  Distributed quantum computation has gained extensive attention since
small-qubit quantum computers seem to be built more practically in the noisy
intermediate-scale quantum (NISQ) era. In this paper, we give a distributed
Bernstein-Vazirani algorithm (DBVA) with $t$ computing nodes, and a distributed
exact Grover's algorithm (DEGA) that solve the search problem with only one
target item in the unordered databases. Though the designing techniques are
simple in the light of BV algorithm, Grover's algorithm, the improved Grover's
algorithm by Long, and the distributed Grover's algorithm by Qiu et al, in
comparison to BV algorithm, the circuit depth of DBVA is not greater than
$2^{\text{max}(n_0, n_1, \cdots, n_{t-1})}+3$ instead of $2^{n}+3$, and the
circuit depth of DEGA is $8(n~\text{mod}~2)+9$, which is less than the circuit
depth of Grover's algorithm, $1 + 8\left\lfloor \frac{\pi}{4}\sqrt{2^n}
\right\rfloor$. In particular, we provide situations of our DBVA and DEGA on
MindQuantum (a quantum software) to validate the correctness and practicability
of our methods. By simulating the algorithms running in the depolarized
channel, it further illustrates that distributed quantum algorithm has
superiority of resisting noise.
