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.
Highlights
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)
Summary
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. A central problem of quantum computation is to find efficient quantum circuits to synthesize desired unitary operation U used in such quantum algorithms. It is shown that the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry. D-dimensional quantum states (qudits) could be more efficient than qubits in quantum information processing such as key distribution in the presence of several eavesdroppers. Due to its long coherence time, it is one of the most promising solid state systems as quantum information processors
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