Quantum computing
Abstract
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.