# qIoV: A Quantum-Driven Internet-of-Vehicles-Based Approach for Environmental
Monitoring and Rapid Response Systems

Ankur Nahar<EMAIL_ADDRESS>0000-0001-9996-1167 Indian Institute of
Technology JodhpurDepartment of Computer Science and
EngineeringJodhpurRajasthanIndia342030 ,  Koustav Kumar Mondal
<EMAIL_ADDRESS>0000-0003-1679-1030 Indian Institute of Technology
JodhpurInter-disciplinary Research Division - IoT and
ApplicationJodhpurRajasthanIndia342030 ,  Debasis Das<EMAIL_ADDRESS>0000-0001-6205-4096 Indian Institute of Technology JodhpurDepartment of
Computer Science and EngineeringJodhpurRajasthanIndia342030 and  Rajkumar
Buyya<EMAIL_ADDRESS>0000-0001-9754-6496 University of
MelbourneComputing and Information SystemsMelbournVICAustralia3052

###### Abstract.

This research addresses the critical necessity for advanced rapid response
operations in managing a spectrum of environmental hazards. These include
leaks in urban pipelines, industrial release of hazardous gases, methane
emissions from landfill sites, chlorine gas leaks from water treatment
facilities, and carbon monoxide emissions from residential areas, all of which
are critical to ensuring public safety and environmental protection. We
propose a novel framework, qIoV that integrates quantum computing with the
Internet-of-Vehicles (IoV) to leverage the computational efficiency,
parallelism, and entanglement properties of quantum mechanics. Our approach
involves the use of environmental sensors mounted on vehicles for precise air
quality assessment. These sensors are designed to be highly sensitive and
accurate, leveraging the principles of quantum mechanics to detect and measure
environmental parameters. A salient feature of our proposal is the Quantum
Mesh Network Fabric (QMF), a system designed to dynamically adjust the quantum
network topology in accordance with vehicular movements. This capability is
critical to maintaining the integrity of quantum states against environmental
and vehicular disturbances, thereby ensuring reliable data transmission and
processing. Moreover, our methodology is further augmented by the
incorporation of a variational quantum classifier (VQC) with advanced quantum
entanglement techniques. This integration offers a significant reduction in
latency for hazard alert transmission, thus enabling expedited communication
of crucial data to emergency response teams and the public. Our study on the
IBM OpenQSAM 3 platform, utilizing a 127 Qubit system, revealed significant
advancements in pair plot analysis, achieving over 90% in precision, recall,
and F1-Score metrics and an 83% increase in the speed of toxic gas detection
compared to conventional methods.Additionally, theoretical analyses validate
the efficiency of quantum rotation, teleportation protocols, and the fidelity
of quantum entanglement, further underscoring the potential of quantum
computing in enhancing analytical performance.

Quantum computing, Internet-of-Vehicles, entanglement distribution,
environmental hazards

##  1\. Introduction

Gas leaks in urban areas often lead to highly dangerous situations and can
potentially cause severe harm. The absence of a rapid response system has been
a contributing factor in numerous incidents, such as the over 2,600 gas
pipeline leaks in the United States from 2010 to late 2021 (Pipeline and
Hazardous Materials Safety Administration , Department of Transportation
(DOT)(2023), PHMSA), and 3,695 fatalities in China’s coal mining industry from
2001 to 2018 (Zhou et al., 2022). Additionally, from 2010 to 2022, there were
4,901 oil and gas spills in the U.S., with Texas alone accounting for nearly
40% of these incidents (Shah, 2023). The Bhopal gas leak tragedy in India
(Mishra et al., 2009), resulting in thousands of deaths, underscores the need
for efficient, real-time alert systems. Moreover, the U.S. pipeline
regulator’s recent measures to curb methane leaks from the country’s vast gas
infrastructure highlight the ongoing challenges and urgency in addressing such
hazardous leaks (Volcovici, 2023).

In such scenarios, early warning systems are essential in reducing
environmental disaster impacts (Balis et al., 2013). They enable fast
evacuations, timely medical aid, and quick emergency service mobilization,
which is particularly critical in gas leak scenarios. Classical computing
methods in Hazardous Incident Tracking, such as wireless sensor networks (Dong
et al., 2019) and machine learning algorithms (Liu et al., 2021), have made
significant contributions in detecting and localizing gas leaks. However, they
encounter limitations in real-time data processing, scalability, and
sensitivity to subtle environmental changes. These limitations underscore the
need for a more accurate and timely detection of hazardous incidents. Here,
the quantum computing model can provide real-time, high-fidelity analysis of
environmental data, enabling more accurate and timely detection of hazardous
incidents compared to existing classical methods. The transition to quantum
computing not only promises a significant speedup in processing times but also
introduces a new paradigm in environmental monitoring, where the ability to
detect minute changes in sensor data can lead to earlier warnings and more
effective mitigation of hazards. Quantum computing application within
vehicular networks presents a novel front with potential for enhancing safety
and operational efficiency. This research points at the intersection of
quantum computing and vehicular technology, aiming to leverage the
computational capabilities of quantum systems to address critical challenges
in vehicular sensor data processing and communication. Central to our
investigation are three interconnected challenges: the translation of
classical sensor data into quantum formats, the utilization of quantum
classifiers for the detection of environmental hazards, and the deployment of
quantum entanglement mechanisms for the dissemination of alerts within a
vehicular network. By addressing these challenges, this study aims to
contribute to the development of quantum computing applications that can
surpass the limitations of classical computing paradigms. In this context,
vehicles, with their omnipresence in urban areas, emerge as innovative
carriers for environmental sensors (e.g., MQ2, MQ3, MQ5, MQ6, MQ7, MQ8, and
MQ135), transforming them into mobile monitoring units. These sensors gather
real-time data, which is crucial for hazard detection. Nevertheless,
challenges arise due to this data’s sheer volume and complexity, making
traditional processing methods insufficient (Pramanik et al., 2022). Our
framework in Fig. 1 presents a sustainable approach to environmental safety,
leveraging a quantum classifier, quantum mesh fabric, and quantum server for
enhanced detection and communication of hazardous gas leaks. The process
begins with Step 1, where vehicles equipped with advanced sensors detect toxic
gases emanating from sources such as industrial sites or urban pipelines.
These sensors gather high-resolution environmental data crucial for the early
detection of hazardous gas leaks. In Step 2, this sensor data is converted
into a quantum-compatible format. This quantum data conversion is a critical
process that translates classical sensor readings into quantum states that can
be processed by quantum algorithms. Step 3 involves the core quantum computing
components of the system—Quantum Mesh Fabric and Quantum Server. The Quantum
Mesh Fabric is an adaptive network that manages the entanglement of quantum
states across the vehicular network, ensuring robust and secure communication
channels. The Quantum Server, on the other hand, is tasked with processing the
quantum data using quantum algorithms, notably the variational quantum
classifier, which identifies and classifies the detected gases based on their
quantum state representations. Finally, step 4 is where the processed data
culminates into actionable intelligence. The Quantum Server, utilizing the
quantum entanglement established by the Quantum Mesh Fabric, disseminates
hazard alerts across the network. These alerts are transmitted with minimal
latency using the principles of quantum entanglement, which allow for the
instantaneous relay of information.

Figure 1. qIoV: A Quantum Framework for Toxic Gas Detection

###  1.1. Motivation

Serial incidents of disastrous environmental emergencies and recurring toxic
gas breakouts in the world motivate our research. A report in (Arya et al.,
2006) claims that most tragedies occurring at nocturnal timing laid bare a
critical vulnerability. The existing systems fail to effectively detect,
predict, and warn against nocturnal toxic hazards due to limited sensor
sensitivity and reduced human monitoring during night hours. For example, the
Bhopal gas tragedy in India, a night-time industrial failure resulting in
immediate and widespread loss of life (Palazzi et al., 2015). Similarly, the
Philadelphia refinery explosion in 2019 (Auchincloss and De Roos, 2019), and
China’s toxic gas breakout incidents echoed this necessity, emphasizing the
elevated risks at a time of natural human vulnerability. It underscored the
need for a vigilant, around-the-clock monitoring system. One promising
solution could be public and private vehicles as emergency monitoring units.

However, why vehicles, one might ask? The selection of vehicles as the primary
medium for this research is underpinned by their ubiquity and inherent
mobility. Given their extensive coverage and constant presence in urban areas,
vehicles offer a unique platform for deploying environmental sensing
capabilities. This ubiquity positions them as ideal candidates for monitoring
a range of environmental parameters, including toxic gas concentrations, on a
scale and with a granularity that stationary sensors cannot match (Cooper,
2021). However, the effective realization of this solution is contingent upon
overcoming significant computational challenges. Traditional computing
infrastructures, while capable in many respects, fall short in terms of
processing speed and sensitivity, particularly when rapid data analysis is
crucial—for instance, during nocturnal hours when the absence of human
observers necessitates improved sensor vigilance.

How technology will help? Quantum computing introduces data processing
capabilities, primarily through its exploitation of quantum bits (qubits).
These qubits can exist in multiple states simultaneously (superposition) and
be entangled with other qubits, creating a complex web of probabilistic
relationships that can be manipulated collectively. This quantum superposition
and entanglement enable the parallel processing of information, allowing
quantum systems to analyze vast datasets and execute algorithms at speeds
unattainable by traditional computing systems. In the context of vehicular
networks, this quantum advantage translates into the ability to rapidly
encode, process, and interpret the environmental data collected by vehicular
sensors. Through quantum state encoding, sensor data can be transformed into
quantum states, which are then manipulated using quantum circuits that execute
sophisticated algorithms for data analysis (Danba et al., 2022).

###  1.2. Contributions

This research proposes a framework called qIoV for environmental monitoring
(Ref. Fig. 1), particularly in the detection and analysis of toxic gasses. Our
framework utilizes multipartite entanglement that refers to a quantum state
involving three or more qubits where the state of each qubit cannot be
described independently of the state of the others, even when the qubits are
separated by large distances. Using these entangled states, qIoV framework
encode environmental data, including hazard alerts, into a quantum state
shared across multiple vehicles within the network. The transmission of alerts
is further refined through the application of quantum teleportation technique.
For vehicular networks, this implies that once an alert is encoded into a
quantum state, it can be instantaneously transmitted across the network, from
the detecting vehicle to others, utilizing entanglement patterns designed for
vehicular data. To achieve this, we design quantum circuits that are capable
of generating and manipulating multipartite entangled states, alongside
protocols for entanglement distribution and quantum teleportation. The
circuits include operations i.e., Bell state measurements and controlled
quantum gates, which facilitate the reliable encoding and teleportation of
quantum states corresponding to environmental alerts. The adaptability of
these entangled states to the topology of vehicular networks ensures that
alerts are propagated efficiently, reaching all intended recipients with
minimal delay and maximal fidelity. To summarize, followings are the key
contributions of our research:

  1. (1)

We propose an encoding scheme that aligns the multi-dimensional sensor data
from vehicular sensors with quantum states. Our framework, specifically
calibrated for detecting various toxic gases, relies on optimizing the
rotation angles $\mathbf{R_{\theta}}$ based on the unique patterns of gas
sensor readings.

  2. (2)

We propose multipartite entanglement in vehicular networks based on Quantum
Entangled Feature Maps. The quantum operations systematically entangle qubits
across different vehicles, utilizing controlled-Z (CZ) and controlled-X (CX)
gates to induce correlations that mirror the interconnected data patterns of
vehicular sensors.

  3. (3)

To accommodate the dynamic and potentially large-scale nature of vehicular
networks, we structure the entanglement in layers. Each layer represents a
level of interaction among the vehicles. This allows for scalable and flexible
entanglement patterns that can be adapted based on the network’s size and
complexity.

  4. (4)

We design Adaptive Quantum Circuits to integrate entanglement patterns to
vehicular data. This methodology involves the dynamic adjustment of quantum
circuits to optimize how environmental alerts are encoded into the quantum
states, ensuring efficient and accurate data transmission.

  5. (5)

Our framework applies real-time adaptive quantum circuit optimization, guided
by error syndromes and decoherence patterns identified through stabilizer
codes, to precisely adjust quantum gate parameters, ensuring robust error
correction and maintaining high fidelity in quantum state transmissions across
vehicular networks.

This article is organized as follows: Section 2 discusses the literature on
quantum computing in computation, Section 3 presents the problem definition,
and Section 4 defines the system overview and architectural design. Section 5
proposes the qIoV framework. Finally, Section 6 presents the simulation
findings and testing, and we conclude this paper in Section 7.

##  2\. Related Work

This section discusses the evolving landscape of quantum computing,
highlighting related works that contribute to our understanding of quantum
machine learning, its applications in transportation, and emerging quantum
frameworks and protocols. It also presents insights into quantum technology’s
current state, challenges, and innovations to set a foundational context for
our research.

###  2.1. Quantum Computing Foundations and Data Networks

The convergence of machine learning (ML) algorithms and quantum computing has
been identified as a transformative approach for processing and analyzing
extensive datasets with high-dimensional complexity. Research in (Ramezani et
al., 2020) examined this integration, underscoring the paradigm-shifting
potential of qubits to enhance computational efficiency and data analysis
capabilities. Furthermore, the authored discussed the development of hybrid
quantum-classical systems, designed to exploit quantum computational
advantages while addressing prevalent challenges such as the scarcity of
qubits and the omnipresent issues of noise within quantum systems. Notably,
the authors acknowledged the scalability constraints and noise inherent to
quantum computing frameworks. Subsequently, in (Yang et al., 2023), authors
illuminated significant progress in the domain of quantum hardware, which now
supports configurations scalable to thousands of qubits, thereby facilitating
an era of unprecedented computational speed and efficiency. Despite these
technological advancements, the authors identified enduring challenges,
including the instability of quantum systems, resource limitations,
communication barriers, and vulnerabilities in security protocols. Quantum
machine learning and its intricacies are explored in (Houssein et al., 2022;
Danba et al., 2022). The authors discussed the state of the field amid the
limitations of quantum hardware and algorithm complexity.

The authors in (Fan and Han, 2022) introduced a framework that integrated
quantum and classical computing methodologies to surmount intricate network
resource optimization challenges. The authors applied quantum annealing to
solve pure integer programming problems, while ancillary challenges are
addressed through classical computing techniques. However, the approach faced
substantial challenges in tackling continuous optimization problems. Further,
in (Coccia et al., 2022), the authors revealed a strategic shift from a
predominant focus on hardware development towards a more balanced emphasis on
software innovation. This transition underscores an evolving landscape in
quantum computing, marked by accelerated advancements in quantum image
processing, machine learning, and sensory technologies. Addressing the
complexities in quantum networking, (Chang and Xue, 2022) focuses on the
intricacies of entanglement swapping and the optimization challenges in
quantum repeater chains due to their non-associative nature. The exploration
of quantum data networks (QDNs) in (Qiao et al., 2022) presented a distributed
computing model that aimed to circumvent the scalability limitations of
contemporary quantum computers. By facilitating quantum state information
exchange among geographically dispersed devices, this model aspires to
aggregate the computational power of multiple quantum-enabled devices into a
singular, more potent quantum computing entity. Nevertheless, the
implementation of QDNs encounters significant challenges, including the no-
cloning theorem, quantum channel loss, the stochastic nature of entanglement
link establishment, rapid decoherence of quantum states, and inefficiencies in
single-photon detection. The analytical research into transport layer
protocols for quantum data networks, discussed in (Zhao and Qiao, 2023),
assessed their potential to enable the reliable and efficient exchange of
quantum data bits (qubits) across a network of quantum computers. The authors
highlighted the critical challenge of managing quantum memory, a scarce
resource in quantum computing, necessitating sophisticated mechanisms for its
dynamic allocation and reallocation. A co-design framework named QuantumFlow,
in (Jiang et al., 2021), introduced an innovative method of representing data
as unitary matrices. This enables the encoding of inputs into a reduced number
of qubits, substantially lowering computational cost complexity compared to
classical computing. However, the practical application and scalability of the
QuantumFlow framework are contingent upon the current limitations of quantum
hardware, including qubit availability and error rates. Lastly, the authors in
(Ferrari et al., 2023) addressed the execution challenges of quantum
algorithms that surpass the qubit capacities of existing quantum processors.
By advocating for the utilization of the quantum Internet to distribute
computational tasks across multiple quantum processing units (QPUs), this
approach aims to overcome scalability challenges. The efficacy of this
framework, however, is intrinsically linked to the development and
availability of a robust quantum Internet infrastructure, highlighting a
pivotal area for future research and development in the field of quantum
computing.

###  2.2. Emerging Quantum Frameworks and Protocols

Shifting to sector-specific applications, (Cooper, 2021) investigated the
potential of quantum computing in transportation modeling. However, it
confronted the challenge of translating classical algorithms into quantum
paradigms due to quantum operations’ unitary and reversible nature. In (Zhang
et al., 2021), authors presented a strategy for optimizing edge server
placements, using binary and quantum encoding, but facing challenges due to
its computational intensity. In (Azad et al., 2023), authors applied quantum
approximate optimization algorithms to the vehicle routing problem,
illustrating the challenges posed by the emerging stage of quantum devices.
Innovative approaches and protocols were highlighted in (Narottama and Shin,
2023) and (Ren et al., 2022). The authors proposed novel frameworks for
wireless communication and IoV, integrating federated learning with quantum
teleportation and combining non-fungible tokens with quantum algorithms.
However, both the schemes faced practical challenges of quantum neural network
complexity and IoV scalability. In (Wang et al., 2022), authors introduced an
asynchronous entanglement distribution protocol for quantum networks. However,
the asynchronous nature requires sophisticated coordination among various
network nodes to avoid entanglement swapping conflicts, making the protocol
more complex than synchronous alternatives. The exploration continues with
(Pramanik et al., 2022) and (Leonidas et al., 2023), discussing quantum-
classical hybrid methods in sensor placement and vehicle routing,
acknowledging technological limitations and complexity. Additionally, in
(Bhavsar et al., 2023), authors applied quantum machine learning to asteroid
classification, facing challenges with quantum processors and data management.
In contrast, (Winker et al., 2023) and (Wang et al., 2021) focused on database
query processing and IoV resource management, highlighting scalability,
reliability, and current quantum computing limitations. The research outlined
in (Taneja and Rani, 2024) explored the application of reconfigurable
intelligent surfaces (RISs) within a quantum computing-based algorithm for RIS
selection, aiming to optimize the transmission of qubits from mobile nodes to
access points. This methodology seeks to enhance network performance and
minimize energy consumption while considering the dynamic mobility of
vehicular networks and the consequent variability in line-of-sight (LoS)
conditions. Despite the improvements in communication reliability afforded by
the use of multiple RISs, the technique needs advanced control algorithms to
manage the RISs effectively in a constantly changing vehicular environment.

Distinct from existing literature, we employ entangled quantum feature mapping
for intricate data encoding, a method not explored in previous studies. This
allows for a more accurate representation of sensor data in quantum states.
Additionally, using a parameterized ansatz circuit for quantum state
transformation and a fidelity-based cost function for model optimization
provides a more precise and adaptable approach than traditional methods.
Additionally, applying the quantum Fourier transform and Toffoli gates for
state manipulation advances existing literature, offering a novel solution in
quantum environmental monitoring.

##  3\. Problem Statement

This research addresses explicitly three interconnected challenges: first, the
conversion of sensor data from vehicles into a quantum-compatible format;
second, the application of a quantum variational classifier for accurate
prediction of gas concentrations; and third, the use of quantum entanglement
to facilitate rapid, real-time transmission of hazard alerts within a
vehicular network.

###  3.1. Conversion of Sensor Data to Quantum Data

To address the first challenge, we focus on the data obtained from the
vehicle’s sensors, referred to as vector $\mathbf{S}$. This vector represents
the gas concentration. This vector is crucial in the overall quantum
computation process as it is the initial data point converted into a quantum
state. Our goal is to express these vector measurements as a quantum state
$\ket{\lambda}$ in Hilbert space. The quantum state initialized to 0 undergoes
the implementation of the rotation, denoted as $\mathbb{R_{\theta}}$. The
magnitude of angular displacement, represented by $\theta$, is determined
based on the sensor data.

(1) $\ket{\lambda}=\mathbb{R}_{\theta}(\mathbf{S}))\ket{\lambda_{0}}$

The problem is determining the ideal alignment between classical input and
quantum states to ensure the accuracy of subsequent quantum computations.

###  3.2. Variational Quantum Classifier for Prediction

In our second challenge, we design a VQC. This classifier operates through a
particular quantum circuit, represented as $U(\mathbf{\Phi})$. The
$\mathbf{\Phi}$ is a set of adjustable parameters fine-tuned during the VQC’s
training phase. The classifier makes these adjustments to make accurate
predictions based on the quantum state $\ket{\lambda}$ derived from the
vehicle’s sensor data. The problem state is to find probability distribution
over potential hazard levels.

(2) $P(\text{hazard level}|\mathbf{S})=\text{Tr}\left[\Pi\cdot
U(\mathbf{\Phi})\ket{\lambda}\bra{\lambda}U^{\dagger}(\mathbf{\Phi})\right]$

Here, $\Pi$ signifies the projector onto the measurement basis for different
hazard levels, with Tr representing the trace operation. The effectiveness of
the VQC in accurately predicting hazard levels will be a key focus of our
validation efforts.

###  3.3. Quantum Entanglement for Real-Time Alert System

Finally, we address the challenge of rapid, real-time transmission of hazard
alerts using quantum entanglement. The entire vehicular network is represented
by a multipartite entangled state $\ket{\Psi}$. The alert system’s
responsiveness is conceptualized via entanglement-based quantum teleportation,
where an alert encoded in a quantum state $\ket{\lambda}$ is transmitted to a
designated vehicle or control center. This process is depicted as:

(3)
$\ket{\lambda}_{\text{target}}=\sigma_{x}^{a}\sigma_{z}^{b}(I\otimes\bra{\beta_{ab}})(\ket{\lambda}\otimes\ket{\Psi})$

In this equation, $\bra{\beta_{ab}}$ denotes the Bell state measurement,
$\sigma_{x}$ and $\sigma_{z}$ are the Pauli matrices, and $a,b$ are the
classical bits derived from the measurement, which guide the teleportation
process.

##  4\. System Overview and Architectural Design

Our proposed architectural design is fundamentally driven by the need to
accurately and efficiently detect hazardous gases. Our approach not only
governs the manipulation of quantum states but also seamlessly integrates
these states into vehicle network communication protocols.

Figure 2. Quantum Process for qIoV Framework

Fig. 2 presents the model for environmental monitoring. This system harnesses
the power of quantum computing to process data collected from various sensors
equipped in vehicles. The collected data undergoes normalization and is then
encoded into quantum states, enabling compatibility with quantum computational
processes. This results in a sophisticated and multifaceted system uniquely
built to meet the complex demands of modern environmental monitoring.

###  4.1. Data Collection and Quantum State Encoding

We equipped each vehicle with multiple sensors (Ref. Fig. 3) i.e., MQ2, MQ3,
MQ5, MQ6, MQ7, MQ8, MQ135 and GPS for air quality evaluation and location
monitoring. These sensors form the foundation of the Quantum Mesh Network
Fabric’s (QMF’s) monitoring capabilities. Once the process of data collection
is finished, the data is subjected to normalization and quantum encoding.
Sensor data is standardized to enable its utilization in quantum computing.
The data is then stored in quantum states having multiple simultaneous quantum
states $\ket{\lambda}$. The importance of quantum state encoding resides in
its ability to transform conventional sensor data into a format that quantum
operations can process. The encoding technique is represented by the function
$E:S\rightarrow\ket{\lambda}$.

Figure 3. Environmental Sensing using Vehicular Sensors

###  4.2. Quantum Graph and Network State Representation

The vehicles are considered as quantum entities and present a dynamic quantum
graph $\mathcal{G}(t)$. The edges represent hypothetical quantum
entanglements, while the nodes represent vectors of states in Hilbert space
$(\mathcal{H})$. The network’s state at any given time $t$ is defined by a
density matrix $\rho(t)$ that includes the quantum correlations between the
individual states of the vehicles. The Lindblad master equation governs the
dynamics of $\rho(t)$ as it evolves.

###  4.3. Communication Model: Quantum Teleportation

The QMF achieves real-time communication through the utilization of quantum
teleportation. During monitoring hazardous gasses, the detected hazards are
represented and encoded using a quantum state called $\ket{\lambda}$. The
state in question becomes entangled with the multipartite state of the
network, which is represented as $\ket{\Psi}$. Bell state measurements are
employed in teleportation approach to produce classical bits that aid in
reconstructing the target $\ket{\lambda}$.

##  5\. Proposed Methodology

This section provides a detailed explanation of our framework. Our research
focuses on three key processes: data conversion, entanglement-based
communication, and error management. Initially, multi-dimensional sensor data
is transformed into quantum-compatible states using an optimized encoding
scheme that precisely calibrates rotation angles to reflect distinct
environmental sensor patterns. Subsequently, we deploy a multipartite
entanglement strategy, tailored for vehicular networks, to facilitate rapid
and reliable environmental alert dissemination, employing quantum
teleportation with vehicle-specific entanglement patterns. To counteract the
quantum noise and computational errors inherent in dynamic vehicular
environments, our approach incorporates real-time adaptive quantum circuit
optimization. This step leverages stabilizer codes for error detection and
correction, dynamically adjusting quantum gate parameters to preserve the
fidelity of quantum communications. Together, these processes establish a
robust quantum-enhanced system for environmental monitoring and hazard alert
dissemination within vehicular networks.

###  5.1. Quantum Data and Encoding and Conversion

During the initial stage of our process, we collect environmental data from a
range of vehicle sensors, specifically MQ2, MQ3, MQ5, MQ6, MQ7, MQ8, and
MQ135. Each sensor produces a unique set of environmental data, represented by
the notation $x_{1},x_{2},\ldots,x_{7}$. Symbolized as
$\mathbf{S}\in\mathbb{R}^{m\times n}$, where $n$ represents the number of
sensors and $m$ represents the number of time-dependent data points per
sensor. Every occurrence of $x_{i}$ adds to a thorough dataset, filling a
specific row or column in $\mathbf{S}$, which is then analyzed further.

####  5.1.1. Normalization Process

Given the extensive range of sensor data, standardization is critical. It
ensures that the total data collected from each sensor $\mathbf{S_{i}}$
corresponds precisely to the final quantum state. The data is transformed
using Min-Max scalar normalization, which maps the values to a range between
$[0,1]$. Eq. (4) is used to calculate the normalized value.

(4)
$s^{\prime}_{ij}=\frac{s_{ij}-\min(\mathbf{S}_{i})}{\max(\mathbf{S}_{i})-\min(\mathbf{S}_{i})}$

This ensures the data is appropriate for quantum processing by establishing a
correlation between each reading and the sensor’s range.

####  5.1.2. Quantum State Encoding via Entangled Feature Mapping

Our approach utilizes an entangled quantum feature Map (EQFM) for quantum
state encoding (Ref. Fig. 4), where entanglement significantly enhances data
representation. The encoding, $U_{\theta}^{E}(\boldsymbol{\Phi})$, applies
normalized data to a circuit combining controlled-Z and Hadamard gates,
producing a highly entangled state suited for complex data patterns. The
circuit is defined as:

(5) $U_{\theta}^{E}(\boldsymbol{\Psi})=\bigotimes_{i=1}^{7}\left(H_{i}\cdot
CZ_{i,t}(\boldsymbol{\Psi}_{i})\right),$

Figure 4. Entangled Quantum Feature Map for Advanced Data Encoding

####  5.1.3. Parameterized Ansatz for Quantum State Evolution

We employ a parameterized ansatz circuit $|\omega(\boldsymbol{\theta})\rangle$
(Ref. Fig. 5) for quantum state transformation. This includes multi-qubit
gates (iSWAPs, CPHASE) and adaptive single-qubit rotations, enhancing the
manipulation of quantum states. The processing of evolved sensor data through
this ansatz is:

Figure 5. Enhanced Ansatz Circuit for Advanced Quantum State Evolution

(6)
$|\omega(\boldsymbol{\theta})\rangle=U_{\text{dynamic}}^{(m)}(\boldsymbol{\theta}_{\text{dynamic}})\cdot
U_{\text{multi-qubit}}^{(m)}(\boldsymbol{\theta}_{\text{multi-qubit}}),$

####  5.1.4. Quantum Data Transformation Technique

Our framework encodes normalized sensor data $\mathbf{S^{\prime}}$ into
quantum states using a mapping function
$h:\mathbf{S^{\prime}}\rightarrow\vec{\theta}$, linking data points to
rotation angles for optimal quantum circuit utilization. For each qubit
$q_{i}$, the rotation gate $R_{\text{advanced}}(\theta_{i})$ is:

(7) $R(\theta_{i})=\begin{pmatrix}\cos(\theta_{i})&-i\sin(\theta_{i})\\\
-i\sin(\theta_{i})&\cos(\theta_{i})\end{pmatrix},$

This advanced gate ensures nuanced data encoding. The mapping function $h$ is
adaptive, optimizing sensor data representation in the quantum domain.

####  5.1.5. Quantum Encoding and State Preparation

Sensor data encoding into a quantum state $U(\mathbf{S^{\prime}})$ involves
both single and multi-qubit rotations. The resulting quantum state
$|\lambda(\boldsymbol{\theta})\rangle$ is crucial for quantum computations.
The encoding is performed as follows:

(8) $U(\mathbf{S^{\prime}})=\bigotimes_{i=1}^{n}R(\theta_{i}(s^{\prime}_{i}))$

The initial state $(\ket{\lambda}_{0})$ evolves into the encoded state
$\ket{\lambda}$, with precision in $\theta$ calculations essential for state
fidelity.

###  5.2. Development of Quantum Variational Classifier for Toxic Gas
Prediction

Our primary research aims to develop a quantum classifier that can reliably
forecast quantities of dangerous gasses. This section thoroughly explains the
internal mechanisms of the VQC, beginning from its creation and continuing to
its practical implementation. The development of the VQC involves a multi-
stage approach. Initially, the data obtained from traditional sensors is
converted into a format that quantum computers can understand. We evaluate the
correctness of our quantum model by employing a technique called fidelity-
based cost function. In the final phase, we utilize an advanced optimization
technique to enhance the performance of our model.

###  5.3. Algorithmic Overview

The construction of the VQC, as depicted in Algorithm 1, entails several
fundamental steps:

Algorithm 1 Advanced Variational Quantum Classifier with Adaptive Optimization

1: Input: Sensor data
$\\{x^{(i)}=(x_{1}^{(i)},x_{2}^{(i)},\ldots,x_{7}^{(i)})\\}_{i=1}^{N}$,
Variational parameters $\boldsymbol{\theta}$, Number of layers $M$

2: Output: Predicted gas types for given sensor data

3: for $i=1$ to $N$ do

4: Encode sensor data into quantum states:
$|\lambda^{(i)}(\boldsymbol{\theta})\rangle\leftarrow
U_{\text{entangle}}^{(M)}(\boldsymbol{\theta}_{\text{entangle}})\cdot
U_{\text{rotation}}^{(M)}(\boldsymbol{\theta}_{\text{rotation}})|0\rangle^{\otimes
n}$

5: end for

6: Initialize cost function: $C(\boldsymbol{\theta})\leftarrow 0$

7: for $i=1$ to $N$ do

8: Execute quantum circuit:
$U(\boldsymbol{\theta})|\lambda^{(i)}(\boldsymbol{\theta})\rangle$

9: Measure probabilities $P(y_{j}|\boldsymbol{\theta})$ for gas classes
$y_{j}$

10: Calculate fidelity
$F(|\lambda_{\text{expected}}^{(i)}\rangle,U(\boldsymbol{\theta})|\lambda^{(i)}(\boldsymbol{\theta})\rangle)$

11: Update cost function: $C(\boldsymbol{\theta})\leftarrow
C(\boldsymbol{\theta})+(1-F(|\lambda_{\text{expected}}^{(i)}\rangle,U(\boldsymbol{\theta})|\lambda^{(i)}(\boldsymbol{\theta})\rangle))^{2}$

12: end for

13: Optimization:

14: Set initial learning rate $\eta$, threshold $\epsilon$, and maximum
iterations $K$

15: Initialize $\boldsymbol{\theta}_{0}$ randomly

16: $k\leftarrow 0$

17: while $k<K$ or $\Delta C(\boldsymbol{\theta}_{k})>\epsilon$ do

18: Calculate gradient $\nabla C(\boldsymbol{\theta}_{k})$

19: Adjust learning rate: $\eta_{k}\leftarrow\eta/(\sqrt{k+1})$

20: Update parameters:
$\boldsymbol{\theta}_{k+1}\leftarrow\boldsymbol{\theta}_{k}-\eta_{k}\nabla
C(\boldsymbol{\theta}_{k})$

21: $k\leftarrow k+1$

22: end while

23: return Predicted gas types based on optimized $\boldsymbol{\theta}$

####  5.3.1. Quantum State Encoding

Given classical sensor data
$x^{(i)}=(x_{1}^{(i)},x_{2}^{(i)},\ldots,x_{7}^{(i)})$ for $N$ instances, we
prepare the quantum state, denoted as
$|\lambda^{(i)}(\boldsymbol{\theta})\rangle$, by using specially designed
quantum circuits. These circuits are adjustable (’parameterized’) and tailored
to represent our sensor data in the quantum realm.

(9) $|\lambda^{(i)}(\boldsymbol{\theta})\rangle\leftarrow
U_{\text{entangle}}^{(M)}(\boldsymbol{\theta}_{\text{entangle}})\cdot
U_{\text{rotation}}^{(M)}(\boldsymbol{\theta}_{\text{rotation}})|0\rangle^{\otimes
n}.$

Here, $U_{\text{entangle}}^{(M)}(\boldsymbol{\theta}_{\text{entangle}})$ and
$U_{\text{rotation}}^{(M)}(\boldsymbol{\theta}_{\text{rotation}})$ represent
entangling and single-qubit rotation gates with $M$ layers, parameterized by
$\boldsymbol{\theta}_{\text{entangle}}$ and
$\boldsymbol{\theta}_{\text{rotation}}$ respectively.

####  5.3.2. Cost Function Formulation

A ’fidelity-based cost function’ in quantum computing measures how closely our
quantum model’s predictions match the expected outcomes. It serves as a
scoring system that tells us how accurate our model is. The fidelity-based
cost function $C(\boldsymbol{\theta})$ is defined to capture the discrepancy
between expected and measured quantum states:

(10)
$C(\boldsymbol{\theta})\leftarrow\sum_{i=1}^{N}\left(1-F(|\lambda_{\text{expected}}^{(i)}\rangle,U(\boldsymbol{\theta})|\lambda^{(i)}(\boldsymbol{\theta})\rangle)^{2}\right).$

Here,
$F(|\lambda_{\text{expected}}^{(i)}\rangle,U(\boldsymbol{\theta})|\lambda^{(i)}(\boldsymbol{\theta})\rangle)$
represents the fidelity between the expected and measured quantum states.

####  5.3.3. Adaptive Optimization Scheme

Our optimization scheme uses a step-by-step (’iterative’) approach to improve
our model gradually. In each step, we adjust the learning rate $\eta_{k}$ (a
measure of how much the model changes in each step) to ensure steady and
effective improvement.

(11)
$\boldsymbol{\theta}_{k+1}\leftarrow\boldsymbol{\theta}_{k}-\eta_{k}\nabla
C(\boldsymbol{\theta}_{k}),$

where $\nabla C(\boldsymbol{\theta}_{k})$ denotes the gradient of the cost
function concerning the variational parameters. The quantum state encoding,
fidelity-based cost function, and adaptive optimization scheme synergistically
create a robust framework for fine-tuning variational parameters based on
fidelity alterations. This complexity is fundamental in capturing subtle
variations within quantum states derived from sensor data, facilitating
precise gas-type predictions leveraging quantum computational advantages.

####  5.3.4. Extensive Quantum State Processing and Measurement for Hazard
Level Assessment

After the training phase, the VQC deploys its fine-tuned circuit on freshly
encoded quantum sensor data, represented as $\ket{\lambda}$. The resulting
state, $\ket{\lambda^{\prime}}$, achieved through the operation
$U(\mathbf{\Phi})\ket{\lambda}$, reflects the VQC’s analysis of various toxic
gas concentrations. To extract actionable insights, the state
$\ket{\lambda^{\prime}}$ undergoes measurement using a series of projective
operators $\\{\Pi_{i}\\}$, each linked to a specific level of hazard. The
likelihood of encountering a particular hazard level, based on the sensor
data, is determined using the formula:

(12) $P(\text{hazard level}_{i}|\mathbf{S})=\text{Tr}\left[\Pi_{i}\cdot
U(\mathbf{\Phi})\ket{\lambda}\bra{\lambda}U^{\dagger}(\mathbf{\Phi})\right].$

This method, which weaves together data encoding processes, quantum circuit
construction, training methodologies, and practical execution, thoroughly
delineates the development of a VQC for predicting toxic gas levels. It
underscores the system’s potential to significantly boost public safety by
providing early warnings of hazardous conditions.

###  5.4. Quantum Entanglement Process for Toxic Gas Detection

In contemporary quantum physics research, the phenomenon of quantum
entanglement stands as a foundation, particularly in the application to QMF.
Our qIoV framework is designed to facilitate communication within vehicular
networks and provide critical monitoring of hazardous gasses. Entanglement, in
this context, refers to a distinct quantum behavior where the states of
particles (i.e., electrons or photons) become interlinked so that the
condition of one particle instantaneously affects its counterpart,
transcending the constraints of spatial distance.

Figure 6. Quantum Circuit Representation of Communication

Our model leverages quantum entanglement and teleportation for efficient,
secure state transitions, essential in real-time environmental data
transmission. It is based on a quantum circuit with a three-qubit quantum
register, optimized through an analysis of vehicular dynamics and illustrated
in Fig. 6.

We use Bell State Preparation for qubit entanglement, assigning each vehicle a
quantum identifier, $i$, and a corresponding server qubit, $j$, in a network
of $n$ vehicles.

(13)
$|\Psi\rangle_{i}\xrightarrow{\text{Bell}}\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)_{i,n+j}$

Qubits initially transition to a Bell state, a more advanced technique than
Hadamard gates, for superior information encoding.

(14)
$|\Psi\rangle_{i}\xrightarrow{\text{Bell}}\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)_{i,j}$

Next, quantum Fourier transform (QFT) manipulates entanglement states between
qubits for data embedding and transfer.

(15)
$|\Psi\rangle_{i},|\Psi\rangle_{i+1}\xrightarrow{\text{QFT}}QFT(|\Psi\rangle_{i}),QFT(|\Psi\rangle_{i+1})$

Enhancements include a Toffoli gate for strengthening quantum correlations and
quantum phase estimation (QPE) for precise phase calculations, ensuring
dynamic network interactions. The protocol concludes with Quantum
Teleportation and a controlled-$Z$ rotation gate for advanced quantum
manipulations.

Algorithm 2 Quantum Communication Protocol

0: vehicle count $(n)$, number of rounds $(R)$, quantum register size per
vehicle $(m)$

0: Quantum communication protocol

1: Initialize a quantum circuit with $3m=3n$ qubits.

2: for $r_{i}$ = $1$ to $R$ do

3: for each vehicle $v_{i}$, $i=1$ to $n$ do

4: Prepare Bell state for qubits $(3i-2,3i-1)$:
$|\Psi\rangle_{3i-2,3i-1}\xrightarrow{\text{Bell}}\frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)$

5: Apply QFT on the third qubit of each vehicle:
$|\Psi\rangle_{3i}\xrightarrow{\text{QFT}}QFT(|\Psi\rangle_{3i})$

6: end for

7: for each pair of vehicles $(v_{i},v_{j})$, $i\neq j$ do

8: Apply Toffoli gate to strengthen quantum correlations:
$\text{Toffoli}(|\Psi\rangle_{3i-1},|\Psi\rangle_{3j-1},|\Psi\rangle_{3i})$

9: Apply QPE for precise phase calculations:
$\text{QPE}(|\Psi\rangle_{3i},|\Psi\rangle_{3j})$

10: end for

11: for each vehicle $v_{i}$ do

12: Perform Quantum Teleportation using a controlled-$Z$ rotation gate:
$\text{Teleport}(|\Psi\rangle_{3i-2},|\Psi\rangle_{3i-1},|\Psi\rangle_{3i})$

13: end for

14: end for

15: Measure all qubits.

16: Transpile the circuit for optimization.

17: return Quantum circuit representing the communication protocol.

##  6\. PERFORMANCE EVALUATION

This section assesses the qIoV framework, focusing on its proficiency in
detecting toxic gases with enhanced precision. We concentrated on accurately
identifying different gas types by utilizing vehicle-mounted sensor data. The
pair plot method was pivotal in analyzing data correlations and enhancing
testing accuracy. Additionally, we probed quantum data distributions under
varying conditions on the IBM OpenQSAM 3 platform, which was equipped with a
127 Qubit system.

###  6.1. Implementation Details of VQC on the IBM OpenQSAM 3 Platform

The experiments were carried out by designing a parameterized quantum circuit
specific to the VQC. Utilizing the quantum circuit composer provided by the
OpenQSAM 3 platform, we arranged Hadamard, Pauli-X, Controlled-Z, and rotation
gates to create an initial entangled state that could capture the complexity
of the sensor data. Sensor data encoding was performed using a customized
quantum feature map, which was developed to transduce the classical gas
concentration readings into quantum states. The optimization was executed
through OpenQSAM 3’s hybrid quantum-classical interface. At each iteration,
the platform computed the cost function’s value by executing the quantum
circuit with the current parameters and measuring the output. The fidelity-
based cost function was then evaluated by calculating the overlap between the
VQC’s output state and the ideal state corresponding to the correct
classification of gas types. Parameter updates were governed by a gradient-
based optimization algorithm. The gradients were estimated using the
parameter-shift rule. To account for the effects of quantum noise and
potential hardware imperfections, we introduced depolarizing noise into our
simulations. This allowed us to assess the VQC’s resilience and adjust our
circuit design and error mitigation strategies accordingly. Post-optimization,
the trained VQC was deployed within the OpenQSAM 3 environment for the
classification of new sensor data. The real-time execution of the quantum
circuit allowed for the immediate classification of gas concentrations, and
the results were integrated into the IoV system to trigger appropriate hazard
alerts. The experimental results, including precision, recall, and F1-Score
metrics, were benchmarked against classical machine learning classifiers to
validate the quantum advantage offered by the VQC. Further, the exploration of
sensor data was based on an advanced pair plot visualization technique. This
approach unraveled complex correlations and distinct attributes of various
gases. The data, categorized into four groups - ’No Gas,’ ’Perfume,’ ’CO2 and
CO Mixture’, and ’Toxic Gases Mixture,’ was intricately displayed through a
matrix of scatter plots and histograms. This visualization provided an
understanding of gas detection. Our theoretical analysis also encompassed
rotation validation, teleportation protocol efficiency, and quantum
entanglement fidelity, offering a holistic view of the system’s functionality.

###  6.2. Pair Plot Analysis

The pair plot analysis is used to reveal correlations, outliers, and clusters
within the data. In our experimetal analysis, correlations between sensor
readings indicate similar sensitivity profiles to certain gas concentrations,
while outliers indicates anomalous detections or sensor malfunctions. Clusters
of data points, as color-coded by gas type, provide visual evidence of the
sensors’ discrimination capabilities between different gas concentrations. The
data matrix S serves as the foundation for a multidimensional analysis of
sensor outputs. The matrix, denoted as D, represents a composite distribution
of sensor readings across multiple gas types, enabling a detailed pairwise
comparison of sensor responses. Each scatter plot within the matrix contrasts
two different sensors’ readings, with the data points color-coded to represent
distinct gas concentrations, thus allowing for the immediate visual
discrimination of distribution patterns. The diagonal of the pair plot matrix
provides histogram representations of the sensor readings, offering insights
into the univariate distribution for each sensor. Fig. 7 visually represents
the procedure and illustrates how the data from the sensors correspond to the
concentrations of the different gasses.

Figure 7. Pair plot showing the relationships between sensors for different
gas types.

We conducted thorough sensitivity and reliability testing to assess the
sensors’ capacity to detect gas concentrations based on our own dataset
111https://github.com/TakMashhido/Gas-Sensors-Measurements-Dataset. The
experimental design consisted of 6,400 data points, categorized into four
groups depending on gas concentration. We allocated 1600 data points evenly
across all groups to provide a comprehensive and unbiased study. The
methodical arrangement of the data was crucial in mitigating biases and
enabling a comprehensive evaluation of the sensor’s performance in various
configurations. In our experiment, positive correlations are evidenced by the
clustering of data points along a line in the scatter plots. For instance, MQ2
and MQ7 display a tight linear cluster suggesting a strong positive
correlation, indicating that these sensors have similar responses to the
varying gas concentrations within the tested range. The degree of spread in
the data points reflects the variability in sensor responses. A wide
dispersion represents a broad detection range or a sensitivity to a variety of
gas types, while a narrow dispersion indicates specificity. Conversely, the
presence of distinct clusters along the scatter plot axes indicates a
differential response from the sensors to specific gases. This is pivotal, as
it demonstrates the array’s capability to differentiate between gases, which
is essential for accurate environmental monitoring. Further, the experiments
reveal the distribution of readings across all tested gas concentrations for a
single sensor, which is critical for understanding the sensor’s sensitivity
range and the likelihood of its activation under different gas concentration
levels. Sensors MQ7 and MQ8 have a broader response distribution, indicating
versatility in detecting a range of gas concentrations, while MQ3 and MQ6 show
a narrower distribution, hinting at more specific gas detection capabilities.
Further, the range of values—minimum to maximum for each sensor also indicate
their operational range and detection thresholds.

  * •

MQ2: Min = 502.0, Max = 824.0

  * •

MQ3: Min = 337.0, Max = 543.0

  * •

MQ5: Min = 291.0, Max = 596.0

  * •

MQ6: Min = 311.0, Max = 524.0

  * •

MQ7: Min = 361.0, Max = 796.0

  * •

MQ8: Min = 220.0, Max = 794.0

  * •

MQ135: Min = 275.0, Max = 589.0

For instance, MQ2’s operational range is from 502 to 824, indicating its
capability to detect higher concentrations, which is suitable for environments
where such conditions are met.

###  6.3. Probability Distribution: Theoretical and Real-Time

In the ideal theoretical probability distribution (Ref. Table 1 ), we observe
a high probability for the ’0000’ state across all three bases (Z, X, Y). This
indicates that the quantum state encoding and preparation processes are highly
effective. The precision in the initial state
$|\lambda(\boldsymbol{\theta})\rangle$ evolving into the encoded state
$|\lambda\rangle$ with accurate $\boldsymbol{\theta}$ calculations is crucial
here. The high fidelity of this state suggests that the quantum entanglement
process and the entangled quantum feature map (EQFM) are functioning
optimally, creating a highly entangled state that accurately represents the
sensor data. The low probability of other outcomes further indicates that the
quantum state preparation and encoding minimize errors and noise in the
system.

Table 1. Theoretical Probability Distribution (Ideal)

Basis | Theoretical Probability Distribution
---|---
Z-Basis (P_Z) | $P_{Z}(^{\prime}0000^{\prime})=\text{High Probability}$
| $P_{Z}(\text{other outcomes})=\text{Low Probability}$
X-Basis (P_X) | $P_{X}(^{\prime}0000^{\prime})=\text{High Probability}$
| $P_{X}(\text{other outcomes})=\text{Low Probability}$
Y-Basis (P_Y) | $P_{Y}(^{\prime}0000^{\prime})=\text{High Probability}$
| $P_{Y}(\text{other outcomes})=\text{Low Probability}$

When introducing errors (Ref. Table 2), the probability of observing the
’0000’ state decreases, while the probabilities of other outcomes increase
across all bases. This change reflects the impact of environmental or systemic
errors on the quantum state. The deviation from the ideal distribution is
attributed to factors like quantum decoherence and operational errors in the
quantum circuit, including gate errors or state preparation and measurement
(SPAM) errors. The presence of errors in quantum state evolution, as handled
by parameterized ansatz circuit $|\omega(\boldsymbol{\theta})\rangle$, also
contributes to these discrepancies.

Table 2. Theoretical Probability Distribution (with error)

Basis | Theoretical Probability Distribution
---|---
Z-Basis Measurement (P_Z_Error) | $P_{Z}\\_Error(^{\prime}0000^{\prime})<\text{High Probability}$
| $P_{Z}\\_Error(\text{other outcomes})>\text{Low Probability}$
X-Basis Measurement (P_X_Error) | $P_{X}\\_Error(^{\prime}0000^{\prime})<\text{High Probability}$
| $P_{X}\\_Error(\text{other outcomes})>\text{Low Probability}$
Y-Basis Measurement (P_Y_Error) | $P_{Y}\\_Error(^{\prime}0000^{\prime})<\text{High Probability}$
| $P_{Y}\\_Error(\text{other outcomes})>\text{Low Probability}$

The simulation results for real-time distribution in Table 3 show a
distribution of probabilities across various states in the Z, X, and Y bases.
Unlike the ideal and error-included theoretical distributions, these results
demonstrate a more uniform distribution, indicating a dynamic interaction of
the quantum system with real-time environmental data. This reflects the
adaptive optimization scheme employed in the methodology, where the quantum
state is iteratively refined to represent the sensor data better. The
variations in probabilities across different states suggest that the quantum
system effectively captures the nuances of the environmental data. Higher
probabilities for specific states (like ’1011’, ’0010’, ’1101’, etc.) in
different bases indicate the successful encoding of sensor data into quantum
states and the effective transformation of these states via the parameterized
ansatz.

Table 3. Simulation Results in the Context of Quantum-Based Real-Time
Vehicular Communication

Basis | Z-Basis | X-Basis | Y-Basis | Basis | Z-Basis | X-Basis | Y-Basis
---|---|---|---|---|---|---|---
’1011’ | 63 | 67 | 62 | ’1000’ | 71 | 75 | 53
’0010’ | 59 | 63 | 66 | ’1110’ | 79 | 63 | 66
’0011’ | 57 | 58 | 59 | ’0101’ | 51 | 62 | 64
’1101’ | 64 | 63 | 70 | ’1010’ | 75 | 62 | 51
’0001’ | 66 | 59 | 60 | ’1100’ | 62 | 66 | 70
’0000’ | 56 | 61 | 56 | ’1001’ | 69 | 64 | 67
’0111’ | 60 | 72 | 74 | ’1111’ | 71 | 61 | 78
’0110’ | 58 | 67 | 53 | ’0100’ | 63 | 61 | 75

The introduction of depolarizing error in real-time communication further
shifts in probabilities. Depolarizing error is a type of quantum noise that
leads to the loss of information about the state, causing it to trend toward a
maximally mixed state. The observed probabilities in Table 4 reflect the
resilience of the quantum system against such noise. Although different from
the ideal scenario, the system’s ability to maintain a coherent distribution
of probabilities indicates the robustness of the quantum encoding, state
preparation, and adaptive optimization process. These results also underscore
the impact of real-world factors and noise on quantum systems and the need for
sophisticated error correction and noise resilience techniques in quantum
computing.

Table 4. Results with Depolarizing Error in Real-Time Vehicular Communication

State | Probabilities | State | Probabilities
---|---|---|---
’1010’ | 71 | ’0100’ | 51
’1111’ | 76 | ’0001’ | 74
’0110’ | 78 | ’1101’ | 67
’1100’ | 59 | ’1110’ | 59
’1011’ | 64 | ’1001’ | 60
’0010’ | 61 | ’0000’ | 55
’0101’ | 73 | ’0011’ | 66
’0111’ | 57 | ’1000’ | 53

###  6.4. VQC Model Prediction Result

####  6.4.1. Objective Function

Fig. 8 illustrates a declining trend in objective function value against
iteration number. It indicates the effectiveness of adaptive optimization
scheme implemented in our research. The results reflects the iterative
refinement of the variational parameters $\theta$ through the application of a
gradient descent algorithm paired with an adaptive learning rate.

Figure 8. Objective Function Values Against Iteration

The initial fluctuations observed in the graph represent the exploratory phase
of the optimization process, where the algorithm searches the parameter space
for a local minimum of the cost function. These fluctuations are an
anticipated aspect of the optimization, attributable to the adaptive
adjustment of the learning rate, which is modulated in response to the
gradient history. This exploratory phase is critical for escaping any local
minima that are not optimal. As the iterations proceed, the objective function
value based on fidelity-based cost function, steadily decreases. This
signifies that the optimization technique is effectively honing in on the
optimal set of parameters that minimize the cost function. The fidelity-based
cost function quantifies the closeness of the predicted quantum state to the
true state, with lower values indicating higher fidelity. Therefore, the
observed minimization of this function is indicative of the quantum
classifier’s improved accuracy in predicting gas concentrations. The adaptive
learning rate plays a pivotal role in this optimization process. By adjusting
the learning rate based on the gradient’s magnitude, the algorithm ensures
that the parameter updates are neither too large—potentially overshooting the
minimum—nor too small, which could result in a prolonged convergence time.
This balance accelerates the convergence of the optimization algorithm while
maintaining the precision of the parameter updates.

####  6.4.2. Confusion Matrix

The confusion matrix in Fig. 9 shows a strong diagonal, indicating highly
accurate positive values for each class. Our quantum state encoding via
entangled feature mapping influences this result. The entangled feature map
increases the dimensionality of the feature space, which leads to better
separation of the classes in the quantum state space. Moreover, the
parameterized ansatz for quantum state evolution allows for a richer
exploration of the quantum state space, potentially providing a more nuanced
separation between classes that appear similar in the classical feature space.

Figure 9. Confusion Matrix

####  6.4.3. Classification Metrics

We have categorized the classification metrics results into three classes
based on precision and recall as shown in Table 5:

Class 0: Exhibits high precision and recall due to the effective normalization
and quantum state encoding methods that preserve the fidelity of the original
sensor data, allowing for distinct features of this class to be well-
represented in the quantum feature space. This indicates that the quantum
circuit has been well-optimized for these features.

Class 1: The balanced precision and recall suggest that while the feature
space for this class is well-mapped, there is some overlap with other classes.
The EQFM and the ansatz need further refinement to distinguish the features of
this class better.

Class 2: The high precision but slightly lower recall implies that when the
classifier predicts an instance to be in class ’2’, it is likely correct, but
it misses some actual instances of class ’2’. This is due to a slight
underrepresentation of class ’2’ features in the entangled quantum feature
map. In the quantum variational classifier, the fidelity-based cost function
is minimized, indicating that the quantum states prepared by the circuit are
close to the expected states corresponding to each class. The adaptive
optimization technique enhances the classifier’s performance by efficiently
finding the optimal parameters resulting in the respective classes’ highest
fidelity states.

Table 5. Classification Performance Metrics

Class | Precision | Recall | F1-Score | Support
---|---|---|---|---
0 | 0.93 | 1.00 | 0.96 | 13
1 | 0.83 | 0.83 | 0.83 | 6
2 | 0.90 | 0.82 | 0.86 | 11

###  6.5. Detection Time Analysis

The gas detection time analysis in Fig. 10 reveals significant insights into
the performance of various detection models. Among the evaluated models, the
qIoV Framework consistently outperforms traditional methods such as Support
Vector Machine (SVM), Random Forest, and Logistic Regression in terms of
detection speed. The dataset, comprising 100 data points, demonstrates that
the qIoV Framework achieves detection times significantly lower than its
counterparts. The technical superiority of the qIoV Framework is attributed to
its optimized algorithmic structure, which leverages advanced data processing
and analysis techniques. Our quantum circuits leverage qubits that can exist
in multiple states simultaneously (quantum superposition), and they utilize
quantum entanglement. These principles allow quantum algorithms to process
complex datasets more efficiently than classical algorithms, leading to
significant improvements in the speed of gas detection and classification.
This efficiency is due to the quantum circuits’ ability to perform multiple
calculations at once and to quickly navigate the solution space of possible
gas detection signatures, identifying hazards more rapidly than traditional
computing methods. Unlike the SVM and Random Forest models, which rely on
complex decision boundaries and ensemble learning respectively, the qIoV
Framework utilizes a more efficient approach to achieve quicker response
times. This efficiency is crucial for real-time gas detection applications
where timely response can mitigate risks and prevent hazardous incidents.

$0$$20$$40$$60$$80$$100$$0.1$$0.2$$0.3$$0.4$Number of Data PointsDetection
Time (Sec)SVMRandom ForestLogistic RegressionProposed Figure 10. Detection
Time Analysis Over Number of Data Points

###  6.6. Theoretical Analysis

Our framework result discussion also includes a comprehensive theoretical and
statistical analysis to validate and assess the efficacy of the proposed
framework. The analysis scrutinized various components to ensure the
robustness and practicality of the QMF in real-world scenarios, particularly
for environmental monitoring and toxic gas detection.

####  6.6.1. Quantum State Fidelity

This theorem establishes the fidelity of the quantum state encoding process.
It asserts that the encoded quantum state $\ket{\lambda}$, derived from
normalized sensor data, accurately represents the original environmental data.
Given a quantum state $\ket{\lambda}$ encoding normalized sensor data and a
density matrix $\rho_{\text{original}}$ representing the original
environmental data, the fidelity $F$ between $\ket{\lambda}$ and
$\rho_{\text{original}}$ is close to 1, indicating an accurate quantum
representation of the original data.

###### Theorem 6.1.

The fidelity $F$ between a pure state $\ket{\lambda}$ and a mixed state
$\rho_{\text{original}}$ is defined as:

$F(\ket{\lambda},\rho_{\text{original}})=\left(\bra{\lambda}\rho_{\text{original}}\ket{\lambda}\right)^{1/2}$

For $F(\ket{\lambda},\rho_{\text{original}})$ to be close to 1, it must be
shown that:

$\bra{\lambda}\rho_{\text{original}}\ket{\lambda}\approx 1$

###### Proof.

Let us assume that the quantum state $\ket{\lambda}$ is optimally constructed
from the normalized sensor data $\mathbf{S^{\prime}}$, and the density matrix
$\rho_{\text{original}}$ accurately reflects the original sensor data
$\mathbf{S}$.

The normalized data $\mathbf{S^{\prime}}$ is a transformation of the original
data $\mathbf{S}$, scaled to a uniform range. The quantum state
$\ket{\lambda}$ is then formulated as a superposition of basis states with
amplitudes derived from $\mathbf{S^{\prime}}$, ensuring that the quantum state
reflects the characteristics of the original data.

$s^{\prime}_{ij}=\frac{s_{ij}-\min(\mathbf{S}_{i})}{\max(\mathbf{S}_{i})-\min(\mathbf{S}_{i})}$

The quantum state $\ket{\lambda}$ is a superposition of basis states:

$\ket{\lambda}=\sum_{k=0}^{N-1}\alpha_{k}\ket{k},$

where $\alpha_{k}$ are related to $\mathbf{S^{\prime}}$.

To calculate fidelity, we consider the overlap between the encoded quantum
state $\ket{\lambda}$ and the density matrix $\rho_{\text{original}}$. A high
overlap implies that the quantum state retains the essential information from
the original data.

$F(\ket{\lambda},\rho_{\text{original}})=\left(\sum_{k=0}^{N-1}\alpha_{k}\bra{k}\rho_{\text{original}}\sum_{l=0}^{N-1}\alpha_{l}\ket{l}\right)^{1/2}$

Assuming high overlap,
$\bra{k}\rho_{\text{original}}\ket{l}\approx\delta_{kl}$.

Since $\ket{\lambda}$ is normalized, the sum of the squares of its amplitudes
equals 1. Therefore, the fidelity calculation simplifies to approximately 1,
validating that $\ket{\lambda}$ is a faithful quantum representation of the
original environmental data.

$F(\ket{\lambda},\rho_{\text{original}})\approx\left(\sum_{k=0}^{N-1}\alpha_{k}^{2}\right)^{1/2}=1$

as $\ket{\lambda}$ is normalized.

The fidelity between $\ket{\lambda}$ and $\rho_{\text{original}}$ being
approximately 1 demonstrates the accuracy of the quantum state encoding
process. This validates the effectiveness of the quantum encoding in
preserving the integrity of the original sensor data within the QMF framework.

∎

####  6.6.2. Normalization Effectiveness

This theorem validates the effectiveness of Min-Max normalization in
preserving the statistical properties of sensor data. It demonstrates that the
normalized data $\mathbf{S^{\prime}}$ maintains the mean and variance of the
original data $\mathbf{S}$ within specific error margins, affirming the
reliability of this normalization method for accurate quantum computations
within the QMF framework.

###### Theorem 6.2.

Consider a matrix $\mathbf{S}\in\mathbb{R}^{m\times n}$ representing original
sensor data, with $m$ sensors and $n$ data points per sensor. The Min-Max
normalized data is denoted as $\mathbf{S^{\prime}}$, with each element defined
as:

$s^{\prime}_{ij}=\frac{s_{ij}-\min(\mathbf{S}_{i})}{\max(\mathbf{S}_{i})-\min(\mathbf{S}_{i})}$

for $1\leq i\leq m$ and $1\leq j\leq n$.

The theorem asserts that the mean and variance of $\mathbf{S^{\prime}}$
approximate those of the original data $\mathbf{S}$ within certain error
margins $\epsilon_{\mu}$ and $\epsilon_{\sigma}$, respectively.

###### Proof.

We begin by analyzing the mean of the data. The mean of each sensor’s data in
$\mathbf{S}$ is given by $\mu_{i}=\frac{1}{n}\sum_{j=1}^{n}s_{ij}$. Post-
normalization, the mean for each sensor in $\mathbf{S^{\prime}}$ is
$\mu^{\prime}_{i}=\frac{1}{n}\sum_{j=1}^{n}s^{\prime}_{ij}$. As normalization
applies a linear transformation to each data point, consisting of a scaling
and a shift based on the range of $\mathbf{S}_{i}$, we can assert that the
transformation preserves the relative mean of the data. Hence, the difference
between $\mu_{i}$ and $\mu^{\prime}_{i}$ is bounded, satisfying
$|\mu_{i}-\mu^{\prime}_{i}|\leq\epsilon_{\mu}$.

Next, we consider the variance. The variance of the $i$-th sensor in
$\mathbf{S}$ is
$\sigma_{i}^{2}=\frac{1}{n}\sum_{j=1}^{n}(s_{ij}-\mu_{i})^{2}$, and after
normalization, it becomes
$(\sigma^{\prime}_{i})^{2}=\frac{1}{n}\sum_{j=1}^{n}(s^{\prime}_{ij}-\mu^{\prime}_{i})^{2}$.
Although normalization changes the scale of the data, it does so uniformly
across all data points. This uniform scaling alters the absolute variance but
preserves the variance’s structure. Consequently, the change in variance due
to normalization is limited, ensuring that
$|\sigma_{i}^{2}-(\sigma^{\prime}_{i})^{2}|\leq\epsilon_{\sigma}$.

Through this proof, we affirm that Min-Max normalization effectively preserves
the critical statistical properties of the sensor data. This preservation is
crucial as it ensures that the quantum state, post-encoding, retains the
intrinsic patterns and characteristics of the original environmental data,
thereby facilitating accurate and meaningful quantum computations within the
QMF framework. ∎

####  6.6.3. Quantum Rotation Accuracy

This theorem assesses the accuracy of quantum rotations in aligning qubits
with their desired states in a QMF. It demonstrates that each rotation
operation $R_{y}(\theta_{i})$ precisely adjusts individual qubits, and the
overall system fidelity is maximized, ensuring minimal cumulative error across
the qubit system. This accuracy is pivotal for the reliability and
effectiveness of quantum computations in the network.

###### Theorem 6.3.

Given a vector of rotation angles
$\vec{\theta}=(\theta_{1},\theta_{2},\ldots,\theta_{n})$, computed from
normalized sensor data, we analyze the precision of the quantum rotation
technique. Each qubit $q_{i}$ is subject to a rotation operation
$R_{y}(\theta_{i})$, defined as:

$R_{y}(\theta_{i})=\begin{pmatrix}\cos(\theta_{i})&-i\sin(\theta_{i})\\\
-i\sin(\theta_{i})&\cos(\theta_{i})\end{pmatrix}.$

This theorem asserts that each $R_{y}(\theta_{i})$ accurately rotates the
corresponding qubit to align with the desired quantum state, and the
cumulative error across all qubits is minimized.

###### Proof.

For each qubit initially in state $\ket{\lambda_{0}}$, the rotation operation
$R_{y}(\theta_{i})$ induces a transformation to a new state
$\ket{\lambda_{i}}$. The accuracy of this transformation is quantified by
comparing $\ket{\lambda_{i}}$ with the target state
$\ket{\lambda_{\text{target},i}}$, which is a representation of the
corresponding sensor data on the Bloch sphere.

1\. Individual Qubit Analysis: The fidelity $F_{i}$ between
$\ket{\lambda_{i}}$ and $\ket{\lambda_{\text{target},i}}$ is given by
$F_{i}=|\langle\lambda_{\text{target},i}|\lambda_{i}\rangle|^{2}$. The goal is
to show that for each $i$, $F_{i}$ is maximized, ideally approaching 1. This
involves proving that the chosen rotation angle $\theta_{i}$ aligns the
qubit’s state as close to its target state on the Bloch sphere. The
calculation of $F_{i}$ is a complex task involving integrating the qubit’s
wave function over the entire state space, factoring in the effects of the
rotation.

2\. System-Wide Fidelity: The overall system comprises $n$ qubits, each
transformed by $R_{y}(\theta_{i})$. The quantum state of the entire system
post-rotation is $\ket{\lambda}=\bigotimes_{i=1}^{n}\ket{\lambda_{i}}$. The
cumulative error in the system is assessed by evaluating the total fidelity
$F_{\text{total}}=|\langle\lambda_{\text{target}}|\lambda\rangle|^{2}$, where
$\ket{\lambda_{\text{target}}}$ is the tensor product of individual target
states. Maximizing $F_{\text{total}}$ confirms the minimal cumulative error
across the system, which is a complex calculation involving the tensor product
of individual state fidelities and accounting for potential error correlations
between qubits.

Theorem 3 proves the high degree of accuracy in the quantum rotation
operations within the QMF, aligning each qubit’s state closely with its
intended target state and ensuring minimal cumulative error across the quantum
system. The precision of these operations is crucial for the reliability and
effectiveness of quantum computations based on these quantum states, impacting
the overall performance and capability of the QMF. ∎

####  6.6.4. Quantum Entanglement Integrity

This theorem establishes that the multipartite entangled state $\ket{\Psi}$
within the quantum network maintains strong and stable quantum correlations,
which are crucial for quantum communication. This is validated using specific
entanglement measures, namely concurrence $C$ and entanglement entropy $S$,
which are shown to exceed critical values, thereby confirming the integrity
and robustness of the entanglement in the network.

###### Theorem 6.4.

Theorem 4 posits that the multipartite entangled state $\ket{\Psi}$ in the
quantum network maintains robust quantum correlations, essential for quantum
communication. The integrity of entanglement is assessed through entanglement
measures, specifically concurrence $C$ and entanglement entropy $S$. We aim to
prove that for $\ket{\Psi}$, these measures exceed specific critical values,
indicative of strong and stable entanglement.

###### Proof.

1\. Entanglement Measures: \- Concurrence $C$ for a pair of qubits in state
$\rho$ is defined as
$C(\rho)=\max\\{0,\varphi_{1}-\varphi_{2}-\varphi_{3}-\varphi_{4}\\}$, where
$\varphi_{i}$ are the square roots of the eigenvalues of $\rho\tilde{\rho}$ in
decreasing order, and
$\tilde{\rho}=(\sigma_{y}\otimes\sigma_{y})\rho^{*}(\sigma_{y}\otimes\sigma_{y})$
with $\rho^{*}$ being the complex conjugate of $\rho$. \- Entanglement entropy
$E$ for a subsystem $A$ of $\ket{\Psi}$ is given by
$S(\rho_{A})=-\text{Tr}(\rho_{A}\log_{2}\rho_{A})$, where $\rho_{A}$ is the
reduced density matrix of subsystem $A$ obtained by tracing out the rest of
the system.

2\. Application to $\ket{\Psi}$: \- For $\ket{\Psi}$, a multipartite entangled
state, we compute concurrence and entropy for various partitions and pairs of
qubits within the state. \- Calculating $C$ and $E$ involves deriving the
reduced density matrices for different subsystems or pairs of qubits in
$\ket{\Psi}$ and applying the formulas.

3\. Threshold Determination: \- Establish threshold values
$C_{\text{threshold}}$ and $E_{\text{threshold}}$ based on theoretical and
empirical standards. \- Demonstrate that $C$ and $E$ for various partitions
and pairs in $\ket{\Psi}$ consistently exceed $C_{\text{threshold}}$ and
$S_{\text{threshold}}$ respectively. This is a critical step involving
detailed calculations and comparisons with the thresholds.

Theorem 4 validates the robustness of quantum entanglement in $\ket{\Psi}$,
the multipartite entangled state of the network. The consistently high values
of concurrence and entanglement entropy, surpassing the established
thresholds, confirm the integrity and stability of entanglement in the system.
This robust entanglement is crucial for the network’s quantum communication
and teleportation capabilities, ensuring high-fidelity and efficient quantum
information processing. ∎

####  6.6.5. Teleportation Protocol Efficacy

This theorem validates the efficacy of a quantum teleportation protocol in
accurately transmitting an alert state using multipartite entanglement. It
demonstrates that the fidelity of the teleported state with the original state
is exceptionally high, approaching a fidelity measure of 1. This signifies
minimal information loss during teleportation, ensuring reliable and efficient
quantum communication within the network.

###### Theorem 6.5.

Given the quantum teleportation protocol involving an initial alert state
$\ket{\lambda}$ and a multipartite entangled state $\ket{\Psi}$, this theorem
aims to prove the high fidelity of the post-teleportation state
$\ket{\lambda}_{\text{target}}$ concerning the original state $\ket{\lambda}$.
The theorem posits that the fidelity measure, defined as
$F=|\langle\lambda|\lambda_{\text{target}}\rangle|^{2}$, approaches 1,
indicating minimal information loss during teleportation.

###### Proof.

Consider the multipartite entangled state $\ket{\Psi}$ and the alert state
$\ket{\lambda}$. The protocol starts with a Bell state measurement on the part
of $\ket{\Psi}$ entangled with $\ket{\lambda}$. This measurement projects the
system onto a Bell state and yields two classical bits, denoted as $a$ and
$b$, which guide the reconstruction of $\ket{\lambda}$ at the target.

1\. Bell State Measurement: \- The measurement projects the combined system
onto one of the Bell states. The representation of this projection, given the
measurement results $a$ and $b$, is a projection operator $P_{ab}$.

2\. State Reconstruction: \- Based on $a$ and $b$, Pauli correction operators
$\sigma_{x}^{a}$ and $\sigma_{z}^{b}$ are applied to a segment of $\ket{\Psi}$
to obtain $\ket{\lambda}_{\text{target}}$. This step is crucial as it
reconstructs the alert state at the target.

3\. Fidelity Analysis: \- The fidelity $F$ is calculated as
$F=|\langle\lambda|\lambda_{\text{target}}\rangle|^{2}$. To prove that $F$ is
close to 1, we express $\ket{\lambda}_{\text{target}}$ in terms of the
original state $\ket{\lambda}$, the Bell state measurement outcome, and the
applied Pauli corrections.

4\. Error Consideration: Any deviations from perfect fidelity are attributed
to errors in the protocol. These errors arise from imperfect entanglement or
inaccuracies in the Bell state measurement and Pauli corrections. We then
analyze these potential sources of error to establish that they do not
significantly impact the overall fidelity, either because they are inherently
negligible or correctable with quantum error correction techniques.

Theorem 5 demonstrates that the quantum teleportation protocol in the network
transmits the encoded alert state with high fidelity. By analyzing each step
of the protocol and confirming that the fidelity of the reconstructed state
remains close to 1, the theorem validates the efficacy and reliability of
quantum teleportation for accurate and efficient quantum communication within
the network. ∎

##  7\. Conclusion

Our research has substantiated the application of a variational quantum
classifier (VQC) for environmental monitoring, with a focus on the detection
of toxic gases. The foundation of our contribution is the successful fusion of
quantum computing methodologies with vehicular communication networks, which
underscores the potential of quantum technology in complex, real-world
systems. Our framework hinged on the intricacies of quantum state manipulation
and the optimization of quantum circuit parameters, ensuring that the VQC
operated with high precision across multi-dimensional parameter spaces.
Further, the depolarizing noise models to simulate errors within the quantum
circuits improved the robustness of our framework. We tested the resilience of
the VQC on IBMOpenQSAM 3 platform. The empirical results align closely with
theoretical predictions, not only reaffirm the model’s resilience but also
attest to the fidelity retention of the quantum states amidst environmental
noise and disturbances. Furthermore, the experimental outcomes corroborate the
feasibility of quantum-enhanced communication systems in dynamic settings,
such as vehicular networks for environmental monitoring. Our findings validate
the practical implementation of quantum computing technologies beyond
theoretical models, showcasing their applicability and adaptability to the
stringent demands of real-world operational conditions.

Looking forward, the scope for future work involves the investigation into
fault-tolerant quantum computing designs that could further mitigate error
rates in quantum circuits, thus enhancing the VQC’s resilience and
reliability. We also plan to deploy proposed framework and solutions on
real/industrial quantum computing environments such as IBM, Microsoft, and AWS
quantum clouds such QFaaS (Nguyen et al., 2024).

## References

  * (1)
  * Arya et al. (2006) Anand S Arya, Anup Karanth, and Ankush Agarwal. 2006.  Hazards Disasters and Your Community: A Primer for Parliamentarians.  file-lKSyoxYWuX2tK8gHLQOdRVqR Version 1.0, GoI-UNDP Disaster Risk Management Programme.
  * Auchincloss and De Roos (2019) Amy Auchincloss and Anneclaire J De Roos. 2019.  RE: Statement on the Health Effects of Refineries and Implications for the S Philadelphia Refinery.  _The City of Philadelphia Refinery Advisory Group_ NA (2019), 1–4.
  * Azad et al. (2023) Utkarsh Azad, Bikash K. Behera, Emad A. Ahmed, Prasanta K. Panigrahi, and Ahmed Farouk. 2023.  Solving Vehicle Routing Problem Using Quantum Approximate Optimization Algorithm.  _IEEE Transactions on Intelligent Transportation Systems_ 24, 7 (2023), 7564–7573.
  * Balis et al. (2013) Bartosz Balis, Tomasz Bartynski, Marian Bubak, Grzegorz Dyk, Tomasz Gubala, and Marek Kasztelnik. 2013.  A development and execution environment for early warning systems for natural disasters. In _2013 13th IEEE/ACM International Symposium on Cluster, Cloud, and Grid Computing_. IEEE, Delft, Netherlands, 575–582.
  * Bhavsar et al. (2023) Rushir Bhavsar, Nilesh Kumar Jadav, Umesh Bodkhe, Rajesh Gupta, Sudeep Tanwar, Gulshan Sharma, Pitshou N. Bokoro, and Ravi Sharma. 2023.  Classification of Potentially Hazardous Asteroids Using Supervised Quantum Machine Learning.  _IEEE Access_ 11, 1 (2023), 75829–75848.
  * Chang and Xue (2022) Alena Chang and Guoliang Xue. 2022.  Order matters: On the impact of swapping order on an entanglement path in a quantum network. In _IEEE INFOCOM 2022-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)_. IEEE, New York, NY, USA, 1–6.
  * Coccia et al. (2022) Mario Coccia, Saeed Roshani, and Melika Mosleh. 2022.  Evolution of quantum computing: Theoretical and innovation management implications for emerging quantum industry.  _IEEE Transactions on Engineering Management_ 71, 1 (2022), 2270–2280.
  * Cooper (2021) Crispin HV Cooper. 2021.  Exploring potential applications of quantum computing in transportation modelling.  _IEEE Transactions on Intelligent Transportation Systems_ 23, 9 (2021), 14712–14720.
  * Danba et al. (2022) Sedeng Danba, Jingjing Bao, Guorong Han, Siri Guleng, and Celimuge Wu. 2022.  Toward collaborative intelligence in IoV systems: recent advances and open issues.  _Sensors_ 22, 18 (2022), 6995.
  * Dong et al. (2019) Linxi Dong, Zhiyuan Qiao, Haonan Wang, Weihuang Yang, Wensheng Zhao, Kuiwen Xu, Gaofeng Wang, Libo Zhao, and Haixia Yan. 2019.  The gas leak detection based on a wireless monitoring system.  _IEEE Transactions on Industrial Informatics_ 15, 12 (2019), 6240–6251.
  * Fan and Han (2022) Lei Fan and Zhu Han. 2022.  Hybrid quantum-classical computing for future network optimization.  _IEEE Network_ 36, 5 (2022), 72–76.
  * Ferrari et al. (2023) Davide Ferrari, Stefano Carretta, and Michele Amoretti. 2023.  A modular quantum compilation framework for distributed quantum computing.  _IEEE Transactions on Quantum Engineering_ 4, 1 (2023), 1–13.
  * Houssein et al. (2022) Essam H Houssein, Zainab Abohashima, Mohamed Elhoseny, and Waleed M Mohamed. 2022.  Machine learning in the quantum realm: The state-of-the-art, challenges, and future vision.  _Expert Systems with Applications_ 194 (2022), 116512.
  * Jiang et al. (2021) Weiwen Jiang, Jinjun Xiong, and Yiyu Shi. 2021.  A co-design framework of neural networks and quantum circuits towards quantum advantage.  _Nature communications_ 12, 1 (2021), 579.
  * Leonidas et al. (2023) Ioannis D. Leonidas, Alexander Dukakis, Benjamin Tan, and Dimitris G. Angelakis. 2023.  Qubit efficient quantum algorithms for the vehicle routing problem on NISQ processors.  arXiv:2306.08507 [quant-ph]
  * Liu et al. (2021) Li Liu, Guangjie Han, Zhengwei Xu, Lei Shu, Miguel Martinez-Garcia, and Bao Peng. 2021.  Predictive boundary tracking based on motion behavior learning for continuous objects in industrial wireless sensor networks.  _IEEE Transactions on Mobile Computing_ 21, 9 (2021), 3239–3249.
  * Mishra et al. (2009) Pradyumna K Mishra, Ravindra M Samarth, Neelam Pathak, Subodh K Jain, Smita Banerjee, and Kewal K Maudar. 2009.  Bhopal gas tragedy: review of clinical and experimental findings after 25 years.  _International journal of occupational medicine and environmental health_ 22, 3 (2009), 193.
  * Narottama and Shin (2023) Bhaskara Narottama and Soo Young Shin. 2023.  Federated Quantum Neural Network With Quantum Teleportation for Resource Optimization in Future Wireless Communication.  _IEEE Transactions on Vehicular Technology_ 72, 11 (2023), 14717–14733.
  * Nguyen et al. (2024) Hoa T Nguyen, Muhammad Usman, and Rajkumar Buyya. 2024.  Qfaas: A serverless function-as-a-service framework for quantum computing.  _Future Generation Computer Systems_ 154 (2024), 281–300.
  * Palazzi et al. (2015) E Palazzi, F Currò, and B Fabiano. 2015.  A critical approach to safety equipment and emergency time evaluation based on actual information from the Bhopal gas tragedy.  _Process safety and environmental protection_ 97 (2015), 37–48.
  * Pipeline and Hazardous Materials Safety Administration , Department of Transportation (DOT)(2023) (PHMSA) Pipeline and Hazardous Materials Safety Administration (PHMSA), Department of Transportation (DOT). 2023.  Pipeline Safety: Gas Pipeline Leak Detection and Repair.  _Federal Register_ 88, 96 (2023), 31890.  file-Fx7XnWMs7bX3btIOm1qiLN3M Docket No. PHMSA–2021–0039, RIN 2137–AF51.
  * Pramanik et al. (2022) Sayantan Pramanik, Vishnu Vaidya, Gajendra Malviya, Sudhir Sinha, Shripad Salsingikar, M Girish Chandra, C V Sridhar, Godfrey Mathais, and Vidyut Navelkar. 2022.  Optimization of Sensor-Placement on Vehicles using Quantum-Classical Hybrid Methods. In _2022 IEEE International Conference on Quantum Computing and Engineering (QCE)_. IEEE, Broomfield, CO, USA, 820–823.
  * Qiao et al. (2022) Chunming Qiao, Yangming Zhao, Gongming Zhao, and Hongli Xu. 2022.  Quantum data networking for distributed quantum computing: Opportunities and challenges. In _IEEE INFOCOM 2022-IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS)_. IEEE, New York, NY, USA, 1–6.
  * Ramezani et al. (2020) Somayeh Bakhtiari Ramezani, Alexander Sommers, Harish Kumar Manchukonda, Shahram Rahimi, and Amin Amirlatifi. 2020.  Machine learning algorithms in quantum computing: A survey. In _2020 International joint conference on neural networks (IJCNN)_. IEEE, Glasgow, UK, 1–8.
  * Ren et al. (2022) Yuzheng Ren, Renchao Xie, F Richard Yu, Tao Huang, and Yunjie Liu. 2022.  NFT-based intelligence networking for connected and autonomous vehicles: A quantum reinforcement learning approach.  _IEEE Network_ 36, 6 (2022), 116–124.
  * Shah (2023) Preyash Shah. 2023.  Mapped: Oil and Gas Spills in the U.S. Since 2010.  https://www.visualcapitalist.com/mapped-oil-and-gas-spills-in-the-u-s-since-2010/.
  * Taneja and Rani (2024) Ashu Taneja and Shalli Rani. 2024.  Quantum-Enabled Intelligent Resource Control for Reliable Communication Support in Internet-of-Vehicles.  _IEEE Transactions on Consumer Electronics_ 70, 5 (2024), 1–8.
  * Volcovici (2023) Valerie Volcovici. 2023.  U.S. pipeline regulator takes aim at methane leaks.  https://www.reuters.com/business/sustainable-business/us-pipeline-regulator-takes-aim-methane-leaks-2023-05-05/.
  * Wang et al. (2021) Dan Wang, Bin Song, Peng Lin, F Richard Yu, Xiaojiang Du, and Mohsen Guizani. 2021.  Resource management for edge intelligence (EI)-assisted IoV using quantum-inspired reinforcement learning.  _IEEE Internet of Things Journal_ 9, 14 (2021), 12588–12600.
  * Wang et al. (2022) Zhaoying Wang, Jian Li, Kaiping Xue, Shaoyin Cheng, Nenghai Yu, Qibin Sun, and Jun Lu. 2022.  An Asynchronous Entanglement Distribution Protocol for Quantum Networks.  _IEEE Network_ 36, 5 (2022), 40–47.
  * Winker et al. (2023) Tobias Winker, Umut Çalikyilmaz, Le Gruenwald, and Sven Groppe. 2023.  Quantum Machine Learning for Join Order Optimization Using Variational Quantum Circuits. In _Proceedings of the International Workshop on Big Data in Emergent Distributed Environments_. Association for Computing Machinery, New York, NY, USA, Article 5, 7 pages.
  * Yang et al. (2023) Zebo Yang, Maede Zolanvari, and Raj Jain. 2023.  A survey of important issues in quantum computing and communications.  _IEEE Communications Surveys & Tutorials_ 25, 2 (2023), 1059–1094.
  * Zhang et al. (2021) Jie Zhang, Jiawei Lu, Xuan Yan, Xiaolong Xu, Lianyong Qi, and Wanchun Dou. 2021.  Quantified edge server placement with quantum encoding in internet of vehicles.  _IEEE Transactions on Intelligent Transportation Systems_ 23, 7 (2021), 9370–9379.
  * Zhao and Qiao (2023) Yangming Zhao and Chunming Qiao. 2023.  Distributed transport protocols for quantum data networks.  _IEEE/ACM Transactions on Networking_ 31, 6 (2023), 2777–2792.
  * Zhou et al. (2022) Tianmo Zhou, Yunqiang Zhu, Kai Sun, Jialin Chen, Shu Wang, Huazhong Zhu, and Xiaoshuang Wang. 2022.  Variance analysis in China’s coal mine accident studies based on data mining.  _International journal of environmental research and public health_ 19, 24 (2022), 16582.