Table 1 Glossary of Notations

From: Practical Hamiltonian learning with unitary dynamics and Gibbs states

Symbol

Definition

ϵ

Targeted error (in the ℓ∞ norm) for recovering the Hamiltonian coefficients (Definition 1)

δ

Maximum allowable probability that the recovery (up to an error ϵ) fails (Definition 1)

r

Number of coefficients to learn in the Hamiltonian (Definition 1)

\({{{{{{{\mathscr{D}}}}}}}}\)

The degree of the Hamiltonian – measures the connectedness of H (Definition 2)

Ï„

A typical time scale for the Hamiltonian H (Definition 3)

N

Number of samples required in evaluating f at one point (Definition 4)

A

Maximum evolution time prescribed by the Hamiltonian learning algorithm (Definition 4)

L

Fitting polynomial degree prescribed by the Hamiltonian learning algorithm (Definition 4)