Geometry of Quantum Computation with Qudits
نویسندگان
چکیده
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.
منابع مشابه
Counterexamples to Kalai's conjecture C
1 The First Counterexample Let ρ be a quantum state on the space (C) of n qudits (d-dimensional quantum systems). Denote by ρS the reduced state of ρ onto some subset S of the qudits. We partition S further into two nonempty subsets of qudits A and A := S\A (thus S must contain at least two qudits). Denote by Sep(A) the convex set of quantum states which are bipartite separable on S across the ...
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