Quantum searching with continuous variables

TL;DR

This paper introduces a quantum search algorithm for continuous variables, analogous to Grover's algorithm, achieving a quadratic speed-up and demonstrating robustness with generalized Fourier transforms.

Contribution

It presents the first continuous variable quantum search algorithm, extending Grover's algorithm to a new domain with proven robustness.

Findings

Achieves square-root speed-up over classical methods

Uses Fourier transform as a continuous variable Hadamard

Robust to generalized Fourier transformations

Abstract

A fast quantum search algorithm for continuous variables is presented. The result is the quantum continuous variable analog of Grover's algorithm originally proposed for qubits. A continuous variable analog of the Hadamard (i.e., Fourier transform) operation is used in conjunction with inversion about the average of quantum states to allow the approximate identification of an unknown quantum state in a way that gives a square-root speed-up over search algorithms using classical continuous variables. Also, we show that this quantum search algorithm is robust for a generalised Fourier transformation on continuous variables.