Duality Quantum Computing: Computing with Linear Combinations of Unitaries
Gui-Lu Long, APS and IoP Fellow
Usually, a quantum algorithm uses products of unitaries to complete a task. Lack of technique and intuition in algorithm design has hindered the development of quantum algorithm. Proposed in 2002, duality quantum computing (DQC) takes the advantage of particle-wave duality, and uses linear superpositions of unitary operations, or linear combination of unitary operations (LCU) in quantum computing algorithms. Stan Gudder has studied the mathematical properties of LCU, and has shown that all linear bounded operators can be realized by LCU. In recent years, we have witnessed a wave of new quantum algorithms using LCUs, and even an integrated photonic quantum computing chip has recently been fabricated based on the LCU architecture by an international collaboration of English, Chinese and Australian scientists. Here we will examine the basic ideas of DQC, the mathematical properties of LCU, and its applications in quantum algorithm designs. We will also briefly talk about a realistic interpretation of quantum mechanics based on DQC.
 Gui-Lu, Long. "General quantum interference principle and duality computer." Communications in Theoretical Physics 45.5 (2006): 825. It was submitted to SPIE conference “Fluctuations and Noise 2003” as abstract (5111-53) in 2002.
 Gui-Lu, Long, and Liu Yang. "Duality computing in quantum computers." Communications in Theoretical Physics 50.6 (2008): 1303.
 Gui-Lu, Long, Liu Yang, and Wang Chuan. "Allowable generalized quantum gates." Communications in Theoretical Physics 51.1 (2009): 65.
 Gudder, Stan. "Mathematical theory of duality quantum computers." Quantum Information Processing 6.1 (2007): 37-48.
 Long, Gui Lu. "Duality quantum computing and duality quantum information processing." International Journal of Theoretical Physics 50.4 (2011): 1305-1318.
Monday, May 6, 2019
Mike and Ophelia Lazaridis Quantum-Nano Centre (QNC) Room 0101