  Grover search is a renowned quantum search algorithm that leverages quantum
superposition to find a marked item with quadratic speedup. However, when
implemented on Noisy Intermediate-scale Quantum (NISQ) hardware, the required
repeated iterations of the oracle and diffusion operators increase
exponentially with the number of qubits, resulting in significant noise
accumulation. To address this, we propose a hybrid quantum-classical
architecture that replaces quantum iterations with updates from a classical
optimizer. This optimizer minimizes the expectation value of an oracle
Hamiltonian with respect to a parameterized quantum state representing the
target bit string. Our parameterized quantum circuit is much shallower than
Grover search circuit, and we found that it outperforms Grover search on noisy
simulators and NISQ hardware. When the number of qubits is greater than 5, our
approach still maintains usable success probability, while the success
probability of Grover search is at the same level as random guessing.
