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.

翻译：随着强大量子计算机的出现，在含噪中等规模量子时代，开发更高效的量子算法对实现相对于经典方法的量子霸权至关重要。尽管Grover搜索算法及其推广——量子振幅放大——在解决多种重要科学问题时提供了二次加速，但其指数级时间复杂度限制了可扩展性，因为量子电路深度随量子比特数量呈指数增长。为克服这一挑战，我们提出变分量子搜索（VQS），一种基于变分量子算法和参数化量子电路的新型算法。我们证明，对于由$n$+1个量子比特表示的$2^n$个元素，一个深度为10的Ansatz可将$k$（$k \geq 1$）个目标元素的总概率从$k/2^n$放大至接近1（在$n$不超过26时已验证），且VQS中量子电路的最大深度随量子比特数量线性增长。我们的实验结果验证了VQS的有效性，并证明其在电路深度上相对于Grover算法（最多26量子比特）具有指数级优势。我们展示VQS中深度为56的电路可替代Grover算法中深度为270,989的电路。展望其潜力，VQS有望加速解决关键问题。