Quantum computers have much more capacity than classical ones.Quantum computations are of parallelism and wholeness.Some quantum arithmetic can be of acceleration.Quantum computations bring us new philosophical implications such as the relationship between mathematics and physics,the reality of wave-function,and capacity of solving computation complexity.
Quantum computers have much more capacity than classical ones.Quantum computations are of parallelism and wholeness.Some quantum arithmetic can be of acceleration.Quantum computations bring us new philosophical implications such as the relationship between mathematics and physics,the reality of wave-function,and capacity of solving computation complexity.
Quantum computing operates by manipulating the quantum state of a system to solve problems intractable for classical computing. These problems, previously considered limitations of classical algorithms, have solutions through quantum approaches. Therefore, quantum computing suggests that the complexity of such problems lies in the current epistemic state rather than the objective state of the problem. Computational complexity can be classified into objective and epistemic complexity. Some classical problems exhibiting exponential complexity fall into the epistemic category, as their solutions depend on the current state of human knowledge and available tools. Quantum computing suggests that even mathematics isn’t entirely objective, and mathematics, in one sense, is human-made and a kind of technology, which reflects our intention and planning. Computational complexity, therefore, bridges the objective and subjective. Overcoming classical complexity necessitates advancements in scientific theories, algorithms, and quantum technology, all of which rely on the development of human cognitive abilities. Quantum computing is not just a mathematical construct, but also has physical meaning. If it were purely mathematical, classical physics and systems could potentially achieve the same results. What makes the quantum world special is its empirical nature—the physical reality of quantum chips, quantum algorithms, and quantum evolution. Quantum supremacy, or quantum advantage, refers to the potential superiority of quantum computers over classical ones. Controllable quantum systems offer an overwhelming advantage in terms of manipulation and dominance compared to classical systems. Essentially, quantum computing has the potential to significantly outperform classical computing. Many experts, including Shor, have proposed that quantum computing’s power stems from its ability to perform multiple computations simultaneously—a concept often referred to as the Quantum parallelism thesis. Rather, some argue that the true source of quantum computing acceleration lies in the fundamental differences between classical and quantum logic. However, it’s important to note that quantum logic, while providing a new perspective, does not directly address the core principle of quantum parallelism. This dominance stems from quantum physics’ unique properties: Exponential storage capacity, parallel computing inherent to its nature (ontological), and the ability to perform calculations with exponential speedup through quantum algorithms.
This work presents a comprehensive and rigorous examination of quantum computing, spanning its mathematical foundations, physical principles, algorithmic developments, hardware architectures, and philosophical implications. Beginning with linear algebra over Hilbert spaces and the postulates of quantum mechanics, the manuscript develops the formal structure of quantum information theory, including qubits, entanglement, quantum channels, and noise models. The work provides in-depth treatments of the quantum circuit model, alternative computation paradigms such as measurement-based, adiabatic, and topological quantum computation, and the theoretical framework of quantum error correction, including stabilizer and surface codes. Foundational and modern quantum algorithms are analysed in detail, including Shor’s factoring algorithm, Grover’s search, variational quantum eigensolvers, QAOA, and emerging quantum machine learning approaches. Beyond algorithms and implementations, the manuscript addresses scalability challenges, fault tolerance, computational complexity limits, and the implications of quantum computing for cryptography and the extended Church–Turing thesis. The concluding sections explore philosophical questions concerning interpretation, measurement, and the relationship between computation and physical reality. This work is intended as both a reference text and a research-level synthesis for advanced students, researchers, and practitioners in quantum computing, theoretical computer science, and quantum physics.
Quantum computation is a new quantum mechanics-based computation,which is considered to have most probability of breaking through the traditional equipments' computing ability.Quantum computation has the feature of counter-intuitive.This makes many of our life no longer common sense knowledge,and meanwhile,something without our general cognitive ability,even something like mentalism may become impelling evidence of that quantum computation exceeds traditional computation.The tremendous development of quantum computation(especially quantum computer)in recent years tells us that philosophy is an advanced stage of the scientific development.Philosophy explains the development and progress of science and promotes the development of science.The limitations of the scientific development may exist,but perhaps at a higher level,philosophy can offer solutions to this limitation.
"Information is physical and any processing of information is always performed by physical means," an innocent-sounding statement, but its consequences are profound. When quantum effects become important, for example, at the level of single atoms and photons, the classical theory of computation becomes fundamentally inadequate. Entirely new modes of computation and information processing become possible. In the last few years there has been an explosion of theoretical and experimental research in quantum computation. In this brief review we describe some of these developments.
The study presented here focuses on the ontological status of the wave function as a central element of the formal apparatus of quantum theory. It investigates whether the wave function represents only an instrumental computational tool for generating probabilistic predictions or an ontologically binding representation of physical reality. The analysis builds on the main conceptual frameworks and traces their consequences for interpretations of quantum mechanics, the nature of ontological commitments of scientific theories and the relationship between mathematical formalism and the metaphysical structure of the world. The goal is to identify the philosophical implications of these approaches and to clarify the fundamental tensions between realism and instrumentalism in the contemporary philosophy of physics.
A model of parallel optical computer for Fourier transform tasks is built. The computer operates in both quantum and classical modes. The quantum computer (QC) works with entangled photons and the input gates are n-qubit sensitive, while the classical computer (CC) operates without entanglement. The information capacity (I) for both CC and QC is given as a function of number of qubits and Np (number of photons per input pixel). It is shown that the information capacity significantly increases for the quantum computer compared to the classical one as the number of qubits is increased, assuming that Np is constant for both the QC and CC, i.e. same amount of energy input is assumed for the computers. However, it is also pointed out that the complexity of the QC significantly increases, too. To quantify this, we introduce a new physical quantity called physical complexity (noted as Q). We define the physical complexity (Q) of a computer as ∑i,klog2nkai where k runs over all the gates/elements in the computer; nai is the number of distinguishable states what a gate can set for ai. For QC ai is defined as the ith coefficient of the wave function. For CC it is the ith independent component of the Fourier transform of the energy flow what a particular gate is able to control. By using this definition we show that, for both the quantum and classical computers built in this work, I ≤ Q, in other words the information capacity is less or equal than the physical complexity. Intuitively we suggest that this is a general law that is valid for every computer irrespectively of type, quantum or classic, and architecture.