The belief that the realization of qubits and quantum computing cannot be approached solely through mathematical logic, independent of harnessing fundamental particles, stems from several reasons:
Quantum mechanics as a physical theory: Quantum mechanics, which provides the framework for understanding the behavior of quantum systems, is a physical theory based on the properties of fundamental particles. It describes how these particles and their associated quantum states interact and evolve over time. Mathematical logic alone cannot capture the full richness and complexity of quantum behavior, as it requires understanding the underlying physical principles and properties of quantum systems.
Superposition and entanglement: The unique properties of qubits, such as superposition and entanglement, are inherently physical phenomena that arise from the quantum nature of particles. Superposition allows qubits to exist in multiple states simultaneously, and entanglement enables correlations between particles that cannot be explained solely through classical logic. These phenomena are a consequence of the underlying quantum mechanics and cannot be fully understood or harnessed without considering the physical systems that exhibit them.
Measurement and collapse of the wavefunction: The act of measuring a qubit causes it to collapse into a definite state. This collapse is a fundamental aspect of quantum mechanics and is not purely a result of mathematical logic. The probabilities associated with the collapse are determined by the superposition amplitudes, which are physical quantities inherent to quantum systems. The measurement process involves an interaction between the quantum system and the measuring apparatus, which introduces physical effects that cannot be accounted for solely through mathematical reasoning.
Quantum gates and operations: Quantum computing relies on the ability to manipulate qubits using quantum gates and operations. These operations are physical processes that alter the quantum state of the qubits and enable quantum computations. While they can be represented and analyzed using mathematical formalisms, their implementation requires physical systems and control over the interactions between particles. Mathematical logic alone cannot substitute for the physical processes involved in quantum operations.
In summary, while mathematical logic is essential for understanding and analyzing quantum systems, the unique properties and behaviors of qubits, such as superposition, entanglement, and quantum operations, arise from the underlying physical nature of quantum mechanics. The realization of qubits and quantum computing relies on harnessing the fundamental particles and their quantum behavior, which cannot be fully captured by mathematical logic alone.