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IEEE Communications Surveys & Tutorials

Quantum Search Algorithms for Wireless Communications

Panagiotis Botsinis, Dimitrios Alanis, Zunaira Babar, Hung Viet Nguyen, Daryus Chandra, Soon Xin Ng, Lajos Hanzo

Published Nov 20, 2018• 149 citations
Publisher

Abstract

Faster, ultra-reliable, low-power, and secure communications has always been high on the wireless evolutionary agenda. However, the appetite for faster, more reliable, greener, and more secure communications continues to grow. The state-of-the-art methods conceived for achieving the performance targets of the associated processes may be accompanied by an increase in computational complexity. Alternatively, a degraded performance may have to be accepted due to the lack of jointly optimized system components. In this survey we investigate the employment of quantum computing for solving problems in wireless communication systems. By exploiting the inherent parallelism of quantum computing, quantum algorithms may be invoked for approaching the optimal performance of classical wireless processes, despite their reduced number of cost-function evaluations. In this contribution we discuss the basics of quantum computing using linear algebra, before presenting the operation of the major quantum algorithms, which have been proposed in the literature for improving wireless communications systems. Furthermore, we investigate a number of optimization problems encountered both in the physical and network layer of wireless communications, while comparing their classical and quantum-assisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.

DOI
10.1109/comst.2018.2882385

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While the commercial deployment of 5G networks and beyond is a reality, the first work for the definition and study of 6G networks has started. The scientific community agrees that these networks will be characterised by a very high spatial density of access points, heterogeneity of access technologies, an increased number of users per access point, and demand for ubiquitous connectivity that must combine ultra-low latency, very high bandwidth, and high energy efficiency [1, 2]. Among the emerging challenges, holographic communications, high-precision manufacturing, the ubiquitous introduction of intelligence, and the incorporation of new technologies based on sub-terahertz (THz) or Visible Light Communications (VLC) are real issues. These are taking place in a truly three-dimensional coverage framework, integrating terrestrial and aerial radio to meet the needs with cloud-based capabilities where and when needed (on-demand). 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They involve three elements in the system: a person as a physical carrier; an intelligent device with which the person interacts; collects data and executes commands from an application running on the person's device [4]. The 6G radio networks will provide the means of communication and data gathering necessary to accumulate information. Still, a system's approach will be required for the 6G technology market as a whole involving data analytics, artificial intelligence (AI), and next-generation computation capabilities via HPC and quantum computing [3, 5]. This tremendous amount of data may be harnessed, with strong processing and learning capabilities, to manage the network at different levels. To this end, quantum computing methods can play a significant enabling role and can provide a guaranteed security platform. 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Quantum channels can increase the achievable capacity. As a result, error correction without redundancy is possible on noisy channels. Quantum computers can enable exponentially complex combinatorial ML decoding in classical systems [5, 6]. To cope with latency-critical scenarios such as automated cars and medical applications, communication must be accomplished in a concise time. Achieving latency of only a few milliseconds is a real challenge. To achieve low latency and ultra-high reliability, it is essential to develop powerful high-end processors that consume little power. Quantum computing seems to be a reliable solution to this issue [8]. With variable quality of service (QoS) requirements, a variable radio resource must be allocated to the user. This can be of variable bandwidth, variable power, or both. Another challenging aspect of 6G is that with the propagation frequency, the signal can attenuate quickly and have a high penetration loss at high frequencies [9]. The signal is also automatically attenuated when accessing homes, residences, or workplaces. As the frequency increases, radio waves attenuate and may have difficulty penetrating the walls of buildings and homes while affecting users' QoS requirements. Therefore, it is very important to develop stable, fast and accurate quantum algorithms to handle 6G communication requirements by dynamically allocating variable resources [10]. The current 5G standard does not address the issue of quantum computing but relies on traditional cryptography. The development towards cloud and edge native infrastructures is expected to continue in 6G networks. While large-scale quantum computing can be expected to take a longer duration, it is time to prepare for the shift to cryptography that is secure in the post-quantum world. According to current knowledge, contemporary symmetric cryptography remains secure for the most part, even after the advent of quantum computing. Furthermore, authentication by a physical layer signature, such as RF fingerprinting, and some other technologies, such as randomisation of MIMO transmission coefficients, coding, etc., could potentially be used in 6G [5, 11]. Whether it is for the optimisation of heterogeneous resources in 6G networks that result in the solution of ‘NP-complete’ combinatorial problems, for the compensation of non-linear effects of a communication chain or the optimisation of MIMO transmitter pre-coding matrix, future network nodes and devices will have to be equipped with learning and decision-making capabilities through AI and machine learning, so that they autonomously optimise their operation in response to changes in the environment [5]. In this context, the use of optimisation techniques based on quantum computing and AI applied to the field of 6G networks could be of considerable interest. Besides, quantum computing allows NP-hard optimisation problems to be solved in linear time, making it possible to solve and execute network optimisation problems in a much faster time, even in real-time [5, 11]. Regulatory and standardisation work will impact our future technology solutions in 5G networks and beyond. Protecting individual privacy and identity has long been a challenge for standards bodies, as countries have very different perspectives and regulations in this area. International standards bodies such as JTC 1 have committees working on privacy frameworks and are making progress, but there is still much to be done [13]. To conclude, we believe that our readers will find this opinion piece useful in giving an overview of the importance of Quantum Computing/communications in shaping the next communication systems and its security platforms. This is a technology in its infancy and a lot of research remains to be carried out to achieve sustainable solutions and overcome the current challenges. The use of intelligent systems (AI, ML and other techniques) will be essential in achieving solutions faster and providing sustainable outcomes. But IoT devices as well as cloud and edges nodes must be AI-ready and be able to support the use of intelligent algorithms.

IET Quantum Communication•Sep 1, 2021•13 citations
Faster, ultra-reliable, low-power, and secure communications has always been high on the wireless evolutionary agenda. However, the appetite for faster, more reliable, greener, and more secure communications continues to grow. The state-of-the-art methods conceived for achieving the performance targets of the associated processes may be accompanied by an increase in computational complexity. Alternatively, a degraded performance may have to be accepted due to the lack of jointly optimized system components. In this survey we investigate the employment of quantum computing for solving problems in wireless communication systems. By exploiting the inherent parallelism of quantum computing, quantum algorithms may be invoked for approaching the optimal performance of classical wireless processes, despite their reduced number of cost-function evaluations. In this contribution we discuss the basics of quantum computing using linear algebra, before presenting the operation of the major quantum algorithms, which have been proposed in the literature for improving wireless communications systems. Furthermore, we investigate a number of optimization problems encountered both in the physical and network layer of wireless communications, while comparing their classical and quantum-assisted solutions. Finally, we state a number of open problems in wireless communications that may benefit from quantum computing.
Owing to its outstanding parallel computing capabilities, quantum computing (QC) has been a subject of continuous attention. With the gradual maturation of QC platforms, it has increasingly played a significant role in various fields such as transportation, pharmaceuticals, and industrial manufacturing, achieving unprecedented milestones. In modern society, wireless communication stands as an indispensable infrastructure, with its essence lying in optimization. Although artificial intelligence (AI) algorithms such as reinforcement learning (RL) and mathematical optimization have greatly enhanced the performance of wireless communication, the rapid attainment of optimal solutions for wireless communication problems remains an unresolved challenge. QC, however, presents a new alternative. This paper aims to elucidate the fundamentals of QC and explore its applications in wireless communications and networking. First, we provide a tutorial on QC, covering its basics, characteristics, and popular QC algorithms. Next, we introduce the applications of QC in communications and networking, followed by its applications in miscellaneous areas such as security and privacy, localization and tracking, and video streaming. Finally, we discuss remaining open issues before concluding.
Next-generation wireless communication systems should have very low latency, high reliability, the ability to connect a lot of devices, and better security.Artificial intelligence (AI) is an important part of intelligent network management because it makes channel estimation, spectrum allocation, beamforming, and network optimization more efficient.But classical AI methods have a lot of problems when used on large wireless networks, such as being very hard to compute, using a lot of energy, and not being able to grow.Recently quantum artificial intelligence i.e.QAI which combines quantum computing with machine learning has become a promising way to get around these problems.By using quantum mechanics ideas like superposition, entanglement and quantum parallelism QAI could speed up optimization tasks, make pattern recognition better and make secure communication better.This paper gives a full overview of QAI and how it could be used in the next generation of wireless communication systems.The study talks about the basics of quantum computing, how AI can help wireless networks, and new quantum machine learning models that are being developed.Also, quantum algorithms like Grover's search algorithm and the Quantum Approximate Optimization Algorithm (QAOA) are looked at in relation to problems with optimizing wireless networks.Lastly, we talk about the problems that QAI-enabled wireless communication systems face right now and the research that needs to be done in the future.
Quantum computing, with its potential to solve complex problems exponentially faster than classical computers, is poised to revolutionize various fields, including wireless networks security. This survey paper provides a comprehensive overview of the intersection between quantum computing and wireless networks security. We examine the potential threats quantum computing poses to classical encryption algorithms, such as RSA and ECC, which are foundational to the security of current wireless networks. Additionally, we explore emerging quantum-resistant cryptographic techniques designed to safeguard against these threats. The paper also discusses quantum key distribution (QKD) as a promising solution for achieving theoretically unbreakable encryption in wireless networks. Furthermore, we review the current state of research in applying quantum computing to wireless network security, including its implications for authentication, confidentiality, and integrity. Finally, we identify challenges and future directions for integrating quantum computing into wireless network security, emphasizing the need for continued research to ensure the resilience of wireless networks in the quantum era.
Multiple-input multiple-output (MIMO) technology utilizes multiple antennas at the transmitter and receiver to enhance data transmission speeds and reliability. Traditional MIMO decoding methods, however, can become increasingly complex as the number of antennas and modulation order rises. Quantum computing brings forth a new realm of information processing with significant potential. This study investigates the applicability of quantum algorithms for decoding information in MIMO wireless communication systems. Specifically, the Dürr-Høyer quantum search, based on Grover’s algorithm, and optimal quantum sorting algorithms are leveraged to reduce the query complexity with an analysis of the complexity and achievable bit error rate performance of the quantum-assisted decoders. The study considers cases of MIMO diversity, spatial modulation, and multiplexing transmission using both maximum-likelihood and fixed-complexity sphere decoders. By examining a variety of communication scenarios, this work aims to assess the applicability of quantum algorithms across different operational regimes and aids in extending the methodology to other communication systems.
A comprehensive coverage of the state-of-the-art in quantum machine learning (QML) methodologies, with a unique perspective on their applications for wireless communications, is presented. The paper begins by delving into the fundamental principles of quantum computing, and then goes through different operations and techniques that are involved in QML deployments. Subsequently, it provides an in-depth look at various methods peculiar to quantum computing, such as quantum search algorithms, and discusses their potentials towards maximizing the performance of wireless systems. The integration of quantum-based learning models into the existing machine learning methodologies, such as within the frameworks of unsupervised learning and reinforcement learning, are then examined. Taking the viewpoint of wireless communications, diverse studies in the literature that employ QML-based optimization methods are also highlighted. Finally, to ensure the applicability and feasibility of QML for optimizing wireless systems, potential solutions for deployment challenges are addressed.
While the commercial deployment of 5G networks and beyond is a reality, the first work for the definition and study of 6G networks has started. The scientific community agrees that these networks will be characterised by a very high spatial density of access points, heterogeneity of access technologies, an increased number of users per access point, and demand for ubiquitous connectivity that must combine ultra-low latency, very high bandwidth, and high energy efficiency [1, 2]. Among the emerging challenges, holographic communications, high-precision manufacturing, the ubiquitous introduction of intelligence, and the incorporation of new technologies based on sub-terahertz (THz) or Visible Light Communications (VLC) are real issues. These are taking place in a truly three-dimensional coverage framework, integrating terrestrial and aerial radio to meet the needs with cloud-based capabilities where and when needed (on-demand). Radio frequencies are used in wireless telecommunications, but the need for very high throughput requires wider bandwidths, hence very high frequencies, in particular THz bands. Moving to a higher frequency range—from 100 GHz to 10 THz—is expected to significantly increase the bandwidth of the radio channel, which will make it possible to serve a significant number of users. In this case, we are not talking about the connection of cell phones, tablets, or computers (and even smart cars)—we are considering the use of Internet of Things (IoT) devices, which within one base station can be quite a lot. Therefore, the technologies for beamforming, device location, etc., developed for the 5G generation that is just being implemented now should also remain but will be used at higher frequencies [3]. For which 6G is primarily intended, IoT solutions have been given a particular name: ‘human-machine-things’. They involve three elements in the system: a person as a physical carrier; an intelligent device with which the person interacts; collects data and executes commands from an application running on the person's device [4]. The 6G radio networks will provide the means of communication and data gathering necessary to accumulate information. Still, a system's approach will be required for the 6G technology market as a whole involving data analytics, artificial intelligence (AI), and next-generation computation capabilities via HPC and quantum computing [3, 5]. This tremendous amount of data may be harnessed, with strong processing and learning capabilities, to manage the network at different levels. To this end, quantum computing methods can play a significant enabling role and can provide a guaranteed security platform. Towards provisioning this massive connectivity and efficiently processing the voluminous data available at the user and network sides, quantum-powered computing methods have a strong potential in realising the ambitions of a service-driven, fully intelligent 6G communication network. There is every reason to believe that the integration of quantum technology can improve the throughput, efficiency, and security of 6G networks. In addition to the advantages mentioned above, this technology also has benefits in computing speed, guaranteed security, and minimal storage requirements. This makes it ideally suited for various future quantum communication network applications. Research is needed on many fronts to evaluate the potential opportunities of quantum computing in 6G applications. In 5G, a functional division is operated in both the RAN and core networks to meet the ultra-low latency and ultra-high efficiency requirements of 5G verticals. Notably, RAN functions are split into cloud-deployed services with interfacing capabilities. This new architecture has a significant impact on the efficient implementation of security processes [6]. One of the key challenges in deploying secure 5G networks is analysing how current cryptographic algorithms for secure authentication and data transmission can adapt to provide secure authentication between services and secure data encryption while ensuring that stringent efficiency requirements are met [7]. The powerful parallel processing capability of quantum search algorithms can be leveraged to solve large-scale wireless optimisation problems. (1) Is this ‘beyond 5G?’ This topic is highly exploratory and undoubtedly beyond the boundaries of core 5G R&D. (2) What are the new features and key challenges? Classically, the mutual information between the channel input and output must be maximised. For quantum channels, the capacity must be redefined. Quantum channels can increase the achievable capacity. As a result, error correction without redundancy is possible on noisy channels. Quantum computers can enable exponentially complex combinatorial ML decoding in classical systems [5, 6]. To cope with latency-critical scenarios such as automated cars and medical applications, communication must be accomplished in a concise time. Achieving latency of only a few milliseconds is a real challenge. To achieve low latency and ultra-high reliability, it is essential to develop powerful high-end processors that consume little power. Quantum computing seems to be a reliable solution to this issue [8]. With variable quality of service (QoS) requirements, a variable radio resource must be allocated to the user. This can be of variable bandwidth, variable power, or both. Another challenging aspect of 6G is that with the propagation frequency, the signal can attenuate quickly and have a high penetration loss at high frequencies [9]. The signal is also automatically attenuated when accessing homes, residences, or workplaces. As the frequency increases, radio waves attenuate and may have difficulty penetrating the walls of buildings and homes while affecting users' QoS requirements. Therefore, it is very important to develop stable, fast and accurate quantum algorithms to handle 6G communication requirements by dynamically allocating variable resources [10]. The current 5G standard does not address the issue of quantum computing but relies on traditional cryptography. The development towards cloud and edge native infrastructures is expected to continue in 6G networks. While large-scale quantum computing can be expected to take a longer duration, it is time to prepare for the shift to cryptography that is secure in the post-quantum world. According to current knowledge, contemporary symmetric cryptography remains secure for the most part, even after the advent of quantum computing. Furthermore, authentication by a physical layer signature, such as RF fingerprinting, and some other technologies, such as randomisation of MIMO transmission coefficients, coding, etc., could potentially be used in 6G [5, 11]. Whether it is for the optimisation of heterogeneous resources in 6G networks that result in the solution of ‘NP-complete’ combinatorial problems, for the compensation of non-linear effects of a communication chain or the optimisation of MIMO transmitter pre-coding matrix, future network nodes and devices will have to be equipped with learning and decision-making capabilities through AI and machine learning, so that they autonomously optimise their operation in response to changes in the environment [5]. In this context, the use of optimisation techniques based on quantum computing and AI applied to the field of 6G networks could be of considerable interest. Besides, quantum computing allows NP-hard optimisation problems to be solved in linear time, making it possible to solve and execute network optimisation problems in a much faster time, even in real-time [5, 11]. Regulatory and standardisation work will impact our future technology solutions in 5G networks and beyond. Protecting individual privacy and identity has long been a challenge for standards bodies, as countries have very different perspectives and regulations in this area. International standards bodies such as JTC 1 have committees working on privacy frameworks and are making progress, but there is still much to be done [13]. To conclude, we believe that our readers will find this opinion piece useful in giving an overview of the importance of Quantum Computing/communications in shaping the next communication systems and its security platforms. This is a technology in its infancy and a lot of research remains to be carried out to achieve sustainable solutions and overcome the current challenges. The use of intelligent systems (AI, ML and other techniques) will be essential in achieving solutions faster and providing sustainable outcomes. But IoT devices as well as cloud and edges nodes must be AI-ready and be able to support the use of intelligent algorithms.