Can Quantum Entanglement Detection Schemes Improve Search?

TL;DR

This paper proposes a novel quantum search method that leverages quantum entanglement detection schemes to potentially improve search efficiency, deviating from Grover's algorithm by focusing on entanglement properties and unitary operator tuning.

Contribution

It introduces a new quantum search approach combining entanglement detection with operator tuning, exploring an alternative to Grover's algorithm that emphasizes entanglement properties.

Findings

Proposes a quantum search method based on entanglement detection.

Highlights the potential of entanglement properties to infer solutions.

Identifies open questions regarding the operational characterization of positive maps.

Abstract

Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most $O(N)$ time complexity. Grover's algorithm is able to find a solution with high probability in $O(\sqrt{N})$ time through an amplitude amplification scheme. In this work we draw elements from both classical and quantum computation to develop an alternative search proposal based on quantum entanglement detection schemes. In 2002, Horodecki and Ekert proposed an efficient method for direct detection of quantum entanglement. Our proposition to quantum search combines quantum entanglement detection alongside entanglement inducing operators. Grover's quantum search relies on measuring a quantum superposition after having applied a unitary evolution. We deviate from the standard method by focusing on fine-tuning a unitary operator in order to infer the solution with certainty. Our proposal sacrifices space for speed and depends on the mathematical properties of linear positive maps $\Lambda$ which have not been operationally characterized. Whether such a $\Lambda$ can be easily determined remains an open question.