In this section of the study, the concept of oracles will be discussed. Oracles can be defined as black boxes or virtual devices that provide immediate responses to queries. These responses are given without regard to the computations that might be required to answer the query. Essentially, both quantum and classical oracles are assumed to have this abstract property, and therefore, it is considered acceptable to compare their efficiencies (i.e., complexities) by counting the number of oracle queries required in both classical and quantum algorithms to solve a specific problem.

6.3.1. Definition and Characteristics of Oracles

• Black Box Model: Oracles are defined as “black boxes.” This means that the inner workings of the oracle are not known to the algorithm user. In other words, it doesn’t matter what kind of calculations the oracle performs; what matters is that it can provide an immediate response to a given query.
• Virtual Devices: Oracles are not real physical devices but theoretically existing virtual devices. This provides idealized conditions to evaluate the performance of the algorithm.

6.3.2. Response Time of Oracles

Oracles respond to queries immediately. This means that the response time of oracles is independent of the computation time. Therefore, when performing complexity analysis of the algorithm, the response time of oracles is not considered.

6.3.3. Comparison of Quantum and Classical Oracles

• It is assumed that both quantum and classical oracles have the same abstract properties. This means that both types of oracles can respond to queries in a similar manner.
• With this assumption, the efficiencies (i.e., complexities) of both types of oracles can be compared based on the number of queries made by the oracle.

6.3.4. Complexity Estimation

• The complexity of algorithms is measured by the number of oracle queries required to solve a particular problem. This is a metric used to evaluate the efficiency of the algorithm.
• By counting the number of oracle queries in both classical and quantum algorithms, it can be determined which algorithm is more efficient.