Robust quantum spatial search

TL;DR

This paper introduces a recursive quantum spatial search algorithm that is significantly more robust to systematic errors and easier to implement than traditional quantum walk algorithms, especially for large search spaces.

Contribution

A new recursive quantum search algorithm demonstrating exponential improvement in error tolerance and no need for ancilla qubits compared to existing quantum walk methods.

Findings

Tolerates errors of size O(1/√ln N), exponentially better than quantum walk algorithms.

Does not require ancilla qubits, simplifying experimental implementation.

Shows improved robustness to systematic errors in quantum spatial search.

Abstract

Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers significant robustness to certain systematic errors. To search N items, our recursive algorithm can tolerate errors of size O(1/\sqrt{\ln N}) which is exponentially better than quantum walk algorithms for which tolerable error size is only O(\ln N/\sqrt{N}). Also, our algorithm does not need any ancilla qubit. Thus our algorithm is much easier to implement experimentally compared to quantum walk algorithms.