quantax.optimizer.StochasticQNGD#

class quantax.optimizer.StochasticQNGD#

Bases: QNGD

Stochastic 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 \(\bar \epsilon\) is estimated on the samples by the gradient source.

Parameters:

state – Variational state to be optimized.
grad – The gradient source defining \(\bar \epsilon\), e.g. EnergyGrad or OverlapGrad.
imag_time – Whether to use imaginary-time evolution.
solver – The numerical solver for the matrix inverse, default to auto_shift_eig.
updater – The update strategy applied around the equation solve, default to PlainUpdater.
file – The file with stored buffers of the optimizer.

get_Obar(samples: Samples | Array) → 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.

get_Ebar(samples: Samples | Array) → Array#: Compute \(\bar \epsilon\) of the gradient source for given samples.

get_step(samples: Samples | Array) → Array#: Obtain the optimization step by solving the equation \(\bar O \dot \theta = \bar \epsilon\) for given samples.

property VarE: Array | ndarray | bool | number | bool | int | float | complex | None#: Energy variance \(\left< (H - E)^2 \right>\) of the current step, None when the gradient source doesn’t define it.

property energy: Array | ndarray | bool | number | bool | int | float | complex | None#: Energy of the current step, None when the gradient source doesn’t define it.

property hamiltonian: Operator | None#: The Hamiltonian for the evolution, None when the gradient source doesn’t define it.

property holomorphic: bool#: Whether the state is holomorphic.

property imag_time: bool#: Whether to use imaginary-time evolution.

save(file: str | Path | BinaryIO) → None#: Save the optimizer buffers to a file.

solve(Obar: Array, Ebar: Array, buffers: dict) → tuple[Array, dict]#: Generate the optimization step for given \(\bar O\) and \(\bar \epsilon\) by applying the updater strategy around solve_equation.

solve_equation(Obar: Array, Ebar: Array, **solver_kwargs) → Array#

Solve the linear equation \(\bar O \dot \theta = \bar \epsilon\) for given \(\bar O\) and \(\bar \epsilon\). Real and imaginary parts are stacked for non-holomorphic states, and extra keyword arguments are forwarded to the numerical solver.

A diag_preconditioner keyword is handled here: if the solver declares it as an argument (e.g. lsmr), it is passed through; otherwise the right preconditioning is emulated by solving with \(\bar O / d\) and rescaling the output by \(1 / d\).

property state: Variational#: Variational state to be optimized.

property vs_type: VS_TYPE#: The vs_type of the state, see VS_TYPE.