quantax.optimizer.QNGD

class quantax.optimizer.QNGD

Abstract class of quantum natural gradient descent.

The key function of the class is get_step, which provides the update of parameters by solving the quantum natural gradient descent equation \(\bar O \dot \theta = \bar \epsilon\), in which \(\bar O = \frac{1}{\sqrt{N_s}}(\frac{1}{\psi} \frac{\partial \psi}{\partial \theta} - \left< \frac{1}{\psi} \frac{\partial \psi}{\partial \theta} \right>)\) and \(\bar \epsilon\) should be defined in the child class.

__init__(state: Variational, imag_time: bool = True, solver: Callable[[Array, Array], Array] | None = None)

Parameters:

• state – Variational state to be optimized.

• imag_time – Whether to use imaginary-time evolution.

• solver – The numerical solver for the matrix inverse, default to auto_pinv_eig.

property state: Variational

Variational state to be optimized.

property holomorphic: bool

Whether the state is holomorphic.

property vs_type: int

The vs_type of the state, see VS_TYPE.

property imag_time: bool

Whether to use imaginary-time evolution.

get_Ebar(samples: Samples) → Array

Method for computing \(\bar \epsilon\) in QNGD equaion, specified by the child class.

get_Obar(samples: Samples) → Array

Calculate \(\bar O = \frac{1}{\sqrt{N_s}}(\frac{1}{\psi} \frac{\partial \psi}{\partial \theta} - \left< \frac{1}{\psi} \frac{\partial \psi}{\partial \theta} \right>)\) for given samples.

solve(Obar: Array, Ebar: Array) → Array

Solve the equation \(\bar O \dot \theta = \bar \epsilon\) for given \(\bar O\) and \(\bar \epsilon\).

get_step(samples: Samples) → Array

Obtain the optimization step by solving the equation \(\bar O \dot \theta = \bar \epsilon\) for given samples.

save(file: str | Path | BinaryIO) → None

Save the optimizer internal quantities to a file.