Binary superposed quantum decision diagrams

Abstract

Binary superposed decision diagrams (BSQDDs) are a new type of quantum decision diagram that can be used for representing arbitrary quantum superpositions. One major advantage of BSQDDs is that they are dependent on the types of gates used in synthesis and a BSQDD can be used to efficiently generate a quantum array that will initialize the quantum superposition that the BSQDD represents. Transformation rules for BSQDDs allow BSQDDs to be reduced into simpler BSQDDs that represent the same quantum superposition. Canonical forms exist for a broad class of BSQDDs. This allows BSQDDs to be used for synthesizing quantum arrays that are capable of initializing arbitrary quantum superpositions.

Quantum Associative Neural Network with Nonlinear Search Algorithm

“…In Fig. 8, since the nodes b 10 , b 11 , b 12 , b 13 share the same branch, so that the nodes b 14 , b 15 , b 16 , b 17 are merged, which is the same as the nodes b 18 , b 19 , b 20 and b 21 . This paper takes full advantage of the new quantum gate to replace the Pauil matrix (X) and the Identity matrix (I).…”

“…In fact, it is able to implement to store any quantum superposition states, the differences are just the usage of the quantum gates in nodes [16].…”

“…Improved justifications and further version of the quantum nonlinear algorithm are available in [14,15]. Those articles [7,8,[13][14][15][16] have a certain enlightenment for this paper which a new method to construct the quantum array with the binary decision diagrams and based on the analysis of properties of quantum superposition. In fact, it is able to implement to store any quantum superposition states, the differences are just the usage of the quantum gates in nodes.…”

Applications of Singh-Rajput Mes in Recall Operations of Quantum Associative Memory for a Two- Qubit System

“…Rigui et al have recently proposed a model of Ventura's associative memory for multivalued retrieval [12]. More recently, a model of QuAM with nonlinear search algorithm has been developed [13] based on quantum matrix [12] with bilinear decision diagram [14] and nonlinear search algorithm [15] and it has been shown that bit flip channel leaves the QuAM unaffected and the phase and bit phase flip are the most destructive.…”

Concise quantum associative memories with nonlinear search algorithm

“… The model of Quantum Associative Memories (QAM) we propose here consists in simplifying and generalizing that of Rigui Zhou et al. which uses the quantum matrix with the binary decision diagram put forth by David Rosenbaum and the Abrams and Lloyd's nonlinear search algorithm . Our model gives the possibility to retrieve one of the sought states in multi‐values retrieving scheme when a measurement is done on the first register in time complexity.…”