Quantum Computing Stack Exchange is a question and answer site for engineers, scientists, programmers, and computing professionals interested in quantum computing. It only takes a minute to sign up.
Sign up to join this community
I am reading this error mitigation paper by the IBM team and I am slightly confused about the meaning of "coupling coefficients" when describing multi-qubit Hamiltonian.
I have only seen coupling coefficients in terms describing interaction between atom and external electric field. What do these coefficients mean in terms of pauli gates and why are they time dependent?
The set $G_N$ of all $N$-fold tensor products of the identity and Pauli gates $X$, $Y$ and $Z$ is a basis of the real vector space $L_H$ of Hermitian operators on $N$ qubits. Therefore, $K(t)\in L_H$ can be written as a linear combination of elements in $G_N$
$$ K(t) = \sum_\alpha J_\alpha(t) P_\alpha\tag1 $$
where $P_\alpha\in G_N$ and $J_\alpha(t)\in\mathbb{R}$. The coefficients $J_\alpha$ are time-dependent, because $P_\alpha$ are not and $K$ is. In other words, if coefficients $J_\alpha$ were not time-dependent then the right-hand side of $(1)$ would be constant, unlike the left-hand side.
For terms with more than one non-identity Pauli operator, the coefficients can be interpreted as the strength of the corresponding type of interaction.
