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Quantum Computing Review: A Decade of Research

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A review on quantum computing and deep learning algorithms and their applications

• Published: 07 April 2022
• Volume 27 , pages 13217–13236, ( 2023 )

Cite this article

• Fevrier Valdez   ORCID: orcid.org/0000-0002-0159-0407 1 &
• Patricia Melin 1  

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In this paper, we describe a review concerning the Quantum Computing (QC) and Deep Learning (DL) areas and their applications in Computational Intelligence (CI). Quantum algorithms (QAs), engage the rules of quantum mechanics to solve problems using quantum information, where the quantum information is concerning the state of a quantum system, which can be manipulated using quantum information algorithms and other processing techniques. Nowadays, many QAs have been proposed, whose general conclusion is that using the effects of quantum mechanics results in a significant speedup (exponential, polynomial, super polynomial) over the traditional algorithms. This implies that some complex problems currently intractable with traditional algorithms can be solved with QA. On the other hand, DL algorithms offer what is known as machine learning techniques. DL is concerned with teaching a computer to filter inputs through layers to learn how to predict and classify information. Observations can be in the form of plain text, images, or sound. The inspiration for deep learning is the way that the human brain filters information. Therefore, in this research, we analyzed these two areas to observe the most relevant works and applications developed by the researchers in the world.

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1 Introduction

Nowadays, many intelligent algorithms have been proposed to solve complex problems, some are based on nature Baskaran et al. ( 2015 ), evolution Valdez ( 2020 ), brain behavior Krizhevsky et al. ( 2012 ), physics Rere et al. ( 2015 ), etc; which can be found in the literature, it is calculated there are more than 100 different algorithms, and improved algorithms for finding the best results on the complex problems. However, it is not our aim to analyze all existent methods. Instead, our approach will be on the quantum and deep learning algorithms and their applications. Therefore, we have selected the most relevant applications in this work. Although, we have worked with different algorithms in different ways, for example, with neural networks, fuzzy logic, evolutionary computing, QA and DL have demonstrated be two areas in Computational Intelligence to solve several problems as pattern recognition, optimization problems and can be combined with other methods to improve the performance. Therefore, we focused with the applications about quantum and deep learning algorithms.

Quantum computing works with machines that use the properties of quantum physics to store data and perform computations. This can be extremely advantageous for certain tasks where they could vastly outperform even our best supercomputers. In Montiel-Ross ( 2020 ) was made a review of quantum-inspired population-based metaheuristics, in this work, the authors reviewed which quantum-inspired metaheuristics could be translated to be used in the existing quantum computers based on the circuit model programming paradigm. Also, in Montiel-Ross et al. ( 2019 ), was proposed the quantum-inspired Acromyrmex evolutionary algorithm as a highly efficient global optimization method for complex systems.

A review of quantum neural networks is shown in Zhao and Wang ( 2021 ), where the authors observed that the quantum neural networks are higher storage capacity and computational efficiency compared to its classical counterparts. Also, in Beer et al. ( 2020 ), was proposed a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation.

In Figure 1 , is appreciated the domain which belong deep learning. In the figure, we can observe the relationship with machine learning and the artificial intelligence and DL is shown as a sub-field of artificial intelligence, and DL is a specialization of Machine Learning. Therefore, DL represents the advance stage of machine learning which mainly uses neural networks for learning and prediction of data. It is a group of different algorithms. These are used to design complex systems that can take any type of problems and give predictions. It uses the deep graph with numerous processing layers, made up of many linear and nonlinear conversions, (Schmidhuber ( 2015 ), Shinde and Shah ( 2018 )).

Domains of deep learning, machine learning and artificial intelligence

The main contribution in this paper, is to visualize the evolution that QC and DL algorithms have had in the last years. For this reason, we made several queries in Scopus and Web of Science to validate in the best way the obtained results. After, we collected the data in plain text to generate the clusters, networks and relations of works around the world with specific queries of the analyzed applications. To achieve obtain the graphics and presented results corresponding to queries, the VosViewer software was used in this research. VOSviewer is a software tool for constructing and visualizing bibliometric networks. These networks may for instance include journals, researchers, or individual publications, and they can be constructed based on citation, bibliographic coupling, co-citation, or co-authorship relations (Perianes-Rodriguez et al. ( 2016 ), Van Eck and Waltman ( 2014 )). The parameters used in VosViewer to build the networks, clusters and relations presented in the paper are shown in Table 1 .

This paper is organized as follows: in Section 1 a brief introduction about of main contribution is presented, Section 2 describes with detail the literature review analyzed in the paper, Section 3 shows the Applications with Quantum Computing Algorithms, in Section 4 the Applications with Deep Learning are presented, and the following Section presents the conclusions and future works and finally the conclusions in the last section are included.

2 Literature review

In this section, we made an exhaustive review about the topics described above. In this case, the consulted papers were collected from the Scopus database. Also, we made a search in Web of Science (WoS) to analyze the published journals papers with these two areas. In WoS, we made queries with the topic ’quantum computing’. With this query, were obtained as result from WoS 33,230 journal papers. However, is a big number of works with difficulty for analyzing. But, with this query is possible to understand the areas, quantity of paper by areas, authors and countries developing works with quantum computing as is shown in Figure 2 , where, it can be appreciated the number of papers by areas. The Figure only shows the first 10 areas.

Topic ‘quantum computing’. collected data from WoS

Also, we made a query from WoS search is with the topic ’Deep Learning’, and were found 86,829 papers, that represent a major number of works with respect to QC. But, this is because the search was very general. Therefore, in the other section, we made specific queries to filter and refine in the best way this data. Figure 3 , shows the areas with the higher number of published journal papers, where we can highlight the number of works in the area Engineering Electrical Electronic with more than 20,000 papers. Also, this figure only shows the first ten areas.

Topic ‘deep learning’. collected data from WoS

In this part, we presented related works about these two topics (QC and DL) algorithms. The source of collected data were reviewed in Scopus database. The search was made with the topic ’Quantum Computing Algorithms’, the obtained results were 5785 papers in total. However, we are presenting a brief description only of the most relevant and recent works in this area. But, with the topic search above described is possible to find at any time the updated documents. Also, we presented a review about applications using Quantum Computing Algorithms. In this case, we decide to include applications based in Computational Intelligence, such has neural networks, fuzzy logic, intelligent control, robotic, medicine, etc.

Before doing the separate queries, with the topics of QC and DL. A query was made in the Scopus database with the two topics together; this was, to know the authors who in the last 10 years have been working in this field of computational intelligence. Figure 4 shows the result of this query.

Scopus authors working with QC and DL algorithms

From Scopus, with the topic QC and DL we made a query to know the classification of works according to type of document. In Figure 5 it can be appreciated, the types of work carried out in the last 10 years. In Figure 6 it can be noted in that the numbers of papers developed to date is increasing every day.

Document types from Scopus database

Documents from Scopus database in the last 10 years

In a recent work, Pathak et al. ( 2022 ), presented an Algorithm of Quantum Computing During Pandemic Situation of COVID-19. Further, this work presents fundamental about quantum properties such as superposition, entanglement, and quantum programming tools such as Qiskit (IBM), pyQuil (Google), etc. In Potempa and Porebski ( 2022 ) the authors Comparing Concepts of Quantum and Classical Neural Network Models for Image Classification Task. The comparative results of two models: classical and quantum neural networks of a similar number of training parameters, indicate that the quantum network, although its simulation is time-consuming, overcomes the classical network it has better convergence and achieves higher training and testing accuracy. On the other hand, an interesting work was proposed for Enhancing Security Using Quantum Computing. Were, the authors, developed quantum algorithms using qubit that run faster than classical algorithms and these algorithms reduce the time complexity and also it is impossible for the attackers to attack Peelam and Johari ( 2022 ), with this work is highlighting the importance for using quantum algorithms in security problems in the last years. Other use of QC can be seen in Ong and Tan ( 2022 ), where the authors proposed a work using a quantum circuit program generation with a genetic algorithm for the Open Quantum Assembly Language. In other research, was proposed a Supervised Machine Learning Strategies for Investigation of Weird Pattern Formulation from Large Volume Data Using Quantum Computing, in this work, Quantum machine learning accelerated the supervised, unsupervised, and reinforcement learning methods obtained better results than the classical machi Nivelkar and Bhirud ( 2022 ).

In Xiao et al. ( 2021 ) was proposed a stochastic quantum program synthesis framework based on Bayesian optimization, where Quantum computers and algorithms offered an exponential performance improvement over some NP-complete programs which cannot be run efficiently through a Von Neumann computing approach. On the other hand, a classical simulation of the Quantum Approximate Optimization Algorithm was presented, in this work Medvidović and Carleo ( 2021 ), was developed A neural-network of the many qubit wave function, focusing on states relevant for the Quantum Approximate Optimization Algorithm. A practical application can be seen in Dalyac et al. ( 2021 ) where CA was used for hard industrial optimization problems. The case study in the field of smart-charging of electric vehicles. Also, an important application in the cryptography area was presented in Gaj ( 2018 ).

Other important and recent works can be seen in Singh et al. ( 2021a ), Wang et al. ( 2021 ), Yunakovsky et al. ( 2021 ), Gao et al. ( 2021 ), Huber et al. ( 2021 ), Kulkarni et al. ( 2021 ), Ajagekar and You ( 2021 ), Alberts et al. ( 2021 ), Medvidović and Carleo ( 2021 ), Singh et al. ( 2021b ), Im et al. ( 2021 ) Liu et al. ( 2021 ).

3 Applications with quantum computing algorithms

In this section, we presented the most relevant applications in Medicine, Intelligent Control and Robotic. In each area, we made a brief description about the analyzed works. Also, in this part, we are presenting the most cited paper in each field. Table 2 shows the 10 most cited works in the medicine area using QC.

In Table 3 , the 10 most cited works in the area of intelligent control with QC is presented. In this table is shown the difference with respect to the medicine area, where the number of citations is bigger than intelligent control.

Finally, in Table 4 is shown the most cited works in robotic using QC. Here, it is shown that the number of citations is greater than the intelligent control topic, but less than that of medicine.

3.1 Medicine quantum computing

In this section, a review with QA algorithms applied to medicine are shown. We used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to appreciate the formed networks and relations in medicine. From Scopus database, was made a query to calculate the network, relations, clusters with the topic’Medicine Quantum Computing’. We found 114 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus.

The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 1675 keywords, which 292 meet the threshold. For each of the 292 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total 292 keywords were selected to obtain the final results. In Fig.  8 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. Figure  7 shows the citations in the last years. In this figure, we can appreciate how the number of citations has increased significantly each year (Fig.  8 ).

Scopus citations with the topic medicine quantum computing

Network with the topic medicine quantum computing

Also, in this section, are presented a brief description about relevant works with the analyzed topic.

In Boev et al. ( 2021 ), the authors developed a method for solving genome assembly tasks with the use of quantum and quantum-inspired optimization techniques. Within this method, we present experimental results on genome assembly using quantum annealers both for simulated data and the φ X 174 bacteriophages. The results pave a way for a significant increase in the efficiency of solving bioinformatics problems with the use of quantum computing technologies.

Also, in Thomasian and Adashi ( 2021 ), a qualitative review of the medical cybersecurity literature was presented with collation of federal and international legal documents, policy reports, industry frameworks, cyberbreach analyses, and scientific journal papers. On the other hand, fuzzy logic with quantum computing was used in Kumar et al. ( 2020 ), in this the authors proposed a health analytics system by forming a knowledge repository of patient’s symptoms and medicines dosage to prescribe the precise quantum of medicine to cure an ailment and also prevent drug abuse. Also, in this field, Bianconi and Mohseni ( 2020 ), an Infrared detection and imaging are key enabling technologies for a vast number of applications, ranging from communication, to medicine and astronomy, were proposed using quantum computing. In big data applied to medicine have been developed some works with QC, for example, in the healthcare industry, various sources for big data include hospital records, medical records of patients, results of medical examinations, and devices that are a part of internet of things. The authors used QC to manage this quantity of data Dash et al. ( 2019 ).

3.2 Intelligent control quantum computing applications

In the same way that the previous topic, in this section, a review with QC algorithms applied to intelligent control are presented. Also, was used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to distinguish the formed networks and relations in intelligent control. From Scopus database, was made a query to calculate the network, relations, clusters with the topic ‘Intelligent Control Quantum Computing’. We found 141 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus. The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 1329 keywords, which 301 meet the threshold. For each of the 301 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total 301 keywords were selected to obtain the presented results. In Fig.  9 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. Figure  10 shows the density of this network, highlighting with yellow color the area of quantum computing and intelligent control with more strength that other analyzed keywords. Figure  11 shows the citations in the last years from Scopus. In this figure, we can appreciate how the number of citations has increased significantly each year. Also, in this section, are presented a brief description about relevant works with the analyzed topic. In Guan et al. ( 2020 ) proposed new Lyapunov control scheme for quantum systems using a Particle Swarm Optimization algorithm. Also, in Barchatova et al. ( 2015 ) was proposed an Intelligent robust control system based on quantum KB-selforganization. The authors, considered Quantum soft computing and Kansei/affective engineering technologies in this research. On the other hand, Mohanty and Rout ( 2015 ) presented a motion control method for mobile robots in indoor environments based on color object detection using quantum computing. Also, Han and Yuan ( 2014 ), proposed a Multivariable system identification based on double quantum particle swarm optimization and big data, in this case, the authors used an optimization method combined with quantum computing. Finally, in this section, we presented the application of an adaptive quantum particle swarm optimization algorithm for optimal dispatching of cascaded hydro power stations proposed by Zhang et al. ( 2012 )

Network with the topic intelligent control quantum computing

Density with the topic intelligent control quantum computing

Citations from Scopus Scopus citations with the topic ‘Intelligent Control Quantum Computing’

3.3 Robotic control quantum computing applications

Finally, in this section, a review with QC algorithms applied to Robotic are presented. Also, was used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to distinguish the formed networks and relations in Robotic. From Scopus database, was made a query to calculate the network, relations, clusters with the topic’Robotic Control Quantum Computing’. We found 93 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus. The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 1013 keywords, which 197 meet the threshold. For each of the 197 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total, 197 keywords were selected to obtain the final results. In Fig.  12 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. Figure  13 shows the overlay visualization to appreciate clearly how are distributed each one the keywords. In Fig.  14 the density of this network is presented, highlighting with yellow color the area of quantum computing and robotic with more strength that other analyzed keywords. Figure  15 shows the citations in the last years from Scopus. In this figure, we can appreciate how the number of citations has increased significantly each year.

Network with the topic robotic quantum computing

Overlay with the topic robotic quantum computing

Density with the topic robotic quantum computing

Scopus citations with the topic’Robotic Quantum Computing’

Also, in this section are presented some important applications with robotic using QC. Atchade-Adelomou et al. ( 2021 ) proposed a quantum computing approach in mobile robot order picking and batching problem solver optimization, the authors developed a quantum algorithm to minimize the distance traveled in warehouses and distribution centers where order picking is applied. Also, in this field A New Quantum-computing based Algorithm for Robotic Arms and Rigid Bodies’ Orientation was proposed by Zioui et al. ( 2021 ). Also, in Post Quantum Secure Command and Control of Mobile Agents Inserting quantum-resistant encryption schemes in the Secure Robot Operating System Varma et al. ( 2020 ). On the other hand, in Korenkov et al. ( 2020 ) quantum software engineering supremacy in Intelligent robotics was developed. Also, in Ulyanov ( 2020 ) Quantum fuzzy inference based on quantum genetic algorithm: Quantum simulator in intelligent robotics.

4 Applications with deep learning algorithms

In this section, we presented a review about applications using Deep Learning Algorithms. In this case, we decide to include applications based in Computational Intelligence, such has neural networks, fuzzy logic, etc. Also, in this section, we are presenting the most cited paper in each field. Table 5 shows the 10 most cited works in the medicine area using DL. Here, is observed how in the last years, the number of citations is increasing in this field.

In Table 6 , are presented the most cited works in intelligent control with DL. Also, is shown as in the last years this topic is highly used by the researchers.

Finally, in Table 7 , are presented the most cited works in robotic with DL. Also, in this topic the number of citations is increasing in the last years.

4.1 Medicine deep learning applications

Also, in this section, a review with DL algorithms applied to Medicine are presented. Also, was used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to distinguish the formed networks and relations in medicine. From Scopus database, was made a query to calculate the network, relations, clusters with the topic’Robotic Control Quantum Computing’. We found 1011 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus. The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 7782 keywords, which 2355 meet the threshold. For each of the 2355 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total 1000 keywords were selected to obtain the final results. In Fig.  16 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. In Fig.  17 the density of this network is presented, highlighting with yellow color the area of deep learning and human with more strength that other analyzed keywords. Figure  18 shows the citations in the last years from Scopus. In this figure, we can appreciate how the number of citations has increased significantly each year. Also, in this section are presented some applications with deep learning techniques as, neural networks, machine learning, convolutional neural networks, etc., applied to medicine.

Network with the topic medicine deep learning algorithms

Density with the topic medicine deep learning algorithms

Scopus citations with the topic ‘Medicine Deep Learning Algorithms’

Nowadays, several web medical applications evolved in the field of medicine, there is need for an intelligent and efficient extraction technique. Therefore, neural networks, machine learning can be used to improve the obtained results with other classical techniques. For example, in Deepika and Radha ( 2022 ) was presented a study of Abstract-Based Classification of Medical Journals Using Machine Learning Techniques. Other relevant application using deep learning is presented in Gaxiola et al. ( 2018 ), in this work, the authors used modular neural networks for iris recognition. The authors used the human iris database improved with image preprocessing methods. Also, a recent work in the medical area with deep learning techniques is presented by Varela-Santos and Melin ( 2021 ). In this case, the authors used neural networks for classifying coronavirus based on its manifestation on chest X-rays using texture features. In González et al. ( 2015 ), Fuzzy logic with the optimization method gravitational search was used to optimize the architecture of a modular neural networks in echocardiogram recognition. In the same way, the authors presented a work but using type-2 fuzzy logic with pattern recognition with modular neural networks González et al. ( 2016 ). On the other hand, an overview of deep learning in medical imaging was presented by Lundervold and Lundervold ( 2019 ). In this work, the authors review the deep artificial neural networks, machine learning models to image analysis to natural language processing.

4.2 Intelligent control deep learning application

Also, in this section, a review with DL algorithms applied to Medicine are presented. Also, was used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to distinguish the formed networks and relations in medicine. From Scopus database, was made a query to calculate the network, relations, clusters with the topic’Robotic Control Quantum Computing’. We found 1160 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus. The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 8721 keywords, which 2131 meet the threshold. For each of the 2131 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total 1000 keywords were selected to obtain the final results. In Fig.  19 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. In Fig.  20 the density of this network is presented, highlighting with yellow color the area of intelligent control and deep learning with more strength that other analyzed keywords. Figure  21 shows the citations in the last years from Scopus. In this figure, we can appreciate how the number of citations has increased significantly each year.

Network with the topic ‘intelligent control deep learning algorithms’

Density with the topic ‘intelligent control deep learning algorithms’

Scopus citations with the topic ‘Intelligent Control Deep Learning Algorithms’

4.3 Robotic deep learning applications

Also, in this section, a review with DL algorithms applied to Medicine are presented. Also, was used the tool VosViewer Perianes-Rodriguez et al. ( 2016 ) to distinguish the formed networks and relations in medicine. From Scopus database, was made a query to calculate the network, relations, clusters with the topic’Robotic Control Quantum Computing’. We found 516 linked papers considering title, abstract and keyword. The collected data from Scopus, were used in VosViewer to obtain in graph form the obtained results. First, we create a map based on bibliographic data from Scopus. The data were introduced in a csv format. The type of analysis was by Co-occurrence, the counting method was full counting. Finally, the measure unit used was by keywords with a minimum number of occurrences equal to 2. Where, we obtained 4010 keywords, which 990 meet the threshold. For each of the 990 keywords, the total strength of the co-occurrence links with other keywords was calculated. The keywords with the greatest total link strength were selected. In total, 990 keywords were selected to obtain the final results. In Fig.  22 , is shown the network, relations, clusters and links in a form graph of this query using data from Scopus. In Fig.  23 the density of this network is presented, highlighting with yellow color the area of deep learning and learning algorithms with more strength that other analyzed keywords. Figure  24 shows the citations in the last years from Scopus. In this figure, we can appreciate how the number of citations has increased significantly each year.

Network with the topic ‘robotic deep learning algorithms’

Density with the topic ‘robotic deep learning algorithms’

Scopus citations with the topic ‘Robotic Deep Learning Algorithms’

In this field, we can see many works applying robotics with deep learning methods. Therefore, in this section are presented the most relevant and recent in this area. For example, in Wu et al. ( 2019 ) implemented a robot to make an automatic choreography system based on the deep learning technology. On the other hand, King and Hwang ( 1989 ). The authors proposed a ring VLSI systolic architecture for implementing neural networks with applications to robotic processing. Also, Liao et al. ( 2021 ) proposed an unsupervised fault detection and recovery for intelligent robotic rollators using deep neural networks. The experiments under several conditions confirmed that the method, which leverages machine learning-enhanced algorithms, exhibits reliable performance. Also, Chen et al. ( 2020 ) proposed a robotic device capable of introducing needles and catheters into deformable tissues such as blood vessels to draw blood or deliver fluids autonomously. Robotic cannulation is driven by predictions from a series of deep convolutional neural networks that encode information from multimodal image sequences to guide real-time serving. Also, in Alzubaidi et al. ( 2021 ) was made a review about applications in robotic with deep learning, convolutional neural networks architectures, challenges, etc. In this study, the authors attempt to provide a more comprehensive survey of the most important aspects of Deep Learning and including those enhancements recently added to the field.

5 Conclusions

After performing an analysis from Scopus, an undertaking an exhaustive study about the applications and importance of Quantum Computing and Deep Learning; we can conclude that these areas have achieved an important advancement in the last years. We can observe, the increment of number of citations, for example, in Scopus, the tendency is developed every day more works based on these two fields of the computational intelligence. Also, we have found, the networks, clusters, and built relationships around the world by many researches that are working with the analyzed topics. As future works, other topics of WoS, Google Scholar, or other databases can be analyzed with this software to compare the number of citations or relevance considering other sources. Also, specific queries with other bibliometric software such as CiteSpace, Zhang et al. ( 2010 ), that is a free software for visualizing and analyzing trends and patterns in the scientific literature can be used. The relevance of the review is that with this paper, the researchers can observe the trends for using QC and DL in several areas. However, the paper can serve as reference to make other queries, with other topics from different databases. Also, the same searches can be explored to view the updated information about the analyzed topics in this review. Although, only were reviewed medicine, robotic and intelligent control to make the research, the paper can be extended with other important areas. We decided to explore these areas because we have some works in computational intelligence with these topics.

Data availability

Not applicable

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A blueprint for making quantum computers easier to program

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When MIT professor and now Computer Science and Artificial Intelligence Laboratory (CSAIL) member Peter Shor first demonstrated the potential of quantum computers to solve problems faster than classical ones, he inspired scientists to imagine countless possibilities for the emerging technology. Thirty years later, though, the quantum edge remains a peak not yet reached. Unfortunately, the technology of quantum computing isn’t fully operational yet. One major challenge lies in translating quantum algorithms from abstract mathematical concepts into concrete code that can run on a quantum computer. Whereas programmers for regular computers have access to myriad languages such as Python and C++ with constructs that align with standard classical computing abstractions, quantum programmers have no such luxury; few quantum programming languages exist today, and they are comparatively difficult to use because quantum computing abstractions are still in flux. In their recent work, MIT researchers highlight that this disparity exists because quantum computers don’t follow the same rules for how to complete each step of a program in order — an essential process for all computers called control flow — and present a new abstract model for a quantum computer that could be easier to program.

In a paper soon to be presented at the ACM Conference on Object-oriented Programming, Systems, Languages, and Applications, the group outlines a new conceptual model for a quantum computer, called a quantum control machine, that could bring us closer to making programs as easy to write as those for regular classical computers. Such an achievement would help turbocharge tasks that are impossible for regular computers to efficiently complete, like factoring large numbers, retrieving information in databases, and simulating how molecules interact for drug discoveries. “Our work presents the principles that govern how you can and cannot correctly program a quantum computer,” says lead author and CSAIL PhD student Charles Yuan SM ’22. “One of these laws implies that if you try to program a quantum computer using the same basic instructions as a regular classical computer, you’ll end up turning that quantum computer into a classical computer and lose its performance advantage. These laws explain why quantum programming languages are tricky to design and point us to a way to make them better.” Old school vs. new school computing One reason why classical computers are relatively easier to program today is that their control flow is fairly straightforward. The basic ingredients of a classical computer are simple: binary digits or bits, a simple collection of zeros and ones. These ingredients assemble into the instructions and components of the computer’s architecture. One important component is the program counter, which locates the next instruction in a program much like a chef following a recipe, by recalling the next direction from memory. As the algorithm sequentially navigates through the program, a control flow instruction called a conditional jump updates the program counter to make the computer either advance forward to the next instruction or deviate from its current steps. By contrast, the basic ingredient of a quantum computer is a qubit, which is a quantum version of a bit. This quantum data exists in a state of zero and one at the same time, known as a superposition. Building on this idea, a quantum algorithm can choose to execute a superposition of two instructions at the same time — a concept called quantum control flow.

The problem is that existing designs of quantum computers don’t include an equivalent of the program counter or a conditional jump. In practice, that means programmers typically implement control flow by manually arranging logical gates that describe the computer’s hardware, which is a tedious and error-prone procedure. To provide these features and close the gap with classical computers, Yuan and his coauthors created the quantum control machine — an instruction set for a quantum computer that works like the classical idea of a virtual machine. In their paper, the researchers envision how programmers could use this instruction set to implement quantum algorithms for problems such as factoring numbers and simulating chemical interactions.

As the technical crux of this work, the researchers prove that a quantum computer cannot support the same conditional jump instruction as a classical computer, and show how to modify it to work correctly on a quantum computer. Specifically, the quantum control machine features instructions that are all reversible — they can run both forward and backward in time. A quantum algorithm needs all instructions, including those for control flow, to be reversible so that it can process quantum information without accidentally destroying its superposition and producing a wrong answer.

The hidden simplicity of quantum computers According to Yuan, you don’t need to be a physicist or mathematician to understand how this  futuristic technology works. Quantum computers don’t necessarily have to be arcane machines, he says, that require scary equations to understand. With the quantum control machine, the CSAIL team aims to lower the barrier to entry for people to interact with a quantum computer by raising the unfamiliar concept of quantum control flow to a level that mirrors the familiar concept of control flow in classical computers. By highlighting the dos and don’ts of building and programming quantum computers, they hope to educate people outside of the field about the power of quantum technology and its ultimate limits.

Still, the researchers caution that as is the case for many other designs, it’s not yet possible to directly turn their work into a practical hardware quantum computer due to the limitations of today’s qubit technology. Their goal is to develop ways of implementing more kinds of quantum algorithms as programs that make efficient use of a limited number of qubits and logic gates. Doing so would bring us closer to running these algorithms on the quantum computers that could come online in the near future.

“The fundamental capabilities of models of quantum computation has been a central discussion in quantum computation theory since its inception,” says MIT-IBM Watson AI Lab researcher Patrick Rall, who was not involved in the paper. “Among the earliest of these models are quantum Turing machines which are capable of quantum control flow. However, the field has largely moved on to the simpler and more convenient circuit model, for which quantum lacks control flow. Yuan, Villanyi, and Carbin successfully capture the underlying reason for this transition using the perspective of programming languages. While control flow is central to our understanding of classical computation, quantum is completely different! I expect this observation to be critical for the design of modern quantum software frameworks as hardware platforms become more mature.” The paper lists two additional CSAIL members as authors: PhD student Ági Villányi ’21 and Associate Professor Michael Carbin. Their work was supported, in part, by the National Science Foundation and the Sloan Foundation.

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Quantum Computing

Quantum Computing merges two great scientific revolutions of the 20th century: computer science and quantum physics. Quantum physics is the theoretical basis of the transistor, the laser, and other technologies which enabled the computing revolution. But on the algorithmic level, today's computing machinery still operates on ""classical"" Boolean logic. Quantum Computing is the design of hardware and software that replaces Boolean logic by quantum law at the algorithmic level. For certain computations such as optimization, sampling, search or quantum simulation this promises dramatic speedups. We are particularly interested in applying quantum computing to artificial intelligence and machine learning. This is because many tasks in these areas rely on solving hard optimization problems or performing efficient sampling.

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Improving the Variational Quantum Eigensolver Using Variational Adiabatic Quantum Computing

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm for finding the minimum eigenvalue of a Hamiltonian that involves the optimization of a parameterized quantum circuit. Since the resulting optimization problem is in general nonconvex, the method can converge to suboptimal parameter values that do not yield the minimum eigenvalue. In this work, we address this shortcoming by adopting the concept of variational adiabatic quantum computing (VAQC) as a procedure to improve VQE. In VAQC, the ground state of a continuously parameterized Hamiltonian is approximated via a parameterized quantum circuit. We discuss some basic theory of VAQC to motivate the development of a hybrid quantum-classical homotopy continuation method. The proposed method has parallels with a predictor-corrector method for numerical integration of differential equations. While there are theoretical limitations to the procedure, we see in practice that VAQC can successfully find good initial circuit parameters to initialize VQE. We demonstrate this with two examples from quantum chemistry. Through these examples, we provide empirical evidence that VAQC, combined with other techniques (an adaptive termination criteria for the classical optimizer and a variance-based resampling method for the expectation evaluation), can provide more accurate solutions than “plain” VQE, for the same amount of effort.

First Step to Quantum Computing

Quantum computing for chemical and biomolecular product design, quantum computing for the brain, introduction to the special issue on design automation for quantum computing, quantum fourier transform to estimate drive cycles.

AbstractDrive cycles in vehicle systems are important determinants for energy consumption, emissions, and safety. Estimating the frequency of the drive cycle quickly is important for control applications related to fuel efficiency, emission reduction and improving safety. Quantum computing has established the computational efficiency that can be gained. A drive cycle frequency estimation algorithm based on the quantum Fourier transform is exponentially faster than the classical Fourier transform. The algorithm is applied on real world data set. We evaluate the method using a quantum computing simulator, demonstrating remarkable consistency with the results from the classical Fourier transform. Current quantum computers are noisy, a simple method is proposed to mitigate the impact of the noise. The method is evaluated on a 15 qubit IBM-q quantum computer. The proposed method for a noisy quantum computer is still faster than the classical Fourier transform.

Quantum Computing for Dealing with Inaccurate Knowledge Related to the Certainty Factors Model

In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge.

Edge Caching in Fog-Based Sensor Networks through Deep Learning-Associated Quantum Computing Framework

Fog computing (FC) based sensor networks have emerged as a propitious archetype for next-generation wireless communication technology with caching, communication, and storage capacity services in the edge. Mobile edge computing (MEC) is a new era of digital communication and has a rising demand for intelligent devices and applications. It faces performance deterioration and quality of service (QoS) degradation problems, especially in the Internet of Things (IoT) based scenarios. Therefore, existing caching strategies need to be enhanced to augment the cache hit ratio and manage the limited storage to accelerate content deliveries. Alternatively, quantum computing (QC) appears to be a prospect of more or less every typical computing problem. The framework is basically a merger of a deep learning (DL) agent deployed at the network edge with a quantum memory module (QMM). Firstly, the DL agent prioritizes caching contents via self organizing maps (SOMs) algorithm, and secondly, the prioritized contents are stored in QMM using a Two-Level Spin Quantum Phenomenon (TLSQP). After selecting the most appropriate lattice map (32 × 32) in 750,000 iterations using SOMs, the data points below the dark blue region are mapped onto the data frame to get the videos. These videos are considered a high priority for trending according to the input parameters provided in the dataset. Similarly, the light-blue color region is also mapped to get medium-prioritized content. After the SOMs algorithm’s training, the topographic error (TE) value together with quantization error (QE) value (i.e., 0.0000235) plotted the most appropriate map after 750,000 iterations. In addition, the power of QC is due to the inherent quantum parallelism (QP) associated with the superposition and entanglement principles. A quantum computer taking “n” qubits that can be stored and execute 2n presumable combinations of qubits simultaneously reduces the utilization of resources compared to conventional computing. It can be analyzed that the cache hit ratio will be improved by ranking the content, removing redundant and least important content, storing the content having high and medium prioritization using QP efficiently, and delivering precise results. The experiments for content prioritization are conducted using Google Colab, and IBM’s Quantum Experience is considered to simulate the quantum phenomena.

Quantum computing formulation of some classical Hadamard matrix searching methods and its implementation on a quantum computer

AbstractFinding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.

Analysis of Carleman Linearization of Lattice Boltzmann

We explore the Carleman linearization of the collision term of the lattice Boltzmann formulation, as a first step towards formulating a quantum lattice Boltzmann algorithm. Specifically, we deal with the case of a single, incompressible fluid with the Bhatnagar Gross and Krook equilibrium function. Under this assumption, the error in the velocities is proportional to the square of the Mach number. Then, we showcase the Carleman linearization technique for the system under study. We compute an upper bound to the number of variables as a function of the order of the Carleman linearization. We study both collision and streaming steps of the lattice Boltzmann formulation under Carleman linearization. We analytically show why linearizing the collision step sacrifices the exactness of streaming in lattice Boltzmann, while also contributing to the blow up in the number of Carleman variables in the classical algorithm. The error arising from Carleman linearization has been shown analytically and numerically to improve exponentially with the Carleman linearization order. This bodes well for the development of a corresponding quantum computing algorithm based on the Lattice Boltzmann equation.

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What’s Next in Quantum is   quantum-centric supercomputing

A key factor in classical supercomputing is the intersection of communication and computation. The same holds true for quantum. Quantum-centric supercomputing utilizes a modular architecture to enable scaling. It combines quantum communication and computation to increase system capacity, and uses a hybrid cloud middleware to seamlessly integrate quantum and classical workflows. To realize this next wave in quantum we are building a new system called Quantum System Two. See our quantum development roadmap

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Breakthrough promises secure quantum computing at home

The full power of next-generation quantum computing could soon be harnessed by millions of individuals and companies, thanks to a breakthrough by scientists at Oxford University Physics guaranteeing security and privacy. This advance promises to unlock the transformative potential of cloud-based quantum computing and is detailed in a new study published in the influential U.S. scientific journal Physical Review Letters .

Quantum computing is developing rapidly, paving the way for new applications which could transform services in many areas like healthcare and financial services. It works in a fundamentally different way to conventional computing and is potentially far more powerful. However, it currently requires controlled conditions to remain stable and there are concerns around data authenticity and the effectiveness of current security and encryption systems.

Several leading providers of cloud-based services, like Google, Amazon, and IBM, already separately offer some elements of quantum computing. Safeguarding the privacy and security of customer data is a vital precursor to scaling up and expending its use, and for the development of new applications as the technology advances. The new study by researchers at Oxford University Physics addresses these challenges.

"We have shown for the first time that quantum computing in the cloud can be accessed in a scalable, practical way which will also give people complete security and privacy of data, plus the ability to verify its authenticity," said Professor David Lucas, who co-heads the Oxford University Physics research team and is lead scientist at the UK Quantum Computing and Simulation Hub, led from Oxford University Physics.

In the new study, the researchers use an approach dubbed "blind quantum computing," which connects two totally separate quantum computing entities -- potentially an individual at home or in an office accessing a cloud server -- in a completely secure way. Importantly, their new methods could be scaled up to large quantum computations.

"Using blind quantum computing, clients can access remote quantum computers to process confidential data with secret algorithms and even verify the results are correct, without revealing any useful information. Realising this concept is a big step forward in both quantum computing and keeping our information safe online'' said study lead Dr Peter Drmota, of Oxford University Physics.

The researchers created a system comprising a fibre network link between a quantum computing server and a simple device detecting photons, or particles of light, at an independent computer remotely accessing its cloud services. This allows so-called blind quantum computing over a network. Every computation incurs a correction which must be applied to all that follow and needs real-time information to comply with the algorithm. The researchers used a unique combination of quantum memory and photons to achieve this.

"Never in history have the issues surrounding privacy of data and code been more urgently debated than in the present era of cloud computing and artificial intelligence," said Professor David Lucas. "As quantum computers become more capable, people will seek to use them with complete security and privacy over networks, and our new results mark a step change in capability in this respect."

The results could ultimately lead to commercial development of devices to plug into laptops, to safeguard data when people are using quantum cloud computing services.

Researchers exploring quantum computing and technologies at Oxford University Physics have access to the state-of-the-art Beecroft laboratory facility, specially constructed to create stable and secure conditions including eliminating vibration.

Funding for the research came from the UK Quantum Computing and Simulation (QCS) Hub, with scientists from the UK National Quantum Computing Centre, the Paris-Sorbonne University, the University of Edinburgh, and the University of Maryland, collaborating on the work.

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Materials provided by University of Oxford . Note: Content may be edited for style and length.

Journal Reference :

• P. Drmota, D. P. Nadlinger, D. Main, B. C. Nichol, E. M. Ainley, D. Leichtle, A. Mantri, E. Kashefi, R. Srinivas, G. Araneda, C. J. Ballance, D. M. Lucas. Verifiable Blind Quantum Computing with Trapped Ions and Single Photons . Physical Review Letters , 2024; 132 (15) DOI: 10.1103/PhysRevLett.132.150604

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The Current State of Quantum Machine Learning

Given the recent advances in quantum computing, researchers attending the 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) investigated how to expand the number of use cases for QML in the workshop ‘ Quantum Machine Learning: From Foundations to Applications .’

Researchers Volker Tresp, Steffen Udluft, Daniel Hein, and Werner Hauptmann from Siemens AG, Technology in Munich, Germany, Martin Leib from IQM in Munich, Christopher Mutschler and Daniel D. Scherer from Fraunhofer IIS in Nuremberg, and Wolfgang Mauerer of Technical University of Applied Sciences Regensburg Siemens AG, Technology in Regensburg/Munich, Germany outlined the purpose and outcomes of the workshop.

The Goals of the Workshop

The workshop brought together researchers and industry practitioners from AI, ML, software and systems engineering, physics, and other disciplines to discuss the challenges QML currently faces and how it can be used to support the advancement of QML as an effective tool with diverse applications.

Currently, QML shows the potential to operate using fewer data points than traditional ML, as is the case with quantum support vector machines.

At the same time, subtle issues present limitations. Many of the challenges stem from the fact that quantum computers are sensitive to noise, and since qubits can assume an infinite number of states, errors can be hard to correct.

To best address QML’s challenges, the researchers felt it was most suitable to raise the topic in the quantum community instead of the ML community, which is already crowded with discourse. This made IEEE’s International Conference on Quantum Computing and Engineering (QCE) an ideal venue for the workshop.

A Call for Contributions

To bring more ideas to the table and encourage a diverse, international array of voices, the team encouraged participants to submit four different kinds of papers:

• Research papers
• System papers
• Experiments and analysis papers
• Application papers

The desired outcomes included:

• Publishing, presenting, and discussing research
• Allowing participants to form interest groups
• Enhance understanding regarding how to compare QML solutions holistically
• Identify research and application opportunities for QML
• Form relationships between those from industry and those from academia around the potential of QML
• Share ideas between the machine learning and quantum computing communities.

The target audience for the workshop was broad: Anyone interested in learning about the challenges faced and opportunities presented by QML, regardless of whether they hail from computer science, physics, or engineering.

Eight Papers Accepted

The team used a triple-anonymous peer review process that evaluated submissions according to their relevance, novelty, technical soundness, appropriateness, depth of literary coverage, and presentation.

The process resulted in eight papers being accepted. These addressed three primary topics:

• Applications of QML, such as for sentiment analysis in the finance sector
• Quantum reinforcement learning can improve sampling efficiency, optimize circuit compilation, and involve multiple quantum processing units (QPUs) in distributed training.
• General quantum machine learning, including computing the principle components of a matrix, Betti numbers, and persistent Bettis numbers.

Results: An Accurate Picture of the Current State of QML

When looked at as a whole, the papers depict an accurate vista of the QML field. It’s still very difficult to execute unconditional speedups in a QML setting due to a lack of understanding regarding QML and the wide range of approaches already driving classical ML systems.

The small size, as well as the noise and imperfections of existing QML machines, makes it difficult to extrapolate larger-scale uses of QML.

These difficulties are exacerbated by a few different factors. Classical ML research is based on computational models and doesn’t depend on physical structures, while QML needs to be run and tested in a physical environment due to a lack of reliable error correction techniques. In addition, the relatively small size of the QML community limits the number of people available to address these challenges, which inhibits the pace of progress.

At the same time, the workshop was a significant step forward towards overcoming these and other challenges. It surfaced papers that broadened the understanding of QML’s potential and united stakeholders from a variety of backgrounds around the advancement of QML. For a deeper dive into the workshop and the contributions of participants and authors, download the full paper

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Quantum computers

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Over the past several decades, quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit unique quantum properties? Today it is understood that the answer is yes, and many research groups around the world are working towards the highly ambitious technological goal of building a quantum computer, which would dramatically improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for quantum computation. However, it remains unclear which technology, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain the major challenges for the future.

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Acknowledgements

We thank R. Hanson, M. D. Lukin, and W. D. Oliver for comments. We acknowledge support from NSF, EPSRC, QIP IRC, IARPA, ERC, the Leverhulme Trust, CREST-JST, DFG, BMBF and Landesstiftung BW. J.L.O’B. acknowledges a Royal Society Wolfson Merit Award.

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Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5, Canada ,

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The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-0198, Japan ,

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Ladd, T., Jelezko, F., Laflamme, R. et al. Quantum computers. Nature 464 , 45–53 (2010). https://doi.org/10.1038/nature08812

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Get set for World Quantum Day 2024

Matin Durrani explains how you can join in the celebrations for the third World Quantum Day, which takes place on Sunday 14 April 2024

Sunday 14 April 2024 will be the third World Quantum Day . An annual celebration “promoting public awareness and understanding of quantum science and technology around the world”, it’s a bottom-up initiative from scientists in more than 65 nations from Algeria to Zambia. The day of 14 April has been chosen because “4.14” are the first three digits of Planck’s constant when rounded up: 4.14 × 10 –15 eVs.

The pedant in me is irked a bit by the date. Unless you live in the US, 14 April is surely 14.4 not 4.14. Plus, I’ve always known Planck’s constant as 6.63 × 10 –34 Js not 4.14 × 10 –15 eVs. Putting that aside, World Quantum Day is a brilliant initiative. These are great times for quantum physics, with burgeoning applications of “quantum 2.0” technology such as quantum computing, sensing and cryptography.

Can you solve this quantum cryptic word search?

As James McKenzie describes in his recent feature article , overall private investment in quantum tech stood at $1.2bn in 2023 according to the State of Quantum 2024 report. Sure, that figure has dropped sharply since 2022, but up to $50bn in public cash has already been ploughed into quantum science. In fact, 33 countries around the world have government initiatives in quantum technology, including 20 with full-scale national strategies.

One person with an overview of the quantum-technology landscape is Mauro Paternostro from Queens’ University Belfast, editor-in-chief of the IOP Publishing journal Quantum Science and Technology . In a wide-ranging interview to be published next week, he argues that the most advanced quantum technology is actually quantum sensing.

In fact, as Steve Brierley – chief executive of Riverlane – points out in his recent opinion article , quantum computers will only ever be properly useful once we can properly deal with error correction.

But quantum tech holds great promise, including in Africa, where “steady progress” is being made, according to Farai Mazhandu and Mhlambululi Mafu . Output from African researchers in quantum-related fields is relatively small, but with a young, digitally native population and a burgeoning quantum workforce, they believe the continent is “poised to take advantage of the coming ‘second quantum revolution’”.

If all this talk of technology is too much, check out the feature by Philip Ball , who looks at the work of “quantum plumbers”. Meanwhile, Robert P Crease, Jennifer Carter and Gino Elia examine “Wigner’s friend” – a quantum thought experiment that has stumped physicists and philosophers for more than 60 years. And why not try our quantum-physics cryptic word search and see if you can reveal the hidden message.

Finally, do check out the Physics World quantum channel as well as a special collection of quantum-themed research articles, focus issues and ebooks from IOP Publishing, which publishes Physics World .

And don’t forget to sign up for the first Physics World Live event – an online panel debate in partnership with Reports on Progress in Physics where you can hear from leading researchers, including Nicole Metje from the University of Birmingham in the UK, discuss the latest on quantum sensors.

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