In this talk, we examine potential developments in the field of computing.Recall that Computer Science is defined as the science of algorithms.The development of Computer Science and its applications have relied on two cornerstones: Mathematical logic and semiconductor technology.Computing, i.e., execution of an algorithm, is a process of evaluating a logical expression.Thanks to semiconductor technology, logical operations can be implemented in a substantial manner with high density, high reliability, and low cost.Based on these two cornerstones, the complexity theory has been the major theoretical development of Computer Science.According to this theory, computing problems can be classified as "easy" and "hard".Easy ones are those in which the computation time is bounded by a polynomial of input size.Most computing applications today are in this category.In the future, we must focus on hard problems.One approach is to use nonsemiconductor-based physical devices; initial work in quantum computers would fall within this category.Another approach is to develop heuristic algorithms with much lower complexity; this is very much an objective of "Artificial Intelligence" development.The third approach is to leverage properties inherently embedded in input data, which calls for the development of Data Science.
In this talk, we examine potential developments in the field of computing.Recall that Computer Science is defined as the science of algorithms.The development of Computer Science and its applications have relied on two cornerstones: Mathematical logic and semiconductor technology.Computing, i.e., execution of an algorithm, is a process of evaluating a logical expression.Thanks to semiconductor technology, logical operations can be implemented in a substantial manner with high density, high reliability, and low cost.Based on these two cornerstones, the complexity theory has been the major theoretical development of Computer Science.According to this theory, computing problems can be classified as "easy" and "hard".Easy ones are those in which the computation time is bounded by a polynomial of input size.Most computing applications today are in this category.In the future, we must focus on hard problems.One approach is to use nonsemiconductor-based physical devices; initial work in quantum computers would fall within this category.Another approach is to develop heuristic algorithms with much lower complexity; this is very much an objective of "Artificial Intelligence" development.The third approach is to leverage properties inherently embedded in input data, which calls for the development of Data Science.
Computer science and physics have been closely linked since the birth of modern computing. This book is about that link. John von Neumann’s original design for digital computing in the 1940s was motivated by applications in ballistics and hydrodynamics, and his model still underlies today’s hardware architectures. Within several years of the invention of the first digital computers, the Monte Carlo method was developed, putting these devices to work simulating natural processes using the principles of statistical physics. It is difficult to imagine how computing might have evolved without the physical insights that nurtured it. It is impossible to imagine how physics would have evolved without computation. While digital computers quickly became indispensable, a true theoretical understanding of the efficiency of the computation process did not occur until twenty years later. In 1965, Hartmanis and Stearns [227] as well as Edmonds [139, 140] articulated the notion of computational complexity, categorizing algorithms according to how rapidly their time and space requirements grow with input size. The qualitative distinctions that computational complexity draws between algorithms form the foundation of theoretical computer science. Chief among these distinctions is that of polynomial versus exponential time. A combinatorial problem belongs in the complexity class P (polynomial time) if there exists an algorithm guaranteeing a solution in a computation time, or number of elementary steps of the algorithm, that grows at most polynomially with input size. Loosely speaking, such problems are considered computationally feasible. An example might be sorting a list of n numbers: even a particularly naive and inefficient algorithm for this will run in a number of steps that grows as O(n2), and so sorting is in the class P. A problem belongs in the complexity class NP (non-deterministic polynomial time) if it is merely possible to test, in polynomial time, whether a specific presumed solution is correct. Of course, P ⊆ NP: for any problem whose solution can be found in polynomial time, one can surely verify the validity of a presumed solution in polynomial time.
Quantum computing represents a revolutionary leap in computational power, leveraging the principles of quantum mechanics to process information in fundamentally new ways. Unlike classical computers, which use bits to represent data as 0s or 1s, quantum computers use quantum bits or qubits, enabling the phenomena of superposition and entanglement to perform complex calculations more efficiently (Nielsen & Chuang, 2010). This article explores the basic principles of quantum computing, the different models and algorithms that have been developed, and the current state of quantum hardware. The power of quantum computing lies in its ability to solve certain types of problems exponentially faster than classical computers. For instance, Shor's algorithm can factorize large integers in polynomial time, posing a significant threat to classical encryption methods (Shor, 1997). Similarly, Grover's algorithm provides a quadratic speedup for unstructured search problems, showcasing the potential for dramatic improvements in database search capabilities (Grover, 1996). These algorithms exemplify how quantum computing can revolutionize fields that rely on complex computations. Quantum hardware, however, is still in its nascent stage, with significant challenges to be overcome. Current quantum computers, such as those developed by IBM and Google, have demonstrated quantum supremacy but are limited by issues of qubit coherence and error rates (Arute et al., 2019). Quantum error correction and the development of more stable qubit technologies are critical areas of ongoing research (Preskill, 2018). Despite these challenges, recent advancements in quantum hardware and algorithms continue to drive the field forward, promising transformative impacts on industries such as cryptography, drug discovery, and artificial intelligence. As quantum computing continues to advance, it holds the promise of solving problems that are currently intractable for classical computers, paving the way for unprecedented technological and scientific advancements (Shor, 1997; Grover, 1996). This article provides a comprehensive overview of the current landscape of quantum computing, discussing its foundational principles, key algorithms, hardware challenges, and potential applications. By understanding these aspects, we can better appreciate the profound implications of quantum computing for the future of technology and science.
In 1981, Richard Feynman proposed a device called a "quantum computer" to take advantage of the laws of quantum physics to achieve computational speed-ups over classical methods. Quantum computing promises to revolutionize how and what we compute. Over the course of three decades, quantum algorithms have been developed that offer fast solutions to problems in a variety of fields including number theory, optimization, chemistry, physics, and materials science. Quantum devices have also significantly advanced such that components of a scalable quantum computer have been demonstrated; the promise of implementing quantum algorithms is in our near future. I will attempt to explain some of the mysteries of this disruptive, revolutionary computational paradigm and how it will transform our digital age.
In the computer based solutions of the problems in today's world; if the problem has a high complexity value, different requirements can be addressed such as necessity of simultaneous operation of many computers, the long processing times for the operation of algorithms, and computers with hardware features that can provide high performance. For this reason, it is inevitable to use a computer based on quantum physics in the near future in order to make today's cryptosystems unsafe, search the servers and other information storage centers on internet very quickly, solve optimization problems in the NP-hard category with a very wide solution space and analyze information on large-scale data processing and to process high-resolution image for artificial intelligence applications. In this study, an examination of quantum approaches and quantum computers, which will be widely used in the near future, was carried out and the areas in which such innovation can be used was evaluated. Malicious or non-malicious use of quantum computers with this capacity, the advantages and disadvantages of the high performance which it provides were examined under the head of security, the effect of this recent technology on the existing security systems was investigated.
Quantum physics is a fascinating area from a computational viewpoint. The features that make quantum systems prohibitively hard to simulate classically are precisely the aspects exploited by quantum computation to obtain exponential speedups over classical computers. In this talk I will survey our current understanding of the power (and limits) of quantum computers, and prospects for experimentally realizing them in the near future. I will also touch upon insights from quantum comuptation that have resulted in new classical algorithms for efficient simulation of certain important quantum systems.
Current cryptographic solutions used in information technologies today like Transport Layer Security utilize algorithms with underlying computationally difficult problems to solve. With the ongoing research and development of quantum computers, these same computationally difficult problems become solvable within reasonable (polynomial) time. The emergence of large-scale quantum computers would put the integrity and confidentiality of today’s data in jeopardy. It then becomes urgent to develop, implement, and test a new suite of cybersecurity measures against attacks from a quantum computer. This paper explores, understands, and evaluates this new category of cryptosystems as well as the many tradeoffs among them. All the algorithms submitted to the National Institute of Standards and Technology (NIST) for standardization can be categorized into three major categories, each relating to the new underlying hard problem: namely error code correcting, algebraic lattices (including ring learning with errors), and supersingular isogenies. These new mathematical hard problems have shown to be resistant to the same type of quantum attack. Utilizing hardware clock cycle registers, the work sets up the benchmarks of the four Round 3 NIST algorithms in two environments: cloud computing and embedded system. As expected, there are many tradeoffs and advantages in each algorithm for applications. Saber and Kyber are exceedingly fast but have larger ciphertext size for transmission over a wire. McEliece key size and key generation are the largest drawbacks but having the smallest ciphertext size and only slightly decreased performance allow a use case where key reuse is prioritized. NTRU finds a middle ground in these tradeoffs, being better than McEliece performance wise and better than Kyber and Saber in ciphertext size allows for a use case of highly varied environments, which need to value speed and ciphertext size equally. Going forward, the benchmarking system developed could be applied to digital signature, another vital aspect to a cryptosystem.