notesum.ai

Published at December 6

cs.CE

cs.NA

math.NA

Released Date: December 6, 2024

Authors: Giorgio Tosti Balducci¹, Boyang Chen¹, Matthias Möller, Roeland De Breuker¹

Aff.: ¹Aerospace Structures and Materials TU Delft

n

N

Pauli decomposition

Multi-qubit decomposition

I_{1}I_{0}

I_{1}X_{0}

X_{1}X_{0}

Y_{1}Y_{0}

\text{SWAP}_{(1-0)}

I_{1}I_{0}

Z_{1}Z_{0}

I_{1}X_{0}

I_{2}I_{1}I_{0}

I_{2}I_{1}X_{0}

I_{2}X_{1}X_{0}

I_{2}Y_{1}Y_{0}

X_{2}X_{1}X_{0}

X_{2}Y_{1}Y_{0}

Y_{2}X_{1}Y_{0}

Y_{2}Y_{1}X_{0}

I_{2}\text{SWAP}_{(1-0)}

I_{2}I_{1}I_{0}

I_{2}Z_{1}Z_{0}

I_{2}I_{1}X_{0}

\text{CS}_{(2-0)}

Z_{2}I_{1}Z_{0}

Z_{2}Z_{1}I_{0}

I_{3}I_{2}I_{1}I_{0}

I_{3}I_{2}I_{1}X_{0}

I_{3}I_{2}X_{1}X_{0}

I_{3}I_{2}Y_{1}Y_{0}

I_{3}X_{2}X_{1}X_{0}

I_{3}X_{2}Y_{1}Y_{0}

I_{3}Y_{2}X_{1}Y_{0}

I_{3}Y_{2}Y_{1}X_{0}

X_{3}X_{2}X_{1}X_{0}

X_{3}X_{2}Y_{1}Y_{0}

X_{3}Y_{2}X_{1}Y_{0}

X_{3}Y_{2}Y_{1}X_{0}

Y_{3}X_{2}X_{1}Y_{0}

Y_{3}X_{2}Y_{1}X_{0}

Y_{3}Y_{2}X_{1}X_{0}

Y_{3}Y_{2}Y_{1}Y_{0}

I_{3}I_{2}I_{1}I_{0}

I_{3}I_{2}Z_{1}Z_{0}

I_{3}I_{2}I_{1}X_{0}

I_{3}I_{2}\text{SWAP}_{(1-0)}

I_{3}\text{CS}_{(2-0)}

I_{3}Z_{2}I_{1}Z_{0}

I_{3}Z_{2}Z_{1}I_{0}

\text{CS}^{(2)}_{(3-0)}

Z_{3}I_{2}I_{1}Z_{0}

Z_{3}I_{2}Z_{1}I_{0}

Z_{3}Z_{2}I_{1}I_{0}

Z_{3}Z_{2}Z_{1}Z_{0}

n_{\text{terms}}

$2$^{n}

$2$^{n-1}+n