No, a quantum computer with only one qubit can still have some utility, although its capabilities would be limited compared to larger-scale quantum computers.
With a single qubit, you can perform basic quantum operations such as superposition, where the qubit exists in a combination of multiple states simultaneously, and entanglement, where the qubit becomes correlated with another qubit or system. These properties can be harnessed to perform certain types of calculations or algorithms that exhibit quantum advantages over classical computers, even with just one qubit.
For example, a single qubit can be used to implement simple quantum gates, such as the Pauli gates (X, Y, Z), the Hadamard gate (H), or the phase gate (S). These gates can manipulate the quantum state of the qubit and perform basic computations.
Additionally, a single qubit can be used to simulate quantum systems or investigate quantum phenomena on a small scale. It can serve as a testbed for understanding the principles of quantum mechanics, conducting experiments, or exploring quantum information protocols.
However, the power of quantum computing comes from the ability to scale up and utilize multiple qubits. Quantum algorithms, such as Shor's algorithm for factoring large numbers or Grover's algorithm for unstructured search, benefit from having a larger number of qubits to exploit quantum parallelism and entanglement effects. As the number of qubits increases, the computational power of a quantum computer grows exponentially.
Therefore, while a single qubit can have some practical applications and serve as a starting point for learning and experimentation, the full potential of quantum computing is realized when working with systems consisting of many qubits.