A new algorithm for producing quantum circuits using KAK decompositions

Details A new algorithm for producing quantum circuits using KAK decompositions A new algorithm for producing quantum circuits using KAK decompositions

2005-09-28

arxiv.org/abs/quant-ph/0509196v4

Physics

Quantum Physics

14 pages, 4 figures, to appear in Quantum Information & Computation, vol. 6, no. 1, 067-080 (2006)

Scientific paper

We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived according to the given Cartan involution. Our algorithm contains, as its special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser decomposition (KGD) in the sense that it derives the same quantum circuits as the ones obtained by them if we select suitable Cartan involutions and square root matrices. The selections of Cartan involutions for computing CSD and KGD will be hown explicitly. As an example, we show explicitly that our method can automatically reproduce the well-known efficient quantum circuit for the n-qubit quantum Fourier transform.

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