optimizer

Quantum natural gradient descent

QNGD	Base class of quantum natural gradient descent.
StochasticQNGD	Stochastic quantum natural gradient descent.
ExactQNGD	Exact quantum natural gradient descent, performed by a full summation in the whole Hilbert space.
SR	Stochastic reconfiguration (SR).
SPRING	SPRING optimizer.
MARCH	MARCH optimizer.
AdamSR	AdamSR optimizer.
ER	Exact reconfiguration, performed by a full summation in the whole Hilbert space.
TimeEvol	Time evolution optimizer, equivalent to real-time SR.

Supervised learning

Supervised	Supervised optimization of the wave function towards a target state by stochastic reconfiguration on the overlap gradient.
SupervisedAdam	Supervised optimization towards a target state with the Adam-like update of AdamSR.
SupervisedExact	Supervised optimization towards a target state by a full summation in the whole Hilbert space.

Gradient sources

EnergyGrad	Energy gradient source defining \(\bar \epsilon\) from the local energies of a Hamiltonian, used for ground-state search and time evolution.
OverlapGrad	Overlap gradient source defining \(\bar \epsilon\) from the amplitude ratios with a target state, used for supervised wave function optimization.

Update strategies

Updater	Base class of update strategies for QNGD optimizers.
PlainUpdater	The plain update \(\dot\theta = \mathrm{solve}(\bar O, \bar\epsilon)\).
Spring	The SPRING update, a variant of SR with momentum stored in the phi buffer.
March	The MARCH update, a variant of SR with first and second order momentum stored in the phi and v buffers.
Adam	The AdamSR update, a variant of SR with first and second order momentum (like Adam) stored in the m, v and t buffers.

Solvers

Iterative solvers

lstsq_shift_cg	Obtain the least-square solver for the linear equation \(Ax=b\) using diagonal shift, corresponding to SR.
minnorm_shift_cg	Obtain the minimum-norm solver for the linear equation \(Ax=b\) using diagonal shift, corresponding to MinSR.
lsmr	Obtain the least-square solver for the linear equation \(Ax=b\) solved by the LSMR method lineax.LSMR.

Non-iterative solvers

minnorm_shift_eig	The MinSR branch of auto_shift_eig, computing \(x = A^† (A A^† + \epsilon I)^{-1} b\) by directly forming the shifted matrix and solving it with a Cholesky solver.
lstsq_shift_eig	The SR branch of auto_shift_eig, computing \(x = (A^† A + \epsilon I)^{-1} A^† b\) by directly forming the shifted matrix and solving it with a Cholesky solver.
auto_shift_eig	Obtain the least-square minimum-norm solver for the linear equation \(Ax=b\) using diagonal shift.
pinvh_solve	Solver for a Hermitian linear equation \(H x = b\) via the pseudo-inverse of \(H\) obtained from its eigendecomposition.
minnorm_pinv_eig	The MinSR branch of auto_pinv_eig, computing \(x = A^† (A A^†)^{-1} b\) via the pseudo-inverse of \(A A^†\) from its eigendecomposition.
lstsq_pinv_eig	The SR branch of auto_pinv_eig, computing \(x = (A^† A)^{-1} A^† b\) via the pseudo-inverse of \(A^† A\) from its eigendecomposition.
auto_pinv_eig	Obtain the least-square minimum-norm solver for the linear equation \(Ax=b\) using pseudo-inverse.
block_pinv_eig	Obtain the layerwise least-square minimum-norm solver for the linear equation \(Ax=b\) using pseudo-inverse.
sgd_solver	The plain stochastic gradient descent solver, returning \(x = A^† b / N_s\) without any preconditioning.