Grover controlled-diffuser (CUs) for quantum Boolean oracles of Grover’s algorithm v2
Ali Al-Bayaty, Marek A. Perkowski · 2024
The Grover controlled-diffuser (CUs) for quantum Boolean oracles (Uω) is introduced as a new approach for Grover’s algorithm [1-3], to search for all solutions for arbitrary logical structures of such oracles, since the standard Grover diffuser (Us) [1-3] is not able to find all correct solutions for some logical structures of Uω. This protocol constructs the quantum circuit of the CUs operator [4] of Grover's algorithm, which relies on the states of the output qubit (as the reflection of Boolean decisions from a Uω) without relying on the conventional phase kickback mechanism. The CUs operator successfully searches for all correct solutions for all Uω regardless of their different logical structures, such as POS, SOP, ESOP, CSP-SAT, XOR-SAT, just to name a few.