It is difficult to provide a definitive answer to your question because the comparison between a quantum computer and a yottascale supercomputer involves several factors, including the specific problem being solved, the algorithms used, and the architecture and efficiency of both systems.
Firstly, it's important to clarify that a yottascale supercomputer refers to a hypothetical computing system capable of performing 10^24 floating-point operations per second (FLOPS). Currently, the most powerful supercomputers in the world operate at the exascale level, which is 10^18 FLOPS.
Quantum computers, on the other hand, are not typically measured solely by FLOPS since their computational power arises from different principles. Quantum computers leverage the superposition and entanglement of qubits to perform certain types of computations more efficiently than classical computers.
To determine the number of qubits required for a quantum computer to surpass a yottascale supercomputer in a given task, we need to consider the nature of the problem and the algorithm being used. Some problems that are challenging for classical computers, such as factoring large numbers, simulating quantum systems, or optimizing complex systems, can potentially be solved more efficiently with quantum computers.
The number of qubits needed depends on the specific quantum algorithm and the problem size. For example, Shor's algorithm for factoring large numbers requires a number of qubits that scales with the logarithm of the number being factored. However, it is important to note that large-scale fault-tolerant quantum computers capable of running such algorithms at scale are still a significant technological challenge.
Quantum computers are still in the early stages of development, and building a large-scale fault-tolerant quantum computer with thousands or millions of qubits remains a formidable task. Currently, the most advanced quantum computers have around 50 to 100 qubits, and they are primarily used for research purposes.
In summary, it is difficult to specify an exact number of qubits required for a quantum computer to surpass a yottascale supercomputer. The development and scaling of quantum computers are active areas of research, and their potential for outperforming classical computers in certain applications is an exciting prospect. However, it will likely take significant advancements in quantum hardware, error correction techniques, and algorithm development to achieve such a milestone.