SIUC Physics Seminar
School of Physics and Applied Physics, Southern Illinois University--Carbondale
2025 February 14 Friday 4:00 PM:
Physics Seminar in Neckers 440
Title: Physically motivated decomposition of qutrit gates
Speaker: Aryan Iliat
Affiliation: Southern Illinois University--Carbondale
Abstract:
Unitary 3×3 matrices (elements in the group U(3)) can be decomposed in numerous ways. One
way is to decompose the matrix into a product of an exponential of a diagonal matrix
and an exponential of an off-diagonal matrix. This decomposition is relevant,
for example, to superconducting qutrits that are typically manipulated using
fixed-frequency resonant control pulses. A key question is whether we can prove
that such a decomposition always exists and is universal in the sense that
it can represent any matrix in U(3). We show that many randomly generated matrices in U(3) can
be represented using this decomposition. Although this is not a mathematically rigorous proof, it
is very strong piece of evidence that this is an acceptable decomposition. We also show that such a
decomposition is possible by identifying a Cartan decomposition for the group. Furthermore, using
the Walsh-Hadamard matrix as an example and a special case of interest, we find a Hamiltonian
that will generate this matrix from a one-parameter subgroup. This method can be used for a
general matrix. In addition, we analyze the relevant energies and find the smallest times needed for
the implementation of qutrit gates.
Last updated on
by K V Shajesh
(kvshajesh@gmail.com).