  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
(https://github.com/hafeezzwiz21/DFGS-BDGS).
