The relationship between the number of qubits and the time it takes to solve a problem on a quantum computer is not straightforward. In general, the number of qubits alone does not directly determine the computational speed or the time required to solve a problem. It's important to consider various factors, such as the complexity of the problem, the algorithm used, the quality of the qubits, and the error correction techniques employed.
Quantum computers can leverage their parallel processing capabilities to potentially solve certain problems more efficiently than classical computers. However, this advantage is not uniform across all problems. Some problems may exhibit exponential speedup on a quantum computer, while others may only show a modest improvement or no improvement at all.
Additionally, the development of large-scale, error-corrected quantum computers with thousands or millions of qubits is still a significant scientific and engineering challenge. While there has been progress in building quantum computers with a few dozen qubits, scaling up to hundreds, thousands, or millions of qubits while maintaining high-quality qubits and low error rates is a complex task that requires advances in hardware, error correction, and control systems.
Given the current state of quantum technology, it is difficult to estimate the exact time it would take to solve a specific problem with a certain number of qubits. The potential speedup and time required will depend on the specific problem, the algorithm used, and the capabilities of the quantum hardware.
However, it's important to note that quantum computers are not expected to be universally faster than classical computers for all types of problems. Quantum computing is particularly promising for certain types of problems, such as factoring large numbers (Shor's algorithm) or simulating quantum systems (quantum chemistry simulations). For other types of problems, classical computers may still be more efficient or provide comparable performance.
In summary, the relationship between the number of qubits and the time required to solve a problem on a quantum computer is complex and depends on multiple factors. The speed and efficiency of quantum computation will vary based on the problem and the development of large-scale, error-corrected quantum computers.