Variational Quantum Search with Shallow Depth for Unstructured Database Search

TL;DR

This paper introduces Variational Quantum Search (VQS), a shallow-depth quantum algorithm that significantly reduces circuit depth compared to Grover's algorithm, enabling scalable unstructured database search on near-term quantum hardware.

Contribution

The paper proposes VQS, a variational quantum algorithm with linear-depth scaling, demonstrating exponential depth reduction over Grover's algorithm for unstructured search.

Findings

VQS amplifies the probability of good elements with shallow circuits.

VQS achieves exponential depth advantage over Grover's algorithm.

Experimental validation up to 26 qubits confirms effectiveness.

Abstract

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.