_{i}} \mid \psi \rangle . \end{aligned}$$
(7)

In Eq. (7) the probabilities \(P_{i} \) with \(i=1,2,3\) for the three hermitian matrixes \(E_{1},E_{2},E_{3}\), shown in step 2, are obtained. The notation for the self-adjoint hermitian operators \(\widehat{E_{i}}\) is used:

$$\begin{aligned} \langle \psi \mid \widehat{E_{i}} \mid \psi \rangle . \end{aligned}$$

Since \(\widehat{E_{i}}\) is a Hermitian operator, both ket or bra may be used indistinctly. Hermitian operators have real eigenvalues and real, orthogonal eigenvectors [74].

The entanglement, until the time of the measurement, does not have a well-defined spin (measurement of the angular momentum due to the rotation of the particle about its own axis), and the variables of the system on which its value depends are not known. It is possible to know the state of an observable particle and its result as expressed by its probability.

Mathematical formulation

In this work, the results of the experiment shown in Fig. 3 are presented. Said experiment uses communication resources, which may be adapted to an underground mine. A scenario is created, in which a tunnel is provided with sensors and actuators that capture, store and transmit humidity, temperature, differential pressure, and CO\(_{2}\) data. The devices are connected to a hub that sends a large amount of data to a central point, which is connected to the cloud computing infrastructure wherein a quantum genetic algorithm is applied and the quantum information is optimized.

Quantum Genetic Algorithms:. A QGA based on quantum mechanics is used. The algorithm searches for a global optimum from the chromosomes and the updating of the quantum gates [75].

Unlike the classical genetic algorithm in which the population evolves genetically by selecting, crossing, and mutating genes; QGA uses the method of chromosome evolution based on the quantum rotating door, increasing its performance and the interference crossover that provides a greater crossover of the [68] chromosomes.

In the evolutionary algorithm, it is possible to record a quantum chromosome gene with one or more qubits that can represent the probability of storing information in states 0, 1 or as a superposition of two quantum states [69] (see Eqs. (1) and (2)). By generalizing, as mentioned in the example of “Quantum systems” for n qubits, the chromosome with length n can be observed in \(2^{n}\) states.

The quantum chromosome is updated from generation to generation to evolve the optimal individual [69]. As shown in Fig. 2, a quantum logic gate may be represented by a \(2\times 2\) matrix, wherein \(\theta \) is the rotation angle:

$$\begin{aligned} \begin{bmatrix} \cos (\theta )&{} -\sin (\theta ) \\ \sin (\theta )&{} \cos (\theta ) \end{bmatrix}. \end{aligned}$$
(8)
Fig. 4
figure 4

a Installation of the communication system in the mine, b FSO transceiver within the mine tunnel, top: outside the tunnel, below: inside the tunnel

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The measurement process of each record allows changing the amplitude of the observable individual, wherein the search for the best solution is determined by updating the chromosome [76]. \(\alpha \) y \(\beta \) are modified (see Eq. (1)) generating an entanglement and the best solution is obtained:

$$\begin{aligned} \begin{bmatrix} \alpha ' \\ \beta ' \end{bmatrix} = \begin{bmatrix} \cos (\theta )&{} -\sin (\theta ) \\ \sin (\theta )&{} \cos (\theta ) \end{bmatrix} x \begin{bmatrix} \alpha \\ \beta \end{bmatrix}. \end{aligned}$$
(9)

In the encoding process, there is a chain of one or more input records for the measurement process of the observable [60]. The new quantum chromosome is obtained:

$$\begin{aligned} CQ = \begin{bmatrix} \alpha _{1}\mid \alpha _{2}\mid \cdots \mid \alpha _{n-1} \mid \alpha _{n} \\ \beta _{1}\mid \beta _{2}\mid \cdots \mid \beta _{n-1} \mid \beta _{n} \\ \end{bmatrix} \end{aligned}$$
(10)

wherein:

$$\begin{aligned} \mid \alpha \mid _{i}^{2} + \mid \beta \mid _{i}^{2} \ = 1 , \forall {i} = 1,2,3,\ldots ,n. \end{aligned}$$
(11)

The number of the population of quantum chromosomes is initialized:

$$\begin{aligned} \left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) . \end{aligned}$$
(12)

A measurement is performed with a group of possible solutions according to the iteration in which the execution is [77]. The global optimum is sought, wherein each solution is particularly observed, saving the best value among the group of solutions [60].

Regarding the optimization formula to be used for the quantum genetic algorithm, the following are maximized in 3-D in real-time: the distance between the sensors \(Z_{i}\) with \(i=1,\ldots , 5\) being the environment or the neighborhood of the object of study \(X_{k}\) where k is the number of objects. Points in space that are close to a given point or that are close neighbors to a fixed point are sought [78].

It is had that by varying the time in a \(\Delta _{t}\) it is possible to identify the optimal sensor for the object \(X_{k}\) in the algorithm Q. The optimization Q has stat-dynamic detection capabilities in a multi-object IoT environment, where the environment is stochastic and dynamic. The optimization Q also evaluates the IoT of the environment with respect to a specific object [15, 27].

The displacement is optimized with the following mathematical model [11]:

$$\begin{aligned} Q=\text {max} \sum _{k=1}^{x} \sum _{j=1}^{z} \sum _{i=1}^{y}\left( w_{i j k} * \sqrt{Y_{i j k}}\right) ^{2}. \end{aligned}$$
(13)

With

\( w_{i j k} \in (0,1)\quad \forall i, j, k=(0, \ldots , 1)\quad \) being the weight associated with the data.

\(Y_{i j k}\quad \) being the environment parameters related to the object and the sensor.

Experiment

The feasibility of improving communications in an underground mining environment with an optimized quantum genetic algorithm will be studied in the experiment.

Description of the system

The experimental system represented in Fig. 3 has the following steps:

Step 1: data acquisition from humidity, gas, temperature, and pressure sensors. As shown in Fig. 4, the sensors are installed at a uniform distance from each other, such that the distance between devices is equidistant within a length of the measured environment. An object having a non-zero measurement probability within the environment is detected and controlled with an Arduino Mega 2560 microcontroller and a TTGO T-Beam Rev1 LoRa Node. The ID, key, frequency, and spread are obtained from each device.

With the radiofrequency nodes in the tunnel, the sensor information is sent to a hub with a fixed position, and an IoT network is built. The physical system is formed by a LoRaWAN Gateway (Raspberry pi + 3B + Hat Dragino PG 1301), a Gigabit Switch, and a Raspberry Pi 4. Three sensor nodes, among which two move away from the hub at regular distance intervals and one is kept at a fixed distance from the hub are configured for obtaining the data. The information is sent from each LoRa node to the hub, which sends the data to the local server.

At the next connection interface stage between sensors, the metrics Received Signal Strength Indicator (RSSI) and Signal-to-Noise Ratio (SNR), associated with the range, instrument reach length (span), and response time variables, are obtained. For each sensor, the following attributes are captured: ID, name, description size, sensor, and device. The data are sent to the central hub and the Backhaul block.

Step 2: Optimization of the Quantum Genetic Algorithms.

The data sent through the Backhaul block are received and the IoT devices are connected to a cloud server acting as a data repository in real-time. The “cloud” is a combination between The Things Network (TTN) server, that manages the LoRaWAN communication and computing services at a local server, wherein the services of optimization of the quantum-genetic algorithm are stored.

A quantum-genetic algorithm is built based on the methods of [79,80,81] and the IBM Quantum experience platform in the Cirq Python library. The quantum circuit is built inspired by the Deutsch–Jozsa (DJ) theory, which improves the distribution of the quantum keys that provide autonomy and robustness [82]. The DJ theory searches the optimum value of the objective function and can be used with the Hadamard logic gate (represented in Fig. 2 and Eq. (14) that allows quantum superposition with equally probable states.

$$\begin{aligned} H= \frac{1}{\sqrt{2}}\begin{bmatrix}1 &{} 1\\ 1 &{} -1 \end{bmatrix}. \end{aligned}$$
(14)

The Hadamard gate is obtained as a linear combination of Pauli matrices and the Pauli gate may operate as a Not gate. It is to be mentioned that the Not gate is the one performing the chromosomic variation and may transform the probability amplitudes of the selected qubits, according to the probability of random mutation, to increase the diversity of the population and reduce the premature convergence, providing robustness since losses of a great part of the information of the population are avoided [61, 83]. The gates are combined and a quantum system as shown in Fig. 5 is built.

Fig. 5
figure 5

Quantum System, Software IBM Q https://quantum-computing.ibm.com/composer/files/6a178b3b75b834bdc4531221f05ef24d2dccd6901192b1edf50c8be7a2104f7b

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The experiment follows the iterative process shown in Fig. 6, which determines the global solution of the maximization problem [68]. The chromosome of the algorithm comes from the creation of a random vector matrix that generates the individual selection process and their genetic crossing. The aim of the process is to vary the chromosome among generations and has a mutation step that preserves the genetic diversity of the population [35, 60].

Fig. 6
figure 6

Selection process. Pc(q) corresponds to the quantum population defined according to the input record defined as qubits. Pq(c) corresponds to the quantum population defined according to the genetic operators for the recorded chromosome. Based on [81]

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For modeling the quantum-genetic algorithm, an adaptation of Eq. (10) will be used as an evaluation or fitness function. Since the algorithm to be modeled is a kind of learning algorithm, it is possible to use neural networks [84, 85].

For accelerating the creation of neural networks and training the model (Fig. 7), the open source Python library \(\text {keras}^{\text {GA}}\) is included in Eq. (15). It is to be mentioned that the prediction is generated depending on the object (for example, people or vehicles working in the tunnel) and the parameters: SNR, RSSI, distance, and a random binary number used for generating the chromosome:

$$\begin{aligned} Q=\text {max} \sum _{k=1}^{x} \sum _{j=1}^{z} \sum _{i=1}^{y}\left( w_{i j k} * \sqrt{\text {keras}^{\text {GA}}}\right) ^{2}. \end{aligned}$$
(15)

With

$$\begin{aligned}{} & {} w_{i,j,k},\epsilon ,(0,1) \quad \forall , i,j,k,= (0,\ldots ,1)\\{} & {} \text {keras}^{\text {GA}}:\text { parameter }Y \text { in } 3\text {-D}. \end{aligned}$$
Fig. 7
figure 7

Forecast

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Experimental results

The GA and QGA algorithms were tested with the objective function shown in Eq. (15) and the database obtained from the laboratory with the parameters SNR, RSSI, the distance and binary number. Ten iterations of five generations each are generated and, as shown in Fig. 8a and b, the quantum genetic algorithm obtains a higher fitness and a shorter computation time than the GA.

Figure 9a shows the distribution of the results. It is observed that GA converges rapidly in the second generation with values close to 1.5173. In relation to QGA, it can be seen in Fig. 9b that the values found are relatively lower at the beginning, and in generation 4 it approaches the global optimum close to 1.9365.

Fig. 8
figure 8

a Fitness and b time

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Fig. 9
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a GA and b QGA. The red dot represents the average

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Table 6 Comparative table
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By comparing the metrics in Table 6, the following advantages of using the quantum genetic algorithm are observed: it gets a higher accuracy, it has a higher computed true experimental value for the objective function, and it is more efficient since a better performance in less average time and costs is obtained.

Finally, in the experiment, the following considerations were taken:

  • A sensor package is not located at a point in the environment, at a shorter distance than another package of the same type.

  • Considering the technical specifications of the sensors since the precision and accuracy can be improved for the sensor package closest to the object.

Table 7 Analysis of advantages and disadvantages of quantum systems
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Discussion

Analysis of QGA and its optimization function

In nonlinear optimization problems, effective and efficient strategies are required for solving complex problems [86]. It is important to find local optima that give a better solution in the search space than those used as regional strategies that are close to the objective function [87].

In relation to the experiment, a rapid convergence was observed that could be caused by entanglement [88]. It should be said that the speed of convergence would not ensure the existence of the optimum and in the case the optimum strays from the local solutions, the solutions could not have a global convergence [89]. On the other hand, in a quantum algorithm, it is possible to have different tuning strategies of the quantum revolving door that could prematurely converge locally at a slow rate, in a state of stagnation [69].

In the optimization function, further analysis of the chromosome function of the quantum genetic algorithm is required [84]. It is necessary to improve the quantum genetic algorithm by analyzing other optimization functions on the chromosome, which do not use only the fitness function as the traditional genetic algorithm and which deliver solutions that have fast convergence to the local optimum. It is noted that different scenarios can be generated in which: (1) the quantum bit of the chromosome is not close to the optimum or (2) in case it is in the optimum, a new chromosome is generated that can move away from the current optimum and affect the convergence of the algorithm [68].

More research is needed on hybrid quantum algorithms, wherein metaheuristics that generate a global search and optimization methods that perform an efficient local search are combined [89].

On the other hand, since the quantum genetic algorithm is integrated into a communications system as shown in Fig. 4, it can exhibit the advantages and disadvantages that are exposed in Table 7.

Feasibility technological

QGA

In the experiment it was possible to generate the QGA algorithm since with the Python Numpy library the spin vector is built and the quantum superposition simulation is performed. Qiskit, SymPy and QuTIP are used to build the quantum circuits and implement the quantum algorithms.

Future research will use IBM Quantum Experience to bring the code to the mining company’s Amazon Web Services (AWS) and Google Cloud Platform (GCP) cloud monitoring service platforms.

Fig. 10
figure 10

QGA conceptual model

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Conceptual design

Figure 10 shows the QGA conceptual model that includes the following steps: (1) the tunnels within the IoT network in mining with the sensors that extract environmental data from the ventilation system; (2) the genetic quantum optimization space which will be hosted in the industrial routers; (3) a control center that will monitor in real time the environmental variables to make timely decisions and avoid risks, for example, if there is excess CO\(_2\), a backup fan could be alerted or activated.

Advantages and limitations

Advantages

As mentioned in “Literature review”, it is feasible to use quantum genetic algorithms in the field of telecommunications which are more robust than conventional algorithms. It is observed that QGA meets the criteria required for the implementation of the experiment shown in “Experiment” since it can process data, performs mathematical modeling, detects objects and can determine energy efficiency (see Table 4).

Another advantage is that incorporating QGA in the communication system makes data transmission more robust and ensures a higher percentage of availability of ventilation systems inside a mine. By receiving more reliable, real-time data on flows within the mine (air flow rates, gas concentrations, temperature conditions, etc.), decision-making and information management would be more efficient and effective [99]. Secure and robust communication would allow for real-time reporting of hazards and timely evacuation of workers [17].

Limitations

Another limitation is that the implementation of QGA depends on the execution environment. In the experiment described in “Experiment”, it was complex to build a QGA runtime environment that could be adapted to a real mining tunnel situation. Many tests were performed in the laboratory to determine which parameters and/or metrics of the sensors and actuators comply with the postulates of quantum mechanics which requires uncertain and non-deterministic data. RSSI and SNR metrics associated with range, span and response time were selected.

Another difficulty was the creation of the database with unstructured information; it was necessary to clean and structure the data so that it could be processed with the quantum genetic optimization algorithm.

On the other hand, to develop a system such as the one shown in Fig. 10 a multidisciplinary group is required since knowledge of different areas related to: Quantum Mechanics, Heuristic Optimization, Electronics, Informatics and Computing and with the knowledge of Data Management to help in the decision-making process.

Conclusions

In this bibliographical review it is shown that there are more practical than analytical cases that have been studied in the field of quantum computing, and that there has not been enough research regarding the quantum approach compared to other traditional methods [10]. In addition, in Tables 1 and 5 it was determined that Telecommunications is the industry field in which quantum algorithms with IoT have been analyzed the most; and that it is possible to obtain metrics for object detection, data processing, and data modeling.

In “Literature review” it was shown that it is possible to use hybrid algorithms that work with metaheuristics and quantum computing. Despite the fact that there are industrial applications in the literature, it has been difficult to understand how they can be applied to a real case since it is necessary to have knowledge and understanding of different fields, such as: quantum mechanics, metaheuristics, function optimization, programming, data analytics, and electrical engineering.

Despite the multidisciplinary nature of the case study presented in this work, it was possible to integrate experimental data obtained with sensors with input parameters of the quantum genetic algorithm to obtain results that are close to the global optimum.

It is necessary to continue investigating and analyzing other optimization functions that could provide more effective and efficient local optimal solutions. If better solutions are obtained, more secure communication in an underground tunnel environment could be obtained with more robust support. This could be implemented into a monitoring and control system that allows to provide safe and optimum environmental conditions for workers as they move through the mine, due to, for example, the timely and safe connection that would exist with the ventilation system.

In the future, new methods and protocols are required to transmit quantum information securely and in real time, so that in the future it will be possible to have a quantum internet in companies to ensure communication between the sender and receiver [100]. With quantum, it would be possible to group quantum devices in a network in the cloud, and it would also be possible to change the configuration currently used in mining to transmit data over the internet with fibre-optic cable networks with short-range coverage that require repeaters (a situation that generates vulnerability) [101].

In our opinion, it should be noted that with the influence of artificial intelligence, there is a growing need for communications systems that are more secure for data transmission and that can withstand the changes brought about by the larger 5 G technology. With quantum, data could be sent over long distances, with secure cryptography.