Geometry of Quantum Computation with Qutrits

Bin Li, Zuhuan Yu, and Shao-Ming Fei

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Submission date: 29. Jan. 2014
published in: Scientific Reports, 3 (2013), art-no. 2594 
DOI number (of the published article): 10.1038/srep02594
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Abstract:
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3ⁿ). As an example, three-qutrit systems are investigated in detail.