Effect of qubit losses on Grover's quantum search algorithm

TL;DR

This paper examines how particle loss affects Grover's quantum search algorithm, showing it converges to mixed states and proposing a method to determine solutions despite losses, relevant for experimental implementations.

Contribution

It analyzes the impact of qubit loss on Grover's algorithm and introduces a procedure to identify solutions without error correction, based on combining multiple trials.

Findings

Algorithm converges to mixed states with 50% overlap with target

Proposed method determines solutions despite particle loss

Applicable to experiments with monitored or unmonitored atom losses

Abstract

We investigate the performance of Grover's quantum search algorithm on a register which is subject to loss of the particles that carry the qubit information. Under the assumption that the basic steps of the algorithm are applied correctly on the correspondingly shrinking register, we show that the algorithm converges to mixed states with 50% overlap with the target state in the bit positions still present. As an alternative to error correction, we present a procedure that combines the outcome of different trials of the algorithm to determine the solution to the full search problem. The procedure may be relevant for experiments where the algorithm is adapted as the loss of particles is registered, and for experiments with Rydberg blockade interactions among neutral atoms, where monitoring of the atom losses is not even necessary.