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IEEE Access

Quantum Computing Integrated Patterns for Real-Time Cryptography in Assorted Domains

Shally Nagpal, Shivani Gaba, Ishan Budhiraja, Meenakshi Sharma, Akansha Singh, Krishna Kant Singh, S. S. Aksar, Mohamed Abouhawwash, Celestine Iwendi

Published Jan 1, 2024• 15 citations
Publisher

Abstract

Quantum computers use quantum-mechanical phenomena for knowledge manipulation and depend on quantum bits or qubits. A qubit can be created in several different ways, and out of this, one way of creating a quantum state is by using superconductivity. They must be held very cold to work on these superconductive qubits for long periods. The key to information storage and manipulation is the skill of all computer systems. Current traditional computers handle single bits stored in binary states of 0 and 1 form. Every temperature factor inside the device may be updated; thus, quantum computers are more excellent than the vacuum of space at temperatures similar to absolute null. Consider how the dilution refrigerator of a quantum computer consisting of over 2000 components provides a cold atmosphere for the inside of the qubits. Researchers from all around the world today are using actual quantum processors for validating algorithms for different fields of operation. Yet quantum computation was a strictly speculative topic a couple of decades ago. Quantum cryptography, also known as quantum encoding, uses quantum mechanics principles to encrypt messages in a way nobody else reads. It benefits quantum states, along with its "theory of no transition," which means that it cannot be disrupted unknowingly. Quantum-improved AI calculations are especially applicable to the area. This work focuses on the implementation patterns of quantum computing in real-time cryptography so that the overall communication will be secured and integrity aware.

DOI
10.1109/access.2024.3401162

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A comprehensive survey for cryptography implementation using quantum computing

Zainab Salih Ageed, Subhi R. M. Zeebaree, Rowaida Khalil Ibrahim

Information is divided into two types: classical and quantum. Quantum computing, quantum cryptography, and quantum teleportation are just a few of the miracles they can do when working together. Some of the uses range from assisting in the prevention of spies reading private messages to assisting in the prevention of spies reading private communications. Quantum purification and quantum error correction are examples of techniques that will make their implementation easier. Although some of these concepts are still beyond present technological capabilities, quantum cryptography has been established. The possibilities for small-scale quantum computer device prototypes by the end of the millennium are promising. This paper is focusing on addressing the depended approaches which deal with implementation cryptography based on quantumcomputing. Remembering that cryptography is a method of encryption that uses the naturally occurring propertiesof quantum mechanics to secure and transmit data in a way that cannot be hacked. Cryptography is the process ofencrypting and protecting data so that only the person who has the right secret key can decrypt it. For decades now, quantum computing has been hailed as one of the next big revolutions. Quantum computing is not just fasterthan traditional computing methods, but a fundamentally different approach to solve seemingly intractable problems. The mathematical operations that most traditional cryptographic algorithms rely on could be cracked with a sufficiently strong quantum computer. This paper aims to explain how quantum computing affects currentcryptography and expose readers to fundamental post-quantum methods. Quantum computing’s influence on IT professionals is becoming increasingly important. As a result, we provide a straightforward introduction to post-quantum cryptography, including quantum-resistant algorithms and quantum key distribution.

AIP conference proceedings•Jan 1, 2024•2 citations

Quantum-Safe (Post-Quantum) Cryptography for Secure Network Infrastructures

Augustine Chidiebere Onuora, Taiwo Adisa Oyeniran, Trajkumar Yesuraj

Cryptography from ages have been designed and used to hide important information from people who they are not meant for. It refers to the art of concealment of information that only the person with right public key decodes or unzips the information for understanding. Due to the growing rise in quantum computers, Post quantum cryptography is now an important topic. This is not about updating or upgrading our normal cryptographic primitives but an architectural shift towards building systems that can without the sheer bruteforce of quantum computation. For one to fully understand why this shift is necessary, we need to look at it from a perceptive that reveals the current limitations of the current classical computers. The devices we use currently in our every day computation like laptops, phones, even the old desktop systems in our university labs, all operate using bits. The bit is either a zero ‘0’ or a one ‘1’ that represents a particular state of the computer like a rigid on or off switch, that means everything a classical computer does, from opening a file to running statistical analysis on data, is built from these two possible states. However, the case is different for a quantum computer. For quantum computers, they introduce a paradigm shift by utilizing the ‘Qubit’ which is a four-state superposition rather than the two-state position of the classical computer. Unlike classical bits that exist strictly as 0 or 1, a qubit can occupy a superposition of multiple states at the same time. Physically, qubits are implemented using real particles such as ions trapped in electromagnetic fields, neutral atoms, individual photons, or electrons confined inside semiconductor structures. These physical carriers are then integrated into quantum processors where they store, manipulate, and transmit quantum information. Simply put, while the classical bit is a single note, the Qubit is a symphony playing simultaneously. This four-state ability is what makes quantum computers potentially more powerful and also what makes our current classical cryptography vulnerable unless we replace them with post-quantum methods. This is why quantum-safe cryptography is essential for the safety of our computing and network infrastructure.

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Quantum computing represents a transformative advancement in computational power, with profound implications for cryptographic systems. This paper explores the intersection of quantum computing and cryptography, examining the potential for quantum computers to both break traditional cryptographic algorithms and enable new forms of secure communication. Classical cryptographic systems, such as RSA and ECC, rely on the computational difficulty of problems like integer factorization and discrete logarithms. However, quantum algorithms, notably Shor's algorithm, can solve these problems exponentially faster than the best-known classical algorithms, posing a significant threat to the security of current cryptographic practices. This vulnerability necessitates the development and implementation of quantum-resistant algorithms to ensure data security in a post-quantum world. The paper reviews the state-of-the-art in quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariate polynomial cryptography. These algorithms are analyzed for their security properties, efficiency, and practicality for real-world deployment. Additionally, the paper discusses the ongoing standardization efforts led by organizations such as NIST, which are crucial for establishing widely accepted quantum-safe cryptographic protocols. Beyond the threat posed by quantum computing, this paper also highlights the potential benefits quantum computing can bring to cryptographic systems. Quantum Key Distribution (QKD) is one such advancement, offering theoretically unbreakable encryption by leveraging the principles of quantum mechanics. QKD enables secure communication channels that are immune to any computational advances, including those of quantum computers, by ensuring that any attempt at eavesdropping can be detected. The practical implementation challenges of QKD and other quantum cryptographic protocols are also addressed, including issues related to transmission distance, error rates, and integration with existing communication infrastructures. Experimental results from recent QKD trials are presented, showcasing significant progress in extending the viability of quantum-secure communication over long distances. Furthermore, the paper delves into the hybrid approaches combining classical and quantum cryptographic techniques. These approaches aim to leverage the strengths of both paradigms to enhance security and performance. For instance, hybrid protocols might use classical encryption for bulk data transfer, supplemented by quantum techniques for key exchange, thereby ensuring robust security even against future quantum adversaries. In conclusion, while quantum computing poses substantial risks to existing cryptographic systems, it also offers novel opportunities for creating highly secure communication protocols. The transition to quantum-safe cryptography is imperative to protect sensitive information in the quantum era. This paper underscores the urgency of advancing quantum-resistant cryptographic research, promoting international collaboration for standardization, and exploring innovative applications of quantum technologies in cryptography. Continued research and development in these areas are essential to stay ahead of the evolving threat landscape and harness the full potential of quantum computing for secure communications.

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Quantum computing and the security of public key cryptography

Kai Li, Pei-Gen Yan, Qing-yu Cai

Compared with electronic computers, quantum parallelism has led to a significant increase in the computing power of quantum computers.However, the computing power of quantum computers will also be limited by the laws of physics, and hence there is no doubt that the computing power of quantum computers is not unlimited.For an algorithm, we need to consider both its space complexity and time complexity.This not only requires quantum computers to achieve large-scale integration, but also requires the quantum coherence time to be sufficiently long.If either of the above two conditions is not met, the task cannot be completed.Shor's algorithm [1] reduced the computational complexity of large integer factorization to the polynomial level.This complexity is of the same order as that of the encryption and decryption for the RSA public key cryptography protocol, which leads to the insecurity of the RSA in universal quantum computing.In addition, some other quantum algorithms show different kinds of enhanced speeds for solving different problems, such as the Grover's search algorithm [2] and its improved works [ 3 , 4 ], and the HHL algorithm [5] .With the remarkable computational power of these quantum algorithms, physicists have begun to seek suitable physical systems for the implementation of quantum computing.The implementation of quantum computing includes several basic technologies, such as preparation, precise control, measurement of the physical qubits, and construction of logical qubits.At present, there are many experimental candidate quantum computing platforms, including the superconducting system [6] , trapped ions system [7] , nitrogenvacancy centers in diamonds [8] , and ultra-cold atoms [9] .Recently, Google experimentally demonstrated quantum supremacy with a superconducting quantum computer [10] , thus placing the research on quantum computing at the forefront.With the booming development of quantum computing technology, the public key cryptosystem also needs to be updated periodically.Thus, cryptographers have to constantly look for public key protocols to resist quantum computing attacks, which leads to the emergence of postquantum cryptography.It is worth noting that although the name of post-quantum cryptography contains the word 'quantum', it essentially consists of protocols of classical cryptography.The current research on post-quantum cryptography mainly includes protocols based on the following four frameworks: the protocols based on Hash function, the pro- * Corresponding author.

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Post-Quantum Cryptography

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Quantum computers are a revolutionary technology based on the principles of quantum mechanics. Unlike conventional computers that work with binary bits (0 or 1), quantum devices use qubits that can exist in multiple states (“superpositions”) and interact with each other through the phenomenon of “quantum entanglement.” Thanks to this, quanta can greatly accelerate the solution of a number of important problems that were previously considered insurmountable for classical machines. This review describes the principles of operation of quantum computers, considers their unique advantages, and demonstrates the potential for their impact on the future of computer science and the technology industry.

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Nobel Symposium 141: Qubits for Future Quantum Information

T. Claeson, Per Delsing, Goran P. Wendin

Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics. Present technology is mainly based upon classical physics such as mechanics and electromagnetism. We now face a similar paradigm shift as was experienced two hundred years ago, at the time of the industrial revolution. Engineered construction of systems is currently increasingly based on quantum physics instead of classical physics, and quantum information is replacing much of classical communication. Quantum computing is one of the most exciting sub-fields of this revolution. Individual quantum systems can be used to store and process information. They are called quantum bits, or qubits for short. A quantum computer could eventually be constructed by combining a number of qubits that act coherently. Important computations can be performed much more quickly than by classical computers. However, while we control and measure a qubit, it must be sufficiently isolated from its environment to avoid noise that causes decoherence at the same time. Currently, low temperature is generally needed to obtain sufficiently long decoherence times. Single qubits of many different kinds can be built and manipulated; some research groups have managed to successfully couple qubits and perform rudimentary logic operations. However, the fundamental problems, such as decoherence, entanglement, quantum measurements and error correction, have yet to be solved. It has been predicted that quantum computers will be able to perform certain complicated computations or simulations in minutes or hours instead of years as with present computers. So far there exist very few useful quantum algorithms; however there is hope that the development of these will be stimulated once there is a breakthrough in hardware. Remarkable progress has been made in quantum engineering and quantum measurements, but a large scale quantum computer is still far off. Quantum communication and cryptography are much closer to the market than a quantum computer. The development of quantum information has meant a large push in the field of quantum physics, that previously could only be studied in the microscopic world. Artificial atoms, realized by circuit technology and mimicking the properties of 'natural' atoms, are one example of the new possibilities opened up by quantum engineering. Several different types of qubits have been suggested. Some are based upon microscopic entities, like atoms and ions in traps, or nuclear spins in molecules. They can have long coherence times (i.e. a long period allowing many operations, of the order of 10 000, to be performed before the state needs to be refreshed) but they are difficult to integrate into large systems. Other qubits are based upon solid state components that facilitate integration and coupling between qubits, but they suffer from interactions with the environment and their coherent states have a limited lifetime. Advanced experiments have been performed with superconducting Josephson junctions and many breakthroughs have been reported in the last few years. They have an advantage in the inherent coherence of superconducting Cooper pairs over macroscopic distances. We chose to focus the Nobel Symposium on Qubits for Future Quantum Information on superconducting qubits to allow for depth in discussions, but at the same time to allow comparison with other types of qubits that may prevail in the long run. The purpose of the symposium was to bring together leading researchers in adjoining fields. Often, microscopic qubits are considered at conferences within atomic, molecular and optical physics, while macroscopic ones belong to the solid state community. At the symposium, we experienced objective comparisons between different types of qubits—pros and cons as well as prospects. One example was the topic of quantum electrodynamics of superconducting circuits where qubits are coupled to a high- Q microwave resonator. This breakthrough technology was covered in several talks and was compared, in detail, with the corresponding case of light coupled to atoms in a cavity. A highlight was the presentation of how arbitrary photon states can be created in a cavity and the measurement of the corresponding Wigner functions. A Nobel Symposium provides an excellent opportunity to bring together a group of outstanding scientists for a stimulating exchange of ideas and results. The present symposium took place in Gothenburg, 25–28 May 2009. In order to allow local researchers and students to get a feeling of what is happening in the field, the first day of the symposium was held at the Chalmers campus. The remaining three days were spent at the mansion built by William Chalmers, the benefactor behind Chalmers University of Technology. Thirty-three speakers gave popular lectures open to the general public, overviews of different types of qubits, quantum phenomena, and quantum computing requirements, as well as specialized contributions in six sessions, and ten posters were displayed. The list of participants, program, abstracts and summaries of presentations is given at www.chalmers.se/mc2/EN/nobel-symposium-2009 . In order to encourage constructive interactions and discussions, ample time was given to extensive critical discussions and to individual meetings in relaxing and stimulating environments. Questions and discussions followed all talks but longer, more extensive, discussions of about one hour ended each session. These discussions were initiated by a special questioner (a kind of 'devil's advocate'). Receptions were given by the President of Chalmers and by the City of Gothenburg. The participants also sailed with SS Bohuslän in the archipelago outside the city. The symposium was sponsored by the Nobel Foundation through its Nobel Symposium Committee and was organized by Thilo Bauch, Tord Claeson, Per Delsing, Ann-Marie Frykestig, Eva Hellberg, Göran Johansson, Göoran Wendin, and Chris Wilson. Special thanks are given to the program committee: John Clarke, Daniel Estève, Steve Girvin, Anne l'Huillier, Anthony Leggett, and Mikko Paalanen. The editor of the proceedings is Göran Johansson.

Physica Scripta•Dec 1, 2009•0 citations
Quantum computers use quantum-mechanical phenomena for knowledge manipulation and depend on quantum bits or qubits. A qubit can be created in several different ways, and out of this, one way of creating a quantum state is by using superconductivity. They must be held very cold to work on these superconductive qubits for long periods. The key to information storage and manipulation is the skill of all computer systems. Current traditional computers handle single bits stored in binary states of 0 and 1 form. Every temperature factor inside the device may be updated; thus, quantum computers are more excellent than the vacuum of space at temperatures similar to absolute null. Consider how the dilution refrigerator of a quantum computer consisting of over 2000 components provides a cold atmosphere for the inside of the qubits. Researchers from all around the world today are using actual quantum processors for validating algorithms for different fields of operation. Yet quantum computation was a strictly speculative topic a couple of decades ago. Quantum cryptography, also known as quantum encoding, uses quantum mechanics principles to encrypt messages in a way nobody else reads. It benefits quantum states, along with its "theory of no transition," which means that it cannot be disrupted unknowingly. Quantum-improved AI calculations are especially applicable to the area. This work focuses on the implementation patterns of quantum computing in real-time cryptography so that the overall communication will be secured and integrity aware.
Information is divided into two types: classical and quantum. Quantum computing, quantum cryptography, and quantum teleportation are just a few of the miracles they can do when working together. Some of the uses range from assisting in the prevention of spies reading private messages to assisting in the prevention of spies reading private communications. Quantum purification and quantum error correction are examples of techniques that will make their implementation easier. Although some of these concepts are still beyond present technological capabilities, quantum cryptography has been established. The possibilities for small-scale quantum computer device prototypes by the end of the millennium are promising. This paper is focusing on addressing the depended approaches which deal with implementation cryptography based on quantumcomputing. Remembering that cryptography is a method of encryption that uses the naturally occurring propertiesof quantum mechanics to secure and transmit data in a way that cannot be hacked. Cryptography is the process ofencrypting and protecting data so that only the person who has the right secret key can decrypt it. For decades now, quantum computing has been hailed as one of the next big revolutions. Quantum computing is not just fasterthan traditional computing methods, but a fundamentally different approach to solve seemingly intractable problems. The mathematical operations that most traditional cryptographic algorithms rely on could be cracked with a sufficiently strong quantum computer. This paper aims to explain how quantum computing affects currentcryptography and expose readers to fundamental post-quantum methods. Quantum computing’s influence on IT professionals is becoming increasingly important. As a result, we provide a straightforward introduction to post-quantum cryptography, including quantum-resistant algorithms and quantum key distribution.
Cryptography from ages have been designed and used to hide important information from people who they are not meant for. It refers to the art of concealment of information that only the person with right public key decodes or unzips the information for understanding. Due to the growing rise in quantum computers, Post quantum cryptography is now an important topic. This is not about updating or upgrading our normal cryptographic primitives but an architectural shift towards building systems that can without the sheer bruteforce of quantum computation. For one to fully understand why this shift is necessary, we need to look at it from a perceptive that reveals the current limitations of the current classical computers. The devices we use currently in our every day computation like laptops, phones, even the old desktop systems in our university labs, all operate using bits. The bit is either a zero ‘0’ or a one ‘1’ that represents a particular state of the computer like a rigid on or off switch, that means everything a classical computer does, from opening a file to running statistical analysis on data, is built from these two possible states. However, the case is different for a quantum computer. For quantum computers, they introduce a paradigm shift by utilizing the ‘Qubit’ which is a four-state superposition rather than the two-state position of the classical computer. Unlike classical bits that exist strictly as 0 or 1, a qubit can occupy a superposition of multiple states at the same time. Physically, qubits are implemented using real particles such as ions trapped in electromagnetic fields, neutral atoms, individual photons, or electrons confined inside semiconductor structures. These physical carriers are then integrated into quantum processors where they store, manipulate, and transmit quantum information. Simply put, while the classical bit is a single note, the Qubit is a symphony playing simultaneously. This four-state ability is what makes quantum computers potentially more powerful and also what makes our current classical cryptography vulnerable unless we replace them with post-quantum methods. This is why quantum-safe cryptography is essential for the safety of our computing and network infrastructure.
Quantum computing represents a transformative advancement in computational power, with profound implications for cryptographic systems. This paper explores the intersection of quantum computing and cryptography, examining the potential for quantum computers to both break traditional cryptographic algorithms and enable new forms of secure communication. Classical cryptographic systems, such as RSA and ECC, rely on the computational difficulty of problems like integer factorization and discrete logarithms. However, quantum algorithms, notably Shor's algorithm, can solve these problems exponentially faster than the best-known classical algorithms, posing a significant threat to the security of current cryptographic practices. This vulnerability necessitates the development and implementation of quantum-resistant algorithms to ensure data security in a post-quantum world. The paper reviews the state-of-the-art in quantum-resistant cryptographic algorithms, including lattice-based, hash-based, code-based, and multivariate polynomial cryptography. These algorithms are analyzed for their security properties, efficiency, and practicality for real-world deployment. Additionally, the paper discusses the ongoing standardization efforts led by organizations such as NIST, which are crucial for establishing widely accepted quantum-safe cryptographic protocols. Beyond the threat posed by quantum computing, this paper also highlights the potential benefits quantum computing can bring to cryptographic systems. Quantum Key Distribution (QKD) is one such advancement, offering theoretically unbreakable encryption by leveraging the principles of quantum mechanics. QKD enables secure communication channels that are immune to any computational advances, including those of quantum computers, by ensuring that any attempt at eavesdropping can be detected. The practical implementation challenges of QKD and other quantum cryptographic protocols are also addressed, including issues related to transmission distance, error rates, and integration with existing communication infrastructures. Experimental results from recent QKD trials are presented, showcasing significant progress in extending the viability of quantum-secure communication over long distances. Furthermore, the paper delves into the hybrid approaches combining classical and quantum cryptographic techniques. These approaches aim to leverage the strengths of both paradigms to enhance security and performance. For instance, hybrid protocols might use classical encryption for bulk data transfer, supplemented by quantum techniques for key exchange, thereby ensuring robust security even against future quantum adversaries. In conclusion, while quantum computing poses substantial risks to existing cryptographic systems, it also offers novel opportunities for creating highly secure communication protocols. The transition to quantum-safe cryptography is imperative to protect sensitive information in the quantum era. This paper underscores the urgency of advancing quantum-resistant cryptographic research, promoting international collaboration for standardization, and exploring innovative applications of quantum technologies in cryptography. Continued research and development in these areas are essential to stay ahead of the evolving threat landscape and harness the full potential of quantum computing for secure communications.
Compared with electronic computers, quantum parallelism has led to a significant increase in the computing power of quantum computers.However, the computing power of quantum computers will also be limited by the laws of physics, and hence there is no doubt that the computing power of quantum computers is not unlimited.For an algorithm, we need to consider both its space complexity and time complexity.This not only requires quantum computers to achieve large-scale integration, but also requires the quantum coherence time to be sufficiently long.If either of the above two conditions is not met, the task cannot be completed.Shor's algorithm [1] reduced the computational complexity of large integer factorization to the polynomial level.This complexity is of the same order as that of the encryption and decryption for the RSA public key cryptography protocol, which leads to the insecurity of the RSA in universal quantum computing.In addition, some other quantum algorithms show different kinds of enhanced speeds for solving different problems, such as the Grover's search algorithm [2] and its improved works [ 3 , 4 ], and the HHL algorithm [5] .With the remarkable computational power of these quantum algorithms, physicists have begun to seek suitable physical systems for the implementation of quantum computing.The implementation of quantum computing includes several basic technologies, such as preparation, precise control, measurement of the physical qubits, and construction of logical qubits.At present, there are many experimental candidate quantum computing platforms, including the superconducting system [6] , trapped ions system [7] , nitrogenvacancy centers in diamonds [8] , and ultra-cold atoms [9] .Recently, Google experimentally demonstrated quantum supremacy with a superconducting quantum computer [10] , thus placing the research on quantum computing at the forefront.With the booming development of quantum computing technology, the public key cryptosystem also needs to be updated periodically.Thus, cryptographers have to constantly look for public key protocols to resist quantum computing attacks, which leads to the emergence of postquantum cryptography.It is worth noting that although the name of post-quantum cryptography contains the word 'quantum', it essentially consists of protocols of classical cryptography.The current research on post-quantum cryptography mainly includes protocols based on the following four frameworks: the protocols based on Hash function, the pro- * Corresponding author.
Quantum computers are a revolutionary technology based on the principles of quantum mechanics. Unlike conventional computers that work with binary bits (0 or 1), quantum devices use qubits that can exist in multiple states (“superpositions”) and interact with each other through the phenomenon of “quantum entanglement.” Thanks to this, quanta can greatly accelerate the solution of a number of important problems that were previously considered insurmountable for classical machines. This review describes the principles of operation of quantum computers, considers their unique advantages, and demonstrates the potential for their impact on the future of computer science and the technology industry.
Quantum mechanics is the most ground-breaking and fascinating theoretical concept developed in physics during the past century. Much of our present understanding of the microscopic world and its extension into the macroscopic world, including modern technical applications, is based upon quantum mechanics. We have experienced a remarkable development of information and communication technology during the past two decades, to a large extent depending upon successful fabrication of smaller and smaller components and circuits. However, we are finally approaching the physical limits of component miniaturization as we enter a microscopic world ruled by quantum mechanics. Present technology is mainly based upon classical physics such as mechanics and electromagnetism. We now face a similar paradigm shift as was experienced two hundred years ago, at the time of the industrial revolution. Engineered construction of systems is currently increasingly based on quantum physics instead of classical physics, and quantum information is replacing much of classical communication. Quantum computing is one of the most exciting sub-fields of this revolution. Individual quantum systems can be used to store and process information. They are called quantum bits, or qubits for short. A quantum computer could eventually be constructed by combining a number of qubits that act coherently. Important computations can be performed much more quickly than by classical computers. However, while we control and measure a qubit, it must be sufficiently isolated from its environment to avoid noise that causes decoherence at the same time. Currently, low temperature is generally needed to obtain sufficiently long decoherence times. Single qubits of many different kinds can be built and manipulated; some research groups have managed to successfully couple qubits and perform rudimentary logic operations. However, the fundamental problems, such as decoherence, entanglement, quantum measurements and error correction, have yet to be solved. It has been predicted that quantum computers will be able to perform certain complicated computations or simulations in minutes or hours instead of years as with present computers. So far there exist very few useful quantum algorithms; however there is hope that the development of these will be stimulated once there is a breakthrough in hardware. Remarkable progress has been made in quantum engineering and quantum measurements, but a large scale quantum computer is still far off. Quantum communication and cryptography are much closer to the market than a quantum computer. The development of quantum information has meant a large push in the field of quantum physics, that previously could only be studied in the microscopic world. Artificial atoms, realized by circuit technology and mimicking the properties of 'natural' atoms, are one example of the new possibilities opened up by quantum engineering. Several different types of qubits have been suggested. Some are based upon microscopic entities, like atoms and ions in traps, or nuclear spins in molecules. They can have long coherence times (i.e. a long period allowing many operations, of the order of 10 000, to be performed before the state needs to be refreshed) but they are difficult to integrate into large systems. Other qubits are based upon solid state components that facilitate integration and coupling between qubits, but they suffer from interactions with the environment and their coherent states have a limited lifetime. Advanced experiments have been performed with superconducting Josephson junctions and many breakthroughs have been reported in the last few years. They have an advantage in the inherent coherence of superconducting Cooper pairs over macroscopic distances. We chose to focus the Nobel Symposium on Qubits for Future Quantum Information on superconducting qubits to allow for depth in discussions, but at the same time to allow comparison with other types of qubits that may prevail in the long run. The purpose of the symposium was to bring together leading researchers in adjoining fields. Often, microscopic qubits are considered at conferences within atomic, molecular and optical physics, while macroscopic ones belong to the solid state community. At the symposium, we experienced objective comparisons between different types of qubits—pros and cons as well as prospects. One example was the topic of quantum electrodynamics of superconducting circuits where qubits are coupled to a high- Q microwave resonator. This breakthrough technology was covered in several talks and was compared, in detail, with the corresponding case of light coupled to atoms in a cavity. A highlight was the presentation of how arbitrary photon states can be created in a cavity and the measurement of the corresponding Wigner functions. A Nobel Symposium provides an excellent opportunity to bring together a group of outstanding scientists for a stimulating exchange of ideas and results. The present symposium took place in Gothenburg, 25–28 May 2009. In order to allow local researchers and students to get a feeling of what is happening in the field, the first day of the symposium was held at the Chalmers campus. The remaining three days were spent at the mansion built by William Chalmers, the benefactor behind Chalmers University of Technology. Thirty-three speakers gave popular lectures open to the general public, overviews of different types of qubits, quantum phenomena, and quantum computing requirements, as well as specialized contributions in six sessions, and ten posters were displayed. The list of participants, program, abstracts and summaries of presentations is given at www.chalmers.se/mc2/EN/nobel-symposium-2009 . In order to encourage constructive interactions and discussions, ample time was given to extensive critical discussions and to individual meetings in relaxing and stimulating environments. Questions and discussions followed all talks but longer, more extensive, discussions of about one hour ended each session. These discussions were initiated by a special questioner (a kind of 'devil's advocate'). Receptions were given by the President of Chalmers and by the City of Gothenburg. The participants also sailed with SS Bohuslän in the archipelago outside the city. The symposium was sponsored by the Nobel Foundation through its Nobel Symposium Committee and was organized by Thilo Bauch, Tord Claeson, Per Delsing, Ann-Marie Frykestig, Eva Hellberg, Göran Johansson, Göoran Wendin, and Chris Wilson. Special thanks are given to the program committee: John Clarke, Daniel Estève, Steve Girvin, Anne l'Huillier, Anthony Leggett, and Mikko Paalanen. The editor of the proceedings is Göran Johansson.