Grover's search algorithms, including various partial Grover searches,
experience scaling problems as the number of iterations rises with increased
qubits, making implementation more computationally expensive. This paper
combines Partial Grover's search algorithm and Bi-directional Search to create
a fast Grover's quantum search algorithm, referred to as Bi-Directional Grover
Search (BDGS). We incorporated a bi-directional search tactic with a partial
Grover search, starting from an initial state and a single marked state in
parallel. We have shown in this article that our novel approach requires
$\frac{\pi}{4\sqrt{2}}\sqrt{N}(1-\sqrt{\frac{1}{b^{r/2k}}})$ iterations over
regular Grover Search and Partial Grover Search (PGS), which takes
$\frac{\pi}{4}\sqrt{N}\sqrt{1-\frac{1}{b}}$ (here, $N=2^r$ elements, $b$ is the
branching factor of partial search, and $k= \lceil\log_2b \rceil$). The
proposed BDGS algorithm is benchmarked against the state-of-the-art Depth-First
Grover's Search (DFGS) and generic Grover's Search (GS) implementations for $2$
to $20$ qubits and provides promising results. The Qiskit Python implementation
of the proposed BDGS algorithm is available on Github
(this https URL).

使用双向搜索策略和部分 Grover 搜索算法，提出了一种引用为双向 Grover 搜索的快速 Grover 量子搜索算法，相比传统的 Grover 搜索和部分 Grover 搜索在同样条件下减少了迭代次数。