Improving Quantum Search on Simple Graphs by Pretty Good Structured Oracles

Matteo G A Paris,Stefano Olivares,Claudia Benedetti

doi:10.3390/sym13010096

Abstract

Quantum search algorithms provide a way to speed up combinatorial search, and have found several applications in modern quantum technology. In particular, spatial search on graphs, based on continuous-time quantum walks (CTQW), represents a promising platform for the implementation of quantum search in condensed matter systems. CTQW-based algorithms, however, work exactly on complete graphs, while they are known to perform poorly on realistic graphs with low connectivity. In this paper, we put forward an alternative search algorithm, based on structuring the oracle operator, which allows one to improve the localization properties of the walker by tuning only the on-site energies of the graph, i.e., without altering its topology. As such, the proposed algorithm is suitable for implementation in systems with low connectivity, e.g., rings of quantum dots or superconducting circuits. Oracle parameters are determined by Hamiltonian constraints, without the need for numerical optimization.

Highlights

Structured databases, as opposed to unstructured ones, are characterized by the existence of a format or some form of organization, which make them searchable in a relational fashion
We have addressed spatial quantum search with quantum walks on graphs, and put forward an alternative search algorithm based on structuring the oracle operator
We have analyzed the use of a structured oracle in order to improve the searching performance of continuous-time quantum walks (CTQW) on ring graphs, as a paradigmatic example of structure with low connectivity

Summary

Introduction

Structured databases, as opposed to unstructured ones, are characterized by the existence of a format or some form of organization, which make them searchable in a relational fashion. Structured data are amenable to spatial search algorithms, i.e., algorithms taking into account the spatial organization of the dataset This is done using tools from graph theory, and exploiting the structure of links within the database. It has been shown [4] that continuous-time quantum walks (CTQWs) over graphs may provide exact solutions to the search problem for certain graph topologies, i.e., exact localization (with unit probability) of the walker on some given target state. We address this problem and put forward an alternative search algorithm, based on structuring the oracle operator, which allows one to improve the localization properties of the walker by tuning only the on-site energies of the graph, i.e., without altering the topology of the graph itself.

Quantum Spatial Search on Graphs

Quantum Search by Structured Oracles

Findings

Conclusions