No, when people refer to a quantum computer gaining a "quadratic speedup" for search algorithms, it means that the complexity of the algorithm is reduced from a classical linear search to a square-root search. In other words, the time required to solve the problem on a quantum computer scales with the square root of the input size, rather than linearly with the input size.
To be more precise, let's consider an example of a search algorithm, such as Grover's algorithm, which is a well-known quantum search algorithm. In classical computing, a linear search would require examining each item in a list of size n, resulting in O(n) complexity. However, Grover's algorithm can achieve a quadratic speedup, reducing the complexity to O(√n).
So, a "quadratic speedup" means that a quantum search algorithm can solve the problem significantly faster than a classical linear search algorithm, with a time complexity of approximately square root of the input size. However, it's important to note that this quadratic speedup is specific to certain types of search problems and quantum algorithms. Quantum computing does not provide a quadratic speedup for all types of computational problems.