No, quantum query complexity is not equivalent to the total number of calls to the quantum computer for any given algorithm. Quantum query complexity refers to the minimum number of queries (or calls) to the input needed by a quantum algorithm to solve a specific problem with a certain probability of success.
The concept of query complexity specifically focuses on the number of times an algorithm accesses or interacts with the input data, rather than the total number of calls to the quantum computer. It measures the efficiency of the algorithm in terms of information retrieval from the input, disregarding other operations that might be performed on the quantum computer.
In quantum computing, there are other factors that can contribute to the overall resource usage of an algorithm, such as the number of quantum gates applied, the number of qubits required, and the depth of the quantum circuit. These factors can impact the total computational cost and time complexity of the algorithm but may not directly correlate with the query complexity.
Therefore, while the number of calls to the quantum computer is a relevant aspect of quantum computing, it does not solely determine the query complexity of an algorithm. Query complexity is a specific measure related to accessing and processing input data efficiently.