Parameterising special unitary group SU(4)


Laboratory of Information Technologies

Seminar of the Scientific Department of Computational Physics

Date and Time: Thursday, 13 June 2024, at 3:00 PM

Venue: room 310, Meshcheryakov Laboratory of Information Technologies, online on Webinar

Seminar topic: “Parameterising the special unitary group SU(4)”

Authors: Arsen Khvedelidze, Astghik Torosyan (MLIT), Dimitar Mladenov (Sofia University, Bulgaria)

Speaker: Dimitar Mladenov


In the present talk a new parameterisation of the special unitary group SU(4) is suggested. This parameterisation is adapted to the right action of the subgroup SU(2) x SU(2) of SU(4) and the left action of the maximal torus 𝑇3 on the Lie algebra su(4) and therefore allowing an explicit description of the double coset SU(2) x SU(2) \SU(4)/𝑇3.

Based on the suggested “coordinatisation” of SU(4) group, the Riemannian bi-invariant metric on the group manifold is derived, the volume 15-form and the volume of SU(4) is calculated.

Our studies are motivated by the demand emerging from the problem of development of methods allowing to apply efficient computational schemes for modelling processes with pair of two level systems, two qubits.