  With the advent of powerful quantum computers, the quest for more efficient
quantum algorithms becomes crucial in attaining quantum supremacy over
classical counterparts in the noisy intermediate-scale quantum era. While
Grover's search algorithm and its generalization, quantum amplitude
amplification, offer quadratic speedup in solving various important scientific
problems, their exponential time complexity limits scalability as the quantum
circuit depths grow exponentially with the number of qubits. To overcome this
challenge, we propose Variational Quantum Search (VQS), a novel algorithm based
on variational quantum algorithms and parameterized quantum circuits. We show
that a depth-10 Ansatz can amplify the total probability of $k$ ($k \geq 1$)
good elements, out of $2^n$ elements represented by $n$+1 qubits, from $k/2^n$
to nearly 1, as verified for $n$ up to 26, and that the maximum depth of
quantum circuits in the VQS increases linearly with the number of qubits. Our
experimental results have validated the efficacy of VQS and its exponential
advantage over Grover's algorithm in circuit depth for up to 26 qubits. We
demonstrate that a depth-56 circuit in VQS can replace a depth-270,989 circuit
in Grover's algorithm. Envisioning its potential, VQS holds promise to
accelerate solutions to critical problems.
