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In this paper, we introduce and study the quantum measurement detection algorithms (QMDA), whose objective is to detect whether unwanted measurements are being taken in a quantum circuit or not by applying the Zeno effect. A QMDA is a quantum circuit that includes three unitary matrices, one of them being applied numerous times consecutively, and whose initial state is fixed when no foreign measurements occur. One example is the Elitzur–Vaidman bomb tester, which is generalized by the QMDA definition, allowing the detection of measurements that are taken in an unknown basis and in circuits with an arbitrary number of qubits. We prove some key properties and limitations of these algorithms, as well as studying the performance of the Elitzur–Vaidman bomb tester and its possible improvements. Some extensions of the definition would lead to algorithms such as the counterfactual communication one. [ABSTRACT FROM AUTHOR]

The standard description of a quantum algorithm consists in three steps. First, encoding the data in a suitable initial quantum state. Second, driving such a state by a convenient sequence of unitary transformations until a final quantum state is reached. Third, measuring the final state and use such a measurement to solve the problem the quantum algorithm was designed for. An alternative description is provided by the stabilizer formalism, which was originally introduced in connection with quantum error correcting codes. In this paradigm, the focus is on the subgroup of elements of the Pauli group stabilizing the initial quantum state, and the transformations that such a subgroup experiments along the algorithm. In this work, we provide an explanation of two foundational quantum algorithms (Bernstein‐Vazinari and Deustch‐Josza) based on such a quantum stabilizer formalism. Doing so, we provide a better understanding and insight into both procedures which yield to see Bernstein‐Vazirani as a particular case of Deustch‐Josza, and to introduce a generalized version of Deustch‐Josza algorithm. [ABSTRACT FROM AUTHOR]