Geometry of Quantum Computation with Qutrits

Understand

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.