Optimizing Quantum Search Using a Generalized Version of Grover's Algorithm

Abstract

Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in quantum states. In this paper, we introduce an optimization of the inversion-by-the-mean step of the algorithm. This optimization serves two purposes: from a practical perspective, it can lead to a performance improvement; from a theoretical one, it leads to a novel interpretation of the actual nature of this step. This step is a reflection, which is realized by (a) cancelling the superposition of a general state to revert to the original all-zeros state, (b) flipping the sign of the amplitude of the all-zeros state, and finally (c) reverting back to the superposition state. Rather than canceling the superposition, our approach allows for going forward to another state that makes the reflection easier. We validate our approach on set and array search, and confirm our results experimentally on real quantum hardware.

7 pages, 16 figures

References in corpus (3)

• A variational eigenvalue solver on a quantum processor
• Grover Adaptive Search for Constrained Polynomial Binary Optimization
• Foundational Patterns for Efficient Quantum Computing

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• Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection
• Qubit Reduction and Quantum Speedup for Wireless Channel Assignment Problem
• Simulation of a Variational Quantum Perceptron using Grover's Algorithm
• Approximate Phase Search and Eigen Estimation using Modified Grover's Algorithm
• Optimizing Quantum Search with a Binomial Version of Grover's Algorithm