Quantum mechanics arose out of the question "Is light a particle or a wave?" and has laid forth a model of reality in which particles are modeled by wave functions. The particle is in a superposition of states and can be entangled with other particles to create more complex systems. Observation of the system collapses the wave function to a single point. By using quantum gates, we can manipulate these particles to create algorithms to solve computational problems. Quantum computing does not collapse the complexity hierarchy by providing an across the board exponential speedup but can provide such a speedup for certain problems using algorithms that are specifically tailored to the nature of the problem, most notable Shor’s algorithm for integer factorization. Presented at the National Collegiate Research Conference at Harvard University, January 2023.
Quantum mechanics arose out of the question "Is light a particle or a wave?" and has laid forth a model of reality in which particles are modeled by wave functions. The particle is in a superposition of states and can be entangled with other particles to create more complex systems. Observation of the system collapses the wave function to a single point. By using quantum gates, we can manipulate these particles to create algorithms to solve computational problems. Quantum computing does not collapse the complexity hierarchy by providing an across the board exponential speedup but can provide such a speedup for certain problems using algorithms that are specifically tailored to the nature of the problem, most notable Shor’s algorithm for integer factorization. Presented at the National Collegiate Research Conference at Harvard University, January 2023.
Quantum machines, grounded in the principles of quantum mechanics, harness the extraordinary computational power derived from quantum bits (qubits), contrasting with classical machines reliant on classical bits. Qubits, distinguished by properties like superposition and entanglement, empower quantum algorithms to solve intricate problems with exponential speedup. Quantum states, fundamental to quantum mechanics, serve as descriptors for quantum systems, laying the foundation for subsequent calculations. Quantum gates, unitary operators manipulating qubits, are pivotal in quantum computing, extending beyond single-particle systems to encompass multi-particle scenarios. This flexibility finds applications in quantum simulation, optimization, cryptography, machine learning, and more. Quantum computing’s potential to revolutionize fields arises from its ability to tackle computationally intractable problems. Applications span quantum simulation, optimization, cryptography, machine learning, chemistry, materials science, financial modeling, and transportation. quantum protocols, including communication and cryptography, leverage unique quantum properties. Prominent quantum algorithms, such as Deutsch-Jozsa, Bernstein-Vazirani, Grover’s, and Shor’s, exploit qubit features for efficient problem-solving. These algorithms harness superposition and entanglement, allowing parallel calculations across multiple possibilities. In the landscape of quantum computing, the interplay of quantum bits, gates, states, and algorithms showcases the potential for transformative advances in computation.
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 has teased scientific imagination ever since Richard Feynman dreamed in 1982 of quantum-mechanical computers, which could solve problems that are effectively out of reach of classical computation thanks to their ability to use superposition and entanglement. This critical survey recalls the field’s journey from theoretical advances to present-day engineering challenges, highlighting the yawning gulf between quantum computing’s lofty promises and its actual realizations. By examining three decades of developments, from Shor’s integer factorization and Grover’s search algorithms to recent demonstrations of quantum supremacy, this paper shows how idealized mathematical models interact with the noisy, resource-constrained realities of physical quantum systems. The author presents a literature review through critically analyzing key achievements in quantum computing research.. This paper concludes that quantum advantage will not arise from brute-force universality, but through application specific co-design, combining noise-adjusted algorithms to quantum hardware restrictions whilst mixing classical and quantum processing modes and fundamentally changing the way we think of error correction through the physics of qubits. This shift in paradigm from theoretical maximalism to engineering pragmatism embodies a realistic roadmap for practical quantum computation.
Quantum computing's most consequential claim — that quantum computers provide exponential computational speedup over classical computation — rests on a specific physical assumption: that superposition is ontologically real, that a qubit genuinely and simultaneously occupies multiple states, and that quantum algorithms exploit this simultaneity as a physical resource. A quantum computer with n qubits is claimed to process 2ⁿ computational paths in parallel by virtue of this simultaneous occupation. This paper argues that all three foundational assumptions are precluded by Quantum-Geometry Dynamics (QGD), the physical theory derived from the Minimal Physically Derivable Theories (MPDT) framework established by the Uniqueness Theorem. In QGD, physical reality is strictly and absolutely deterministic. Every fundamental constituent — every preon(+) — has a definite position and definite intrinsic momentum at every moment. There are no indeterminate states, no superpositions, and no wave function collapse at the fundamental level. What quantum mechanics describes as superposition is not a physical state of simultaneous occupation but an epistemic description of ignorance of the deterministic microstate of a preonic configuration. The wave function is a probabilistic description of deterministic preonic dynamics — a calculational tool that correctly predicts statistical outcomes — not a description of a physical state in which a system genuinely occupies multiple configurations simultaneously. This distinction has a direct and specific consequence for quantum computing. Quantum computing devices are genuine physical systems that exploit real quantum mechanical phenomena — phenomena that QGD derives from the deterministic dynamics of preons(+) and preons(−) in the finite discrete preon(−) lattice. The MPDT framework does not forbid the construction or operation of quantum computing devices. What QGD precludes is the ontological foundation on which the exponential speedup argument rests. A quantum computing device is a deterministic preonic configuration occupying one microstate at each moment. The 2ⁿ simultaneous amplitude states of the quantum formalism are elements of a probabilistic description of that microstate — not physical states simultaneously instantiated in the device. Quantum parallelism is a feature of the formalism, not of the underlying physics. The paper develops this argument systematically across eight sections. Section 2 establishes QGD's account of quantum phenomena as emergent from deterministic preonic dynamics, including the derivation of wave-like interference patterns and Bell correlations without superposition. Section 3 examines precisely what superposition is and is not in QGD, culminating in the formal statement that a qubit in the state α|0⟩ + β|1⟩ is not a system simultaneously occupying both states but a deterministic preonic configuration whose microstate determines measurement outcomes but is not individually accessible at the observational level. Section 4 identifies the exact point at which the exponential speedup argument fails: the physical resource it invokes — simultaneous occupation of 2ⁿ states — does not exist in the physical universe that QGD describes. Sections 5 examines three specific quantum algorithms: Shor's factoring algorithm, whose polynomial-time complexity is demonstrated within the quantum formalism but whose underlying preonic complexity remains an open question; Grover's search algorithm, whose quadratic speedup rests on the same ontological assumption; and quantum simulation, which survives the critique more robustly because it does not require exponential parallelism as a resource. Section 6 addresses decoherence, reinterpreting it not as an engineering challenge to be solved by better isolation but as a fundamental feature of reality — the inevitable influence of the instantaneous gravitational field of the entire preon(−) lattice on every qubit configuration, which cannot be shielded against in principle. Sections 7 and 8 develop the implications for the quantum computing programme and conclude. The argument connects directly to the P vs NP analysis in the companion Physicality of Logic paper. Shor's algorithm is the canonical example of a quantum algorithm claimed to solve a classically hard problem — integer factoring — in polynomial time, with significant implications for the security of RSA encryption. If QGD is correct and the exponential speedup argument fails, the classical hardness of factoring is preserved and the cryptographic implications attributed to quantum computing do not follow. The paper does not claim that quantum computing devices are useless — it claims that the specific resource driving the most dramatic projections for quantum computing does not physically exist, and that whatever computational advantages quantum devices possess must be explained within the deterministic preonic framework rather than by appeal to quantum parallelism. The paper is intended for physicists working on quantum computing and quantum foundations, philosophers of physics, and computer scientists working on computational complexity. It is submitted to Foundations of Physics. It is a companion to the author's papers on the Uniqueness Theorem and the Physicality of Logic, and to the book Quantum-Geometry Dynamics: An Axiomatic Approach to Physics.
"Introduction to Quantum Mechanics And Quantum Computing" is a comprehensive book chapter that provides an in-depth exploration of the groundbreaking field of quantum computing. Beginning with an introduction to the fundamental principles of quantum mechanics, the chapter navigates through the evolution of quantum computing, from its conceptual origins to the challenges faced in its development. The core concepts of quantum bits (qubits) and their unique properties, such as entanglement and superposition, are explained, laying the foundation for understanding quantum information processing. The chapter further delves into the building blocks of quantum computing—qubits—detailing their diverse physical implementations. Quantum gates and circuits, analogous to classical computing, are explored, shedding light on the mechanisms enabling quantum algorithms to perform complex tasks efficiently. Highlighting renowned algorithms like Shor's and Grover's, the chapter emphasizes the potential computational supremacy of quantum computers over classical counterparts. Recognizing the sensitivity of quantum systems to noise and decoherence, the chapter introduces quantum error correction as a crucial aspect of ensuring reliable quantum computation. The exploration concludes with an examination of the current state of quantum computing, outlining progress in industry and academia while addressing the challenges in building large-scale, fault-tolerant quantum computers. The potential applications of quantum computing in cryptography, drug discovery, optimization problems, and beyond are discussed, offering a glimpse into the transformative impact this emerging technology may have on various industries. "Introduction to Quantum Mechanics And Quantum Computing" serves as a comprehensive guide for readers seeking a nuanced understanding of the theoretical foundations and practical applications of quantum computing.
The advent of quantum computing has ushered in a new era of computational capabilities, promising to revolutionize the resolution of complex problems. Unlike classical computers, which rely on binary digits (bits) to process information, quantum computers utilize quantum bits (qubits) that can exist in multiple states simultaneously due to the principles of superposition and entanglement inherent in quantum mechanics. This fundamental difference allows quantum computers to perform certain calculations exponentially faster than their classical counterparts, offering profound implications for fields ranging from cryptography to material science. At the heart of this transformative potential lie quantum algorithms, specifically designed to harness the unique properties of quantum systems to tackle problems currently intractable for classical computers. Notable examples include Shor's algorithm for integer factorization, which threatens the security of widely used cryptographic schemes, and Grover's algorithm for unstructured search, which provides a quadratic speedup over classical approaches. Beyond these pioneering works, ongoing research continues to uncover new quantum algorithms capable of addressing a broad spectrum of applications. The proposed method leverages the principles of quantum mechanics to develop efficient algorithms that outperform classical approaches in solving complex computational problems. By harnessing the unique properties of quantum bits (qubits), such as superposition and entanglement, the method aims to achieve superior accuracy and efficiency in various applications. The performance of the proposed method was evaluated using several key metrics: an accuracy of 94.8%, a Root Mean Squared Error (RMSE) of 0.208, and a Mean Absolute Error (MAE) of 0.406. These metrics collectively underscore the robustness and reliability of the proposed quantum algorithms, highlighting their potential to significantly enhance computational efficiency and accuracy across various domains. This study delves into the development of quantum algorithms, exploring their theoretical foundations, practical implementations, and the challenges faced in their realization. By leveraging the principles of quantum mechanics, these algorithms hold the promise of not only solving existing problems more efficiently but also unlocking new computational paradigms previously deemed unattainable. Through a comprehensive analysis, this research aims to elucidate the current state of quantum algorithm research, highlight the advancements made, and identify the pathways forward in this rapidly evolving field.