geope.lie.pauli_projector

geope.lie.pauli_projector.project_omegas(x, basis, dim)

Project a batch of matrices onto a Lie algebra basis.

Computes the trace inner product of each matrix in x with each basis element, normalised by the Hilbert-space dimension.

Parameters:

Name	Type	Description	Default
x	Array	Array of matrices to project, with shape (N, d, d).	required
basis	Array	Basis tensor Array of shape (K, d, d).	required
dim	int	Hilbert-space dimension \(d\).	required

Returns:

Type	Description
Array	Real Array of shape (N, K) of projected coefficients.

geope.lie.pauli_projector.get_project_omegas_fn(basis)

Create a partial projection function with a fixed basis.

Parameters:

Name	Type	Description	Default
basis	Basis	A Basis instance whose matrices and dimension are bound.	required

Returns:

Type	Description
Callable[[Array], Array]	A Callable[[Array], Array] that accepts an array of
Callable[[Array], Array]	matrices and returns the projected coefficients.

geope.lie.pauli_projector.get_kron_chain(n)

Build a JIT-compiled Kronecker product chain function.

Constructs the four single-qubit Pauli matrices and returns a function that builds an \(n\)-qubit Pauli string via iterated Kronecker products.

Parameters:

Name	Type	Description	Default
n	int	Number of qubits.	required

Returns:

Type	Description
Callable[[Array], Array]	A JIT-compiled Callable[[Array], Array] that accepts a
Callable[[Array], Array]	combination index array of length n (values 0–3) and
Callable[[Array], Array]	returns the corresponding (2^n, 2^n) Pauli matrix.

geope.lie.pauli_projector.get_project_omegas_fn_otf(basis, batch_size=None)

Create an on-the-fly omega projection function.

Instead of storing the full basis in memory, Pauli strings are constructed on the fly via Kronecker products. Useful when the number of qubits exceeds 5.

Parameters:

Name	Type	Description	Default
basis	Basis	A Basis instance (only basis.n is used).	required
batch_size	int | None	Optional number of batches to split the Pauli combinations into. If None, a single vmap is used.	None

Returns:

Type	Description
Callable[[Array], Array]	A vmapped Callable[[Array], Array] that accepts a batch
Callable[[Array], Array]	of matrices and returns projected coefficients.