To clarify, it's important to note that quantum computers, including those that may be considered "supercomputers" in the future, do not need to observe single qubits in the sense of directly observing their wave functions. Quantum systems, including qubits, are governed by the principles of quantum mechanics, which introduce unique behaviors and limitations compared to classical systems.
In a quantum computer, operations are performed on qubits to manipulate their quantum states and perform computations. Observing or measuring a qubit collapses its quantum state into one of the basis states, typically |0⟩ or |1⟩, and extracts classical information from the quantum system. This measurement is a probabilistic process, with the probability of observing a particular outcome determined by the squared magnitudes of the probability amplitudes in the quantum state.
The need for observing single qubits arises from the nature of quantum algorithms and the desire to extract information from the quantum computation. Quantum algorithms, such as Shor's algorithm for factoring large numbers or Grover's algorithm for searching an unsorted database, often involve complex quantum superposition and entanglement. To retrieve the result of a computation, measurements are performed on the final quantum state to obtain classical information that can be interpreted.
As for your question about observing the wave function of a cathode ray with multiplexing information routes, it's worth noting that the behavior of quantum systems is fundamentally different from classical systems. Observing the wave function of a quantum system directly is not feasible due to the principles of quantum mechanics, which restrict the direct access to certain properties.
In quantum experiments, indirect measurement techniques are typically employed to gain information about the state of a system without directly observing its wave function. These techniques rely on quantum interference, entanglement, and other quantum phenomena to extract information probabilistically.
While multiplexing information routes can be useful in classical information processing, applying them directly to observe the wave function of a quantum system is not straightforward. The behavior of quantum systems is governed by the principles of superposition and entanglement, making the direct observation of the wave function challenging.
In summary, in quantum computing, observing single qubits through measurements is necessary to extract classical information and interpret the results of a computation. Observing the wave function of a quantum system directly is not feasible, and the unique nature of quantum systems requires specialized techniques for extracting information probabilistically.