Concise Quantum Associative Memories with Nonlinear Search Algorithm

TL;DR

This paper introduces a simplified and generalized quantum associative memory model utilizing a nonlinear search algorithm, outperforming Grover's algorithm in retrieval efficiency and analyzing its noise susceptibility.

Contribution

The paper presents a new quantum associative memory model that simplifies previous models and incorporates a nonlinear search algorithm for improved retrieval performance.

Findings

Outperforms Grover's algorithm in retrieval efficiency.

Maintains about 70% fidelity under single-qubit noise.

Allows multi-value retrieval with a single measurement.

Abstract

The model of quantum associative memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou \etal \cite{zhou2012} who uses the quantum matrix with binary decision diagram and nonlinear search algorithm in his model. It is worth noting that David Rosenbaum put forth the quantum matrix with binary decision diagram \cite{Rosenbaum2010} and Abrams and Llyod did the nonlinear algorithm. \cite{Abrams1998} Our model gives the possibility to retrieve one of the sought states in multi-values retrieving scheme when a measure on the first register is done. It is better than Grover's algorithm and its modified form which need $\mathcal{O}(\sqrt{\frac{2^n} {m}})$ steps when they are used as the retrieval algorithm. $n$ is the number of qubit of the first register and $m$ the number of values $x$ for which $f(x)=1$. As the nonlinearity makes the system highly susceptible to noise, an analysis of the influence of the single qubit noise channels on the Nonlinear Search Algorithm of our model of QAM, shows a fidelity of about $0.7$ whatever the number of qubits present in the first register.