Binary Subdivision for Quantum Search

TL;DR

This paper proposes a hybrid quantum-classical search method that embeds quantum search within binary search, potentially achieving logarithmic search time by restarting quantum searches with different qubit sequences.

Contribution

It introduces a novel hybrid approach combining quantum and classical search techniques, enabling potentially faster unstructured search.

Findings

Potential to search in O(log N) time using quantum restart strategy

Hybrid quantum-classical approach leverages quantum parallelism effectively

Requires multiple quantum restarts and non-unitary measurements

Abstract

We consider in this paper the possibility of embedding a quantum search algorithm within a classical binary search framework. The result appears promising: taking full advantage of quantum parallelism, we show that it may actually be possible to search an unstructured list in O(lg(N)), provided we are willing to restart the quantum search multiple times with a different sequence of qubits and perform a series of non-unitary measurements at the end of each.