quantax.optimizer.ExactQNGD

class quantax.optimizer.ExactQNGD

Bases: QNGD

Exact quantum natural gradient descent, performed by a full summation in the whole Hilbert space.

The key function of the class is get_step, which provides the update of parameters by solving the quantum natural gradient descent equation \(\bar O \dot \theta = \bar \epsilon\).

__init__(state: Variational, grad: EnergyGrad | OverlapGrad, imag_time: bool = True, solver: Callable[[...], Array] | None = None, symm: Symmetry | 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, default to True.

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

• symm – Symmetry used to construct the Hilbert space, default to be the symmetry of the variational state.

get_Ebar(psi: Array) → Array

Compute \(\bar \epsilon\) of the gradient source in the full Hilbert space.

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.

get_Obar(psi: Array) → Array

Compute \(\bar O\) in the full Hilbert space.

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.

get_step() → Array

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