A new algorithm for producing quantum circuits using
KAK decompositions
(pp067-080)
Yumi
Nakajima, Yasuhito Kawano, and Hiroshi Sekigawa
doi:
https://doi.org/10.26421/QIC6.1-5
Abstracts:
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 shown 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.
Key words:
G=KAG theorem, KGD, CSD, decomposition of the QFT |