Al-Bayaty Ali, Perkowski Marek
Department of Electrical and Computer Engineering, Portland State University, Portland, USA.
Sci Rep. 2024 Oct 9;14(1):23570. doi: 10.1038/s41598-024-74587-y.
A controlled-diffusion operator for Boolean oracles is designed as a new approach for Grover's algorithm to search for solutions for arbitrary logical structures of such oracles, since the Grover diffusion operator is not able to find correct solutions for some logical structures of Boolean oracles. We also show that the Phase oracles do not work sometimes correctly using the Grover diffusion operator. Our proposed controlled-diffusion operator relies on the states of output qubit, as the reflection of Boolean decisions from a Boolean oracle without relying on the phase kickback. We prove that on many examples of Boolean and Phase oracles the Grover diffusion operator is not working correctly. The oracles in these examples are constructed using different structures of POS, SOP, ESOP, CSP-SAT, and XOR-SAT. Our mathematical models and experiments prove that the proposed controlled-diffusion operator successfully searches for all solutions for all Boolean oracles regardless of their different logical structures.
一种用于布尔预言机的受控扩散算子被设计为一种新方法，用于格罗弗算法搜索此类预言机任意逻辑结构的解，因为格罗弗扩散算子无法为布尔预言机的某些逻辑结构找到正确解。我们还表明，使用格罗弗扩散算子时，相位预言机有时不能正确工作。我们提出的受控扩散算子依赖于输出量子比特的状态，作为布尔预言机布尔决策的反映，而不依赖于相位回踢。我们证明，在布尔和相位预言机的许多示例中，格罗弗扩散算子不能正确工作。这些示例中的预言机是使用POS、SOP、ESOP、CSP-SAT和XOR-SAT的不同结构构建的。我们的数学模型和实验证明，所提出的受控扩散算子成功地搜索了所有布尔预言机的所有解，而不管它们不同的逻辑结构如何。
