quantax.optimizer.QNGD#

class quantax.optimizer.QNGD#

Base class of quantum natural gradient descent. It solves the linear equation \(\bar O \dot \theta = \bar \epsilon\), in which \(\bar O\) is the centered Jacobian matrix and \(\bar \epsilon\) is defined by the gradient source grad. The behavior is composed from three pluggable parts: the gradient source (e.g. EnergyGrad), the numerical solver, and the updater strategy (e.g. Spring).

__init__(state: Variational, grad: EnergyGrad | OverlapGrad, imag_time: bool = True, solver: Callable[[...], Array] | None = None, updater: Updater | None = None, file: str | Path | BinaryIO | None = None)#
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.

property state: Variational#

Variational state to be optimized.

property holomorphic: bool#

Whether the state is holomorphic.

property vs_type: VS_TYPE#

The vs_type of the state, see VS_TYPE.

property imag_time: bool#

Whether to use imaginary-time evolution.

property hamiltonian: Operator | None#

The Hamiltonian for the evolution, 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 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.

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 \(1 / d\).

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

Save the optimizer buffers to a file.