Quantum Computing is widely perceived to be one of the ways forward in the future of computation as the end of Moore’s law is almost here. Instead of using bits in classical computers, quantum computers manipulate qubits which are governed by the phenomena of superposition and entanglement. In this paper, we demonstrate the relevance of quantum computing in game theory and database search applications. Through a simple example of coin tossing, we show how it is possible to organise a game where one player adopting a quantum strategy is guaranteed to win. It is also shown that the other player, using a second coin (qubit), can subvert this action to award the wins to themselves without the first player’s knowledge. In another application, a modified Grover’s database search algorithm is applied to clone an arbitrary quantum state of a qubit to a duplicate qubit. In both cases, the comparison of simulated and actual results emphasises on the hardware limitations of the current error-prone quantum computers. The quantum computer programs are designed using quantum gates and simulated in the Quantum Information Software Kit before testing on the IBM Q 5.1 (ibmqx4) quantum computer.
Quantum Computing is widely perceived to be one of the ways forward in the future of computation as the end of Moore’s law is almost here. Instead of using bits in classical computers, quantum computers manipulate qubits which are governed by the phenomena of superposition and entanglement. In this paper, we demonstrate the relevance of quantum computing in game theory and database search applications. Through a simple example of coin tossing, we show how it is possible to organise a game where one player adopting a quantum strategy is guaranteed to win. It is also shown that the other player, using a second coin (qubit), can subvert this action to award the wins to themselves without the first player’s knowledge. In another application, a modified Grover’s database search algorithm is applied to clone an arbitrary quantum state of a qubit to a duplicate qubit. In both cases, the comparison of simulated and actual results emphasises on the hardware limitations of the current error-prone quantum computers. The quantum computer programs are designed using quantum gates and simulated in the Quantum Information Software Kit before testing on the IBM Q 5.1 (ibmqx4) quantum computer.
Quantum computing is an emerging form of computing that uses the rules of quantum physics to process information in ways that are far different from how computers do it now. Quantum computing uses quantum bits, or qubits, which can exist in superpositions of states and get entangled with each other, which is different from classical computing, which uses a bit that represents binary values (0 or 1). These characteristics allow quantum devices to execute parallel computations, enabling significant speedups for specific categories of problems considered intractable for classical machines. This chapter gives a thorough introduction to quantum computing, starting with a historical overview of its foundations in quantum physics and significant theoretical advancements. It analyzes fundamental ideas including superposition, entanglement, quantum interference, and the no-cloning theorem, explaining how these elements distinguish quantum computation from traditional approaches. The advancement of quantum hardware is examined through several architectures, trapped ions, superconducting circuits, photonics, and topological qubits, together with software frameworks like Qiskit, Cirq, and PennyLane, which support algorithm development and simulation. The chapter examines fundamental quantum algorithms, such as Grover’s algorithm for database search, Shor’s algorithm for integer factorization, and hybrid variational methods designed for noisy intermediate-scale quantum devices. The practical applications in domains including as encryption, optimization, machine learning, chemistry, and finance emphasize the real-world significance of quantum technology. Challenges like decoherence, noise, scalability, and algorithmic maturity are rigorously analyzed, followed by an anticipated discourse on future trajectories including fault-tolerant architectures, quantum networking, and the development of quantum cloud services. This chapter presents a fundamental introduction for students, researchers, and practitioners seeking to comprehend the essential principles, functionalities, and possibilities of quantum computing in the post–Moore’s law period.
Quantum computing is based on the exploitation of quantum effects to perform some important computations more efficiently than ever possible on classical computers. Well known quantum algorithms are Shors polynomial time factoring algorithm and Grovers data base search scheme. Their potential is due to the parallelism of a quantum computation increasing exponentially with the size of the computing device. IBM has succeeded in building a first working quantum computing device with up to 7 qubits based on NMR technology, however, the construction of large multi-qubit systems appears to become extremely difficult due to the loss of coherence of the quantum states. Like the design process of modern microprocessors which is carried out by means of sophisticated software, modelling and simulation of the entire QC device is even more relevant. Simulation is required in order to understand the functioning of quantum algorithms, to construct novel quantum algorithms, to write quantum programs, to teach quantum computing, to construct real quantum computers, to understand and fight de-coherence and to understand and control the influence of the environment. Since quantum parallelism increases exponentially with the size of the quantum computer, parallel supercomputers are required for realistic simulations. I intend to give an introduction into the simulation of quantum computers using conventional computers. The simulation is based on a generic physical model of quantum computer hardware. Issues like parallel gate level simulators, modelling of QCs, simulators for physical quantum computers are addressed.
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.
Quantum computation is a part of quantum information theory. By using quantum mechanical phenomena it is possible to speed up the solving of some problems with quantum algorithms over classical probabilistic algorithms. In some cases quantum algorithms can utilise quantum parallelism in order to speed up problem solving. In this thesis experiments on IBM quantum computers are compared with ideal error free simulations. In the first part quantum teleportation is shown in practice, similarly the performance of Deutsch–Jozsa, Bernstein–Vazirani, Simon’s and Grover’s search algorithms are shown in action on IBM quantum computers and each is compared against an ideal simulation. The last experiment shows how the binary success probability of an unsharp measurement using Lüders instrument can be improved by adding sequential measurements by using an ideal simulation and a simulation using simple noise model.
Early researchers attempting to simulate complex quantum mechanical interactions on digital computers discovered that they very quickly consumed the computers’ available memory\nresources, because the state space of a quantum system typically grows exponentially with problem size. Consequently, Richard Feynman proposed in 1982 that perhaps the only way to simulate complex quantum mechanical situations was by simulating them on some quantum mechanical system. Quantum computers attempt to exploit this idea incorporating the special properties of quantum mechanics, such as the superposition of states and entanglement, into a computing device. Two key algorithms have been discovered which would run on this new type of computer, Shor’s factorization algorithm discovered in 1994, which provides an exponential speedup over classical algorithms and Grover’s search algorithm in 1996, which provides a quadratic speedup. Following this in 1999 Meyer initiated the field of quantum game theory by introducing quantum mechanical states into the framework of classical game theory. In this thesis, we firstly investigate the phase estimation procedure, due to its importance as the basis for Shor’s factorization algorithm, for which a new error formula is found using an improved symmetrical definition of the error. Unlike other existing error formulas which require approximations in their derivation, our result is obtained analytically. The work on the phase estimation procedure then motivates the development of computer software written in the Java programming language, which can simulate the common algorithms and visually display their behavior on a circuit board type layout. The software is found useful in verifying the new error formula described above and to test ideas for new algorithms. Being written in Java, it is envisaged that it could be placed online and used as a learning tool for new students to the field. We then investigate the second key algorithm of quantum computing, the Grover search algorithm. It is already known that the Grover search is an SU(2) rotation but the idea is extended by deriving the three generators in terms of the two non-orthogonal basis vectors, representing the solution and initial states. We then demonstrate that the Grover search is equivalent to the precession of the polarization axis of a spin- 1/2 particle in a magnetic field. At this point we introduce geometric algebra (GA), because of its efficient implementation of rotations and its associated visual representation, and hence ideal to describe the Grover search process. It was found to provide a simple algebraic solution to the exact Grover search problem as well providing a simple visual picture describing the general solution to Meyer’s quantum penny flip game, which is a simple two-player quantum game based on the manipulation of a single qubit and hence closely analogous to the Grover search process. We then extend the work on quantum games developing two-player, three-player and N player quantum games in the context of an EPR type experiment, which has the advantage of providing a sound physical basis to quantum games avoiding the common criticism of other quantum game frameworks regarding the proper embedding of the classical game. Using the algebraic approach of GA, we solve the general N player game, without requiring the use of matrices which become unworkable for large N. Games based on non-factorisable joint probabilities were then also developed which provided a more general framework for both classical and quantum games, and allows the field of quantum games to be accessible to nonphysicists, as it does not employ Dirac’s bra-ket notation. In summary, several new results in the field of Quantum computing were produced, including an improved error formula for phase estimation [JMCL11b], a general solution to Meyer’s quantum penny flip game [CILVS09] and a paper producing quantum games from non-factorisable joint probabilities [CIA10], as well as an EPR framework for quantum games [JMCL11a], refer attached papers.
Quantum computing performs computations by tapping the very laws that govern quantum mechanics, thereby making those computations far more efficient than does a classical computer. Quantum computers, through qubits and quantum phenomena like superposition, entanglement, and interference, will be able to solve some complex problems in cryptography, chemistry, optimization, and others. This paper discusses core principles and historical development, theoretical foundations of quantum computing, practical implications, and current challenges. However, as research progresses, quantum computing would change the face of technology, science, and industry.