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arXiv · 1309.3357

Geometry of Quantum Computation with Qutrits

Bin Li·Zu-Huan Yu·Shao-Ming Fei
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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 $SU(3^n)$. As an example, three-qutrit systems are investigated in detail.

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Bin Li, Zu-Huan Yu, Shao-Ming Fei. 2013-09-13. Geometry of Quantum Computation with Qutrits. https://doi.org/10.1038/srep02594

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