Research in contemporary physics is emphasizing the development and evolution of computer systems to facilitate the calculations. Quantum computing is a branch of modern physics is believed promising results for the future, Thanks to the ability of qubits to store more information than a bit. The work of this paper focuses on the simulation of certain quantum algorithms such as the prisoner's dilemma in its quantum version using the MATHEMATICA® software and implementing stochastic version of the software MAPLE ® and the Grover search algorithm that simulates finding a needle in a haystack.
Research in contemporary physics is emphasizing the development and evolution of computer systems to facilitate the calculations. Quantum computing is a branch of modern physics is believed promising results for the future, Thanks to the ability of qubits to store more information than a bit. The work of this paper focuses on the simulation of certain quantum algorithms such as the prisoner's dilemma in its quantum version using the MATHEMATICA® software and implementing stochastic version of the software MAPLE ® and the Grover search algorithm that simulates finding a needle in a haystack.
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.
During the last decade, the field of quantum computation has attracted a lot of interest and motivated many theoretical and experimental studies of n -qubit quantum systems. But apart from the promise of more efficient quantum algorithms, these investigations also revealed a number of obstacles which still have to be overcome in practice. In this context, the use of simulation programs has proved to be an appropriate method. In order to facilitate the simulation of n -qubit quantum systems, we present the Feynman software program to provide the necessary tools to define and to deal with quantum registers as well as the operators acting on them. Using an interactive design within the framework of the computer algebra system Maple, we hope that the Feynman software program will be useful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future.
Abstract According to the Church-Turing Thesis, a Turing machine, and thus the programming languages and computers in existence, can simulate any reasonable computing device. However, there are physical devices that are exponentially more efficient than a Turing machine, and hence would prove exponentially difficult to simulate using such a machine. This chapter explores the concept of quantum computers and their potential not only to simulate quantum physics exponentially faster than classical computers but also to solve other problems exponentially faster. It considers algorithms that break cryptosystems, find needles in haystacks, and predict who can win a game. It first describes particles, waves, and amplitudes in quantum computation before turning to states and operators. It then examines how interference lets a quantum computer learn some things about a function, how quantum computers can solve factoring in polynomial time, the link between factoring and modern cryptography, graph isomorphism and the hidden subgroup problem, and quantum walks and scattering.
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 one of the very promising new fields of the new millennium for basic research in theoretical computer science and computational mathematics. Quantum computers have stimulated great interests due to their promise of being able to solve problems considered infeasible on current computers. From a computer scientist's and mathematician's point of view, the growth in the capacities of the underlying hardware is vital since an inefficient algorithm can solve the problem with the faster new hardware. For decades, this attitude was irrelevant but the deadline to change it is near. That is why quantum computation has led to rapid developments in physics, mathematics and computer science.This tutorial paper summarizes our year long series of multidisciplinary seminars on the topics of using computational algebra in quantum computation for finding new theoretical models for the upcoming generation of computers together with finding the models' computational abilities.
This work introduces an innovative approach from modeling to simulations, integrating quantum fuzzy interpretations, focusing on the expression of membership degrees in quantum circuits, interpreted as a unitary quantum transformation. Our research contrasts Quantum Fuzzy Computing with Classical Computing, particularly in the context of the prisoner's dilemma and parent-child relationships. Through the Qiskit framework, we conduct simulations, demonstrating the differences in results obtained by both approaches. Well-known fuzzy connectives, such as “exclusive or” and “arithmetic means”, provide an algebraic description for the corresponding composition of quantum operators and circuit representations. Thus, such algorithms can easily extend to model multiple agents' relationships, described by multidimensional quantum registers. The Qiskit simulations provide the structure for the algorithms' computation on the actual quantum platforms, indicating a promising direction for future research in this hybrid research area.