Duality Quantum Computing and Duality Quantum Information Processing

Abstract

Quantum mechanical systems exhibit wave-particle duality property. This duality property has been exploited for information processing. A duality quantum computer is a quantum computer on the move and passing through a multi-slits. It offers quantum wave divider and quantum wave combiner operations in addition to those allowed in an ordinary quantum computer. It has been shown that all linear bounded operators can be realized in a duality quantum computer, and a duality quantum computer with n qubits and d-slits can be realized in an ordinary quantum computer with n qubits and a qudit in the so-called duality quantum computing mode. In this article, the main structure of duality quantum computing, their mathematical description and applications are reviewed.

The quest for a Quantum Neural Network

“…However, other ideas of open quantum systems with more than one ground state and attractive dynamics could be a way forward in QNN research that shall be discussed further below. Other alternatives to coherent quantum computing that could be highly interesting for QNN research are measurement-based quantum computing [25], adiabatic quantum computing [26] or duality quantum computing [27].…”

Passive quantum error correction of linear optics networks through error averaging

“…It can also be noted that Eq. (7) can become the appropriate transformation for duality quantum computing by allowing the U i to be arbitrary [11].…”

Existence and construction of a quantum channel with given inputs and outputs

“…Gudder has given the mathematical theory for the duality quantum computer [9,10]. For the further discussions and some applications of duality quantum computers, please refer to [7,8,[12][13][14]. In [13], based on Long's idea of duality quantum computers, we proposed complex duality quantum computers (CDQCs) acting on vector-states and operator-states.…”

“…An evolution of the system is called a quantum operation and denoted by a unitary operator (called a quantum gate) or a completely positive trace-preserving (CPTP) mapping (called a quantum channel). A convex combination of unitary operators is called a generalized quantum gate [2][3][4], which came from a duality quantum computer [5][6][7][8][9][10][11][12][13][14].…”