netket.observable.InfidelityOperator#
- class netket.observable.InfidelityOperator[source]#
Bases:
AbstractObservableInfidelity operator computing the infidelity between an input variational state \(|\Psi\rangle\) and a target state \(|\Phi\rangle\).
The target state can be defined in two ways:
as a variational state that is passed as target_state.
as a state obtained by applying an operator \(U\) to a variational state \(|\Phi\rangle\), i.e., \(|\Phi\rangle \equiv U|\Phi\rangle\).
The infidelity \(I\) among two variational states \(|\Psi\rangle\) and \(|\Phi\rangle\) is defined as:
\[I = 1 - \frac{|\langle\Psi|\Phi\rangle|^2}{\langle\Psi|\Psi\rangle \langle\Phi|\Phi\rangle} = 1 - \frac{\langle\Psi|\hat{I}_{op}|\Psi\rangle}{\langle\Psi|\Psi\rangle},\]where:
\[\hat{I}_{op} = \frac{|\Phi\rangle\langle\Phi|}{\langle\Phi|\Phi\rangle}.\]The Monte Carlo estimator of \(I\) is:
\[I = \mathbb{E}_{\chi}[ I_{loc}(x,y) ] = \mathbb{E}_{\chi}\left[ \frac{\langle x|\Phi\rangle \langle y|\Psi\rangle}{\langle x|\Psi\rangle \langle y|\Phi\rangle} \right],\]where \(\chi(x, y) = \frac{|\Psi(x)|^2 |\Phi(y)|^2}{\langle\Psi|\Psi\rangle \langle\Phi|\Phi\rangle}\) is the joint Born distribution. This estimator can be utilized both when \(|\Phi\rangle = |\Phi\rangle\) and when \(|\Phi\rangle = U|\Phi\rangle\), with \(U\) a (unitary or non-unitary) operator. We remark that sampling from \(U|\Phi\rangle\) is more expensive than sampling from an autonomous state.
For details see Sinibaldi et al. and Gravina et al..
- Inheritance
Methods