The minimum number of qubits needed for universal quantum computing is a topic of ongoing research and debate in the field of quantum computing. However, based on the current understanding, it is generally believed that a quantum computer requires a sufficient number of qubits to perform operations on a large enough computational space to surpass the capabilities of classical computers for certain tasks.
In 1994, Peter Shor introduced a quantum algorithm for factoring large numbers that demonstrated the potential superiority of quantum computers over classical computers in solving certain problems. Shor's algorithm requires a sufficient number of qubits to represent the input number and perform quantum operations. Specifically, the number of qubits required for factoring large numbers using Shor's algorithm is proportional to the logarithm of the input size.
For more general-purpose quantum computing, it is widely believed that a quantum computer with a few hundred high-quality qubits would be sufficient to surpass classical computers in solving certain problems. This belief is based on theoretical considerations, such as the threshold theorem for fault-tolerant quantum computing. The threshold theorem states that if the error rate in a quantum computation is below a certain threshold, error correction techniques can be applied to maintain the reliability of the computation.
However, it's important to note that the number of qubits alone does not determine the capability or performance of a quantum computer. Other factors, such as qubit quality, connectivity between qubits, and error rates, also play crucial roles. Additionally, the choice of algorithms, error correction techniques, and system architecture are essential considerations in achieving universal quantum computing.
As the field of quantum computing continues to progress, researchers are actively working on improving qubit quality, developing error correction methods, and exploring new algorithms that could potentially reduce the required number of qubits for specific tasks. Therefore, while there is no definitive answer to the minimum number of qubits needed for universal quantum computing, it is expected to be in the range of a few hundred high-quality qubits.