qlinks.operators package

Submodules

qlinks.operators.base module

class qlinks.operators.base.OperatorAction(coefficient, config)

Bases: object

One operator action on one computational configuration.

coefficient:

Matrix element contributed by this action.

config:

Resulting configuration after the operator acts. For diagonal operators, this is usually a copy of the input config.

coefficient: complex

config: ndarray[tuple[Any, ...], dtype[int64]]

__init__(coefficient, config)

class qlinks.operators.base.LocalOperator(*args, **kwargs)

Bases: Protocol

Interface for all configuration-space operators.

layout: VariableLayout

name: str

affected_variables()

apply(config)

__init__(*args, **kwargs)

class qlinks.operators.base.DiagonalLocalOperator(*args, **kwargs)

Bases: LocalOperator, Protocol

Configuration-space diagonal operator.

Returning None means the operator gives no action on this config. Returning a complex number means the operator contributes that diagonal matrix element.

diagonal_value(config)

class qlinks.operators.base.BaseLocalOperator

Bases: object

Convenience base for configuration-space local operators.

Notes

Concrete operators should precompute geometry/layout-dependent data in __post_init__() so that apply() only performs cheap indexed array operations.

layout: VariableLayout

name: str

affected_variables()

class qlinks.operators.base.OperatorSum(terms, name='operator_sum')

Bases: object

Formal sum of local operators.

This is still only an action-level object. Sparse matrix construction is handled by the next layer.

terms: tuple[LocalOperator, ...]

name: str

classmethod from_terms(terms, name='operator_sum')

affected_variables()

apply(config)

__init__(terms, name='operator_sum')

qlinks.operators.base.combine_duplicate_actions(actions, *, atol=0.0)

Combine actions that produce the same output configuration.

This is useful before sparse assembly when two terms lead to the same row/column matrix element.

qlinks.operators.diagonal module

class qlinks.operators.diagonal.ConstantDiagonalOperator(layout, coefficient, name='constant_diagonal')

Bases: BaseLocalOperator

Diagonal operator c * I.

layout: VariableLayout

coefficient: complex

name: str

diagonal_value(config)

apply(config)

__init__(layout, coefficient, name='constant_diagonal')

class qlinks.operators.diagonal.LocalValueDiagonalOperator(layout, variable_index, coefficient=1.0, name='local_value_diagonal')

Bases: BaseLocalOperator

Diagonal operator proportional to one variable value.

coefficient * config[variable_index]

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='local_value_diagonal')

class qlinks.operators.diagonal.LocalSquareValueDiagonalOperator(layout, variable_index, coefficient=1.0, name='local_square_value_diagonal')

Bases: BaseLocalOperator

Diagonal operator proportional to one squared variable value.

coefficient * config[variable_index] ** 2

For spin-1 variables m in {-1, 0, +1}, this represents coefficient * (S^z)^2 in the S^z product basis.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='local_square_value_diagonal')

class qlinks.operators.diagonal.LocalSumDiagonalOperator(layout, variable_indices, weights=None, coefficient=1.0, name='local_sum_diagonal')

Bases: BaseLocalOperator

Diagonal operator

coefficient * sum_i weights[i] * config[variable_indices[i]]

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

weights: ndarray[tuple[Any, ...], dtype[int64]] | None

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_indices, weights=None, coefficient=1.0, name='local_sum_diagonal')

class qlinks.operators.diagonal.PatternDiagonalOperator(layout, variable_indices, pattern, coefficient=1.0, name='pattern_diagonal')

Bases: BaseLocalOperator

Diagonal projector-like operator.

If selected variables match pattern, return coefficient * config. Otherwise return no action.

Example

A flippability counter for a plaquette can be represented as a sum of pattern diagonal operators.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

pattern: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_indices, pattern, coefficient=1.0, name='pattern_diagonal')

qlinks.operators.linear module

class qlinks.operators.linear.BasisOperator(basis, operators, combine_duplicates=True, drop_zero_atol=0.0, dtype=<class 'numpy.complex128'>)

Bases: object

Matrix-like wrapper around configuration-space local operators.

The wrapper applies local operators directly by looping over basis states; it does not explicitly build a sparse matrix. It supports matrix-vector products and transpose/Hermitian-adjoint views.

basis

Basis that fixes row/column ordering.

Type:

qlinks.basis.basis.Basis

operators

Local operators to sum.

Type:

tuple[qlinks.operators.base.LocalOperator, …]

combine_duplicates

Whether to combine duplicate actions within a column.

Type:

bool

drop_zero_atol

Absolute threshold for dropping small coefficients.

Type:

float

dtype

Output dtype for matrix-vector products.

Type:

type[Any] | numpy.dtype[Any] | numpy._typing._dtype_like._SupportsDType[numpy.dtype[Any]] | tuple[Any, Any] | list[Any] | numpy._typing._dtype_like._DTypeDict | str | None

Examples

>>> operator = BasisOperator(basis, operators)
>>> y = operator @ vector
>>> y_t = operator.T @ vector
>>> y_h = operator.H @ vector

basis: Basis

operators: tuple[LocalOperator, ...]

combine_duplicates: bool = True

drop_zero_atol: float = 0.0

dtype

alias of complex128

classmethod from_operator(basis, operator, **kwargs)

property shape: tuple[int, int]

property T: TransposedBasisOperator

property H: TransposedBasisOperator

Hermitian adjoint view.

matvec(vector)

Compute self @ vector.

matmat(matrix)

Compute self @ matrix, where matrix has shape (n_basis, n_vecs).

rmatvec(vector)

Compute vector @ self.

rmatmat(matrix)

Compute matrix @ self, where matrix has shape (n_vecs, n_basis).

expectation(vector, *, conjugate=True)

Compute <v|O|v> by default.

If conjugate=False, compute v.T @ O @ v.

__init__(basis, operators, combine_duplicates=True, drop_zero_atol=0.0, dtype=<class 'numpy.complex128'>)

class qlinks.operators.linear.TransposedBasisOperator(parent, conjugate=False)

Bases: object

Transpose or adjoint view of BasisOperator.

parent: BasisOperator

conjugate: bool = False

property shape: tuple[int, int]

property T: BasisOperator | TransposedBasisOperator

property H: BasisOperator

matvec(vector)

Compute A.T @ vector or A.H @ vector.

rmatvec(vector)

Compute vector @ A.T or vector @ A.H.

__init__(parent, conjugate=False)

qlinks.operators.linear.as_basis_operator(basis, operators, **kwargs)

Convenience constructor.

qlinks.operators.plaquette module

class qlinks.operators.plaquette.PlaquettePatternTransition(initial, final, coefficient=1.0)

Bases: object

One allowed plaquette pattern transition.

initial:

Values on plaquette links before the operator acts.

final:

Values on plaquette links after the operator acts.

coefficient:

Matrix element for this transition.

initial: ndarray[tuple[Any, ...], dtype[int64]]

final: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

__init__(initial, final, coefficient=1.0)

class qlinks.operators.plaquette.PlaquettePatternOperator(layout, lattice, plaquette_id, transitions, name='plaquette_pattern')

Bases: BaseLocalOperator

General plaquette transition operator.

It reads the plaquette’s link variables in the lattice plaquette order. If the current values match one of the allowed transition patterns, it returns the corresponding new configuration.

This is suitable for QDM plaquette flips, constrained ring exchanges, and other local loop moves.

layout: VariableLayout

lattice: LatticeGraph

plaquette_id: int

transitions: tuple[PlaquettePatternTransition, ...]

name: str

classmethod qdm_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

Standard binary dimer plaquette flip:

1010 <-> 0101

The order is the plaquette link order supplied by the lattice.

classmethod alternating_binary_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

classmethod alternating_flux_flip(layout, lattice, plaquette_id, coefficient=1.0)

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, plaquette_id, transitions, name='plaquette_pattern')

qlinks.operators.plaquette.qdm_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return diagonal projectors onto the two flippable QDM plaquette patterns:

1010 and 0101

The potential term V * P_p^2 in a QDM-like model can be represented using these diagonal projectors.

qlinks.operators.plaquette.alternating_binary_patterns(length)

Return the two binary alternating patterns on an even plaquette.

Parameters:

length (int) – Plaquette cycle length.

Returns:

Pair of arrays like 1010... and 0101....

Return type:

tuple[ndarray, ndarray]

qlinks.operators.plaquette.alternating_flux_patterns(length)

Return the two {-1, +1} alternating flux patterns.

Parameters:

length (int) – Plaquette cycle length.

Returns:

Pair of opposite alternating flux arrays.

Return type:

tuple[ndarray, ndarray]

qlinks.operators.plaquette.alternating_binary_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return binary flippability projectors for one plaquette.

Parameters:

• layout (VariableLayout) – Variable layout.

• lattice (LatticeGraph) – Lattice containing the plaquette.

• plaquette_id (int) – Plaquette id.

• coefficient (complex) – Diagonal coefficient for each projector.

Returns:

Pair of diagonal projectors onto the two alternating binary patterns.

Return type:

tuple[PatternDiagonalOperator, PatternDiagonalOperator]

qlinks.operators.plaquette.alternating_flux_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return flux flippability projectors for one plaquette.

Parameters:

• layout (VariableLayout) – Variable layout.

• lattice (LatticeGraph) – Lattice containing the plaquette.

• plaquette_id (int) – Plaquette id.

• coefficient (complex) – Diagonal coefficient for each projector.

Returns:

Pair of diagonal projectors onto the two alternating flux patterns.

Return type:

tuple[PatternDiagonalOperator, PatternDiagonalOperator]

qlinks.operators.pxp module

class qlinks.operators.pxp.PXPSpinFlipOperator(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='pxp_spin_flip')

Bases: BaseLocalOperator

Constrained spin flip for PXP/Rydberg-blockade models.

The spin at site_id is flipped only if all neighboring sites are not occupied.

With binary variables:

0 <-> 1

and usually:

occupied_value = 1

layout: VariableLayout

lattice: LatticeGraph

site_id: int

coefficient: complex

occupied_value: int

name: str

property site_variable: int

property neighbor_sites: ndarray[tuple[Any, ...], dtype[int64]]

property neighbor_variables: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='pxp_spin_flip')

qlinks.operators.spin_one module

qlinks.operators.spin_one.spin_one_raise_amplitude(m)

Spin-1 S^+ amplitude.

S^+ |m> = sqrt(S(S+1) - m(m+1)) |m+1>

for S=1 and m in {-1, 0, 1}.

qlinks.operators.spin_one.spin_one_lower_amplitude(m)

Spin-1 S^- amplitude.

S^- |m> = sqrt(S(S+1) - m(m-1)) |m-1>

for S=1 and m in {-1, 0, 1}.

class qlinks.operators.spin_one.SpinOneXYBondOperator(layout, lattice, link_id, coefficient=1.0, name='spin_one_xy_bond')

Bases: BaseLocalOperator

Spin-1 XY bond operator on sites i,j.

H_ij = J_xy * (S^x_i S^x_j + S^y_i S^y_j)

= J_xy/2 * (S^+_i S^-_j + S^-_i S^+_j)

The computational basis is the S^z product basis with values:

m_i in {-1, 0, +1}

layout: VariableLayout

lattice: ChainLattice

link_id: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, link_id, coefficient=1.0, name='spin_one_xy_bond')

class qlinks.operators.spin_one.UpdateSpinOneXYBondOperator(layout, lattice, link_id, coefficient=1.0, name='update_spin_one_xy_bond')

Bases: BaseLocalUpdateOperator

Update-action version of SpinOneXYBondOperator.

The operator returns only local two-site updates instead of allocating full output configurations. It is intended for OptimizedSparseHamiltonianBuilder.

layout: VariableLayout

lattice: ChainLattice

link_id: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply_update(config)

__init__(layout, lattice, link_id, coefficient=1.0, name='update_spin_one_xy_bond')

class qlinks.operators.spin_one.SpinOneXYPairOperator(layout, site_i, site_j, coefficient=1.0, name='spin_one_xy_pair')

Bases: BaseLocalOperator

Hermitian spin-1 XY exchange on an arbitrary ordered site pair.

The operator uses the same matrix-element convention as SpinOneXYBondOperator for real couplings,

0.5 * (t S_i^+ S_j^- + t^* S_i^- S_j^+).

Consequently an allowed |0,0> -> |+,- > transition has matrix element t. Complex t gives a Hermitian Peierls-phase exchange.

layout: VariableLayout

site_i: int

site_j: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, site_i, site_j, coefficient=1.0, name='spin_one_xy_pair')

class qlinks.operators.spin_one.UpdateSpinOneXYPairOperator(layout, site_i, site_j, coefficient=1.0, name='update_spin_one_xy_pair')

Bases: BaseLocalUpdateOperator

Update-action version of SpinOneXYPairOperator.

layout: VariableLayout

site_i: int

site_j: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply_update(config)

__init__(layout, site_i, site_j, coefficient=1.0, name='update_spin_one_xy_pair')

qlinks.operators.toric_code module

class qlinks.operators.toric_code.ToricCodeStarFlipOperator(layout, lattice, site_id, coefficient=-1.0, name='toric_code_star_flip')

Bases: BaseLocalOperator

Toric-code star operator A_v in the Z basis.

It flips all links incident on site v.

layout: VariableLayout

lattice: SquareLattice

site_id: int

coefficient: complex

name: str

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, site_id, coefficient=-1.0, name='toric_code_star_flip')

class qlinks.operators.toric_code.ToricCodePlaquetteFluxOperator(layout, lattice, plaquette_id, coefficient=-1.0, name='toric_code_plaquette_flux')

Bases: BaseLocalOperator

Toric-code plaquette operator B_p in the Z basis.

It is diagonal:

B_p |z> = prod_{l in boundary(p)} z_l |z>

layout: VariableLayout

lattice: SquareLattice

plaquette_id: int

coefficient: complex

name: str

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, lattice, plaquette_id, coefficient=-1.0, name='toric_code_plaquette_flux')

qlinks.operators.transitions module

class qlinks.operators.transitions.SetVariablesOperator(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='set_variables')

Bases: BaseLocalOperator

General local transition operator.

If

config[variable_indices] == initial_values

then produce a new config with

new_config[variable_indices] = final_values

Otherwise return no action.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

initial_values: ndarray[tuple[Any, ...], dtype[int64]]

final_values: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

apply(config)

__init__(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='set_variables')

class qlinks.operators.transitions.BinaryFlipOperator(layout, variable_index, coefficient=1.0, name='binary_flip')

Bases: BaseLocalOperator

Flip one binary variable 0 <-> 1.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_site(layout, site_id, coefficient=1.0)

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='binary_flip')

class qlinks.operators.transitions.NegationFlipOperator(layout, variable_index, coefficient=1.0, name='negation_flip')

Bases: BaseLocalOperator

Flip one sign variable v -> -v.

Useful for internal integer representation of spin-1/2 flux variables with values {-1, +1}.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='negation_flip')

class qlinks.operators.transitions.MultiNegationFlipOperator(layout, variable_indices, coefficient=1.0, name='multi_negation_flip')

Bases: BaseLocalOperator

Simultaneously apply v -> -v to several variables.

Useful as a simple QLM-like plaquette flip when the link variables are represented as {-1, +1}.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

apply(config)

__init__(layout, variable_indices, coefficient=1.0, name='multi_negation_flip')

qlinks.operators.updates module

class qlinks.operators.updates.LocalUpdateAction(coefficient, variable_indices, new_values)

Bases: object

Compact operator action.

Instead of storing the full output configuration, store only

variable_indices new_values

The optimized sparse builder will reuse a scratch array:

scratch[:] = config scratch[variable_indices] = new_values

coefficient: complex

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

new_values: ndarray[tuple[Any, ...], dtype[int64]]

__init__(coefficient, variable_indices, new_values)

class qlinks.operators.updates.LocalUpdateOperator(*args, **kwargs)

Bases: Protocol

Optimized local-operator protocol.

This protocol does not return a full new configuration. It returns only local updates.

layout: VariableLayout

name: str

affected_variables()

apply_update(config)

__init__(*args, **kwargs)

class qlinks.operators.updates.SingleLocalUpdateOperator(*args, **kwargs)

Bases: LocalUpdateOperator, Protocol

Local update operator with at most one action per input config.

single_update(config)

class qlinks.operators.updates.BaseLocalUpdateOperator

Bases: object

Convenience base for update-style local operators.

Subclasses provide a layout and implement update methods that return local variable indices and replacement values instead of full configurations.

layout: VariableLayout

name: str

affected_variables()

class qlinks.operators.updates.UpdateOperatorSum(terms, name='update_operator_sum')

Bases: object

Sum of update-level local operators.

terms: tuple[LocalUpdateOperator, ...]

name: str

classmethod from_terms(terms, name='update_operator_sum')

affected_variables()

apply_update(config)

__init__(terms, name='update_operator_sum')

class qlinks.operators.updates.UpdateSetVariablesOperator(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='update_set_variables')

Bases: BaseLocalUpdateOperator

Optimized version of SetVariablesOperator.

If config[variable_indices] == initial_values, return a local update setting those variables to final_values.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

initial_values: ndarray[tuple[Any, ...], dtype[int64]]

final_values: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='update_set_variables')

class qlinks.operators.updates.UpdateBinaryFlipOperator(layout, variable_index, coefficient=1.0, name='update_binary_flip')

Bases: BaseLocalUpdateOperator

Optimized binary flip 0 <-> 1.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_site(layout, site_id, coefficient=1.0)

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_index, coefficient=1.0, name='update_binary_flip')

class qlinks.operators.updates.UpdateNegationFlipOperator(layout, variable_index, coefficient=1.0, name='update_negation_flip')

Bases: BaseLocalUpdateOperator

Optimized sign flip v -> -v.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_index, coefficient=1.0, name='update_negation_flip')

class qlinks.operators.updates.UpdateMultiNegationFlipOperator(layout, variable_indices, coefficient=1.0, name='update_multi_negation_flip')

Bases: BaseLocalUpdateOperator

Optimized simultaneous sign flip on several variables.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_indices, coefficient=1.0, name='update_multi_negation_flip')

class qlinks.operators.updates.UpdatePlaquettePatternTransition(initial, final, coefficient=1.0)

Bases: object

One local plaquette pattern transition for update operators.

initial

Source local pattern.

Type:

numpy.ndarray[tuple[Any, …], numpy.dtype[numpy.int64]]

final

Target local pattern.

Type:

numpy.ndarray[tuple[Any, …], numpy.dtype[numpy.int64]]

coefficient

Transition coefficient.

Type:

complex

initial: ndarray[tuple[Any, ...], dtype[int64]]

final: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

__init__(initial, final, coefficient=1.0)

class qlinks.operators.updates.UpdatePlaquettePatternOperator(layout, lattice, plaquette_id, transitions, name='update_plaquette_pattern')

Bases: BaseLocalUpdateOperator

Optimized plaquette-pattern transition operator.

This is the update-action version of PlaquettePatternOperator.

layout: VariableLayout

lattice: LatticeGraph

plaquette_id: int

transitions: tuple[UpdatePlaquettePatternTransition, ...]

name: str

classmethod qdm_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

property supports_single_update: bool

single_update(config)

apply_update(config)

__init__(layout, lattice, plaquette_id, transitions, name='update_plaquette_pattern')

class qlinks.operators.updates.UpdatePXPSpinFlipOperator(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='update_pxp_spin_flip')

Bases: BaseLocalUpdateOperator

Optimized PXP constrained spin flip.

Flip site_id only if all neighbors are not occupied.

layout: VariableLayout

lattice: LatticeGraph

site_id: int

coefficient: complex

occupied_value: int

name: str

property site_variable: int

property neighbor_sites: ndarray[tuple[Any, ...], dtype[int64]]

property neighbor_variables: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='update_pxp_spin_flip')

Module contents

class qlinks.operators.BaseLocalOperator

Bases: object

Convenience base for configuration-space local operators.

Notes

Concrete operators should precompute geometry/layout-dependent data in __post_init__() so that apply() only performs cheap indexed array operations.

layout: VariableLayout

name: str

affected_variables()

class qlinks.operators.BaseLocalUpdateOperator

Bases: object

Convenience base for update-style local operators.

Subclasses provide a layout and implement update methods that return local variable indices and replacement values instead of full configurations.

layout: VariableLayout

name: str

affected_variables()

class qlinks.operators.BasisOperator(basis, operators, combine_duplicates=True, drop_zero_atol=0.0, dtype=<class 'numpy.complex128'>)

Bases: object

Matrix-like wrapper around configuration-space local operators.

The wrapper applies local operators directly by looping over basis states; it does not explicitly build a sparse matrix. It supports matrix-vector products and transpose/Hermitian-adjoint views.

basis

Basis that fixes row/column ordering.

Type:

qlinks.basis.basis.Basis

operators

Local operators to sum.

Type:

tuple[qlinks.operators.base.LocalOperator, …]

combine_duplicates

Whether to combine duplicate actions within a column.

Type:

bool

drop_zero_atol

Absolute threshold for dropping small coefficients.

Type:

float

dtype

Output dtype for matrix-vector products.

Type:

type[Any] | numpy.dtype[Any] | numpy._typing._dtype_like._SupportsDType[numpy.dtype[Any]] | tuple[Any, Any] | list[Any] | numpy._typing._dtype_like._DTypeDict | str | None

Examples

>>> operator = BasisOperator(basis, operators)
>>> y = operator @ vector
>>> y_t = operator.T @ vector
>>> y_h = operator.H @ vector

basis: Basis

operators: tuple[LocalOperator, ...]

combine_duplicates: bool = True

drop_zero_atol: float = 0.0

dtype

alias of complex128

classmethod from_operator(basis, operator, **kwargs)

property shape: tuple[int, int]

property T: TransposedBasisOperator

property H: TransposedBasisOperator

Hermitian adjoint view.

matvec(vector)

Compute self @ vector.

matmat(matrix)

Compute self @ matrix, where matrix has shape (n_basis, n_vecs).

rmatvec(vector)

Compute vector @ self.

rmatmat(matrix)

Compute matrix @ self, where matrix has shape (n_vecs, n_basis).

expectation(vector, *, conjugate=True)

Compute <v|O|v> by default.

If conjugate=False, compute v.T @ O @ v.

__init__(basis, operators, combine_duplicates=True, drop_zero_atol=0.0, dtype=<class 'numpy.complex128'>)

class qlinks.operators.BinaryFlipOperator(layout, variable_index, coefficient=1.0, name='binary_flip')

Bases: BaseLocalOperator

Flip one binary variable 0 <-> 1.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_site(layout, site_id, coefficient=1.0)

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='binary_flip')

class qlinks.operators.ConstantDiagonalOperator(layout, coefficient, name='constant_diagonal')

Bases: BaseLocalOperator

Diagonal operator c * I.

layout: VariableLayout

coefficient: complex

name: str

diagonal_value(config)

apply(config)

__init__(layout, coefficient, name='constant_diagonal')

class qlinks.operators.DiagonalLocalOperator(*args, **kwargs)

Bases: LocalOperator, Protocol

Configuration-space diagonal operator.

Returning None means the operator gives no action on this config. Returning a complex number means the operator contributes that diagonal matrix element.

diagonal_value(config)

class qlinks.operators.DiskDiagonalHopOperator(layout, lattice, source_site, target_site, coefficient=1.0, occupied_value=1, empty_value=0, enforce_nearest_neighbor_blockade=True, name='disk_diagonal_hop')

Bases: BaseLocalOperator

Move one hard-core disk along a diagonal bond.

layout: VariableLayout

lattice: SquareLattice

source_site: int

target_site: int

coefficient: complex

occupied_value: int

empty_value: int

enforce_nearest_neighbor_blockade: bool

name: str

classmethod pairs_for_family(lattice, *, family)

affected_variables()

apply(config)

__init__(layout, lattice, source_site, target_site, coefficient=1.0, occupied_value=1, empty_value=0, enforce_nearest_neighbor_blockade=True, name='disk_diagonal_hop')

class qlinks.operators.DiskDiagonalHopProjector(layout, source_site, target_site, coefficient=1.0, occupied_value=1, empty_value=0, name='disk_diagonal_hop_projector')

Bases: BaseLocalOperator

Diagonal projector onto a mobile disk on one directed diagonal bond.

layout: VariableLayout

source_site: int

target_site: int

coefficient: complex

occupied_value: int

empty_value: int

name: str

affected_variables()

diagonal_value(config)

__init__(layout, source_site, target_site, coefficient=1.0, occupied_value=1, empty_value=0, name='disk_diagonal_hop_projector')

class qlinks.operators.LocalOperator(*args, **kwargs)

Bases: Protocol

Interface for all configuration-space operators.

layout: VariableLayout

name: str

affected_variables()

apply(config)

__init__(*args, **kwargs)

class qlinks.operators.LocalSquareValueDiagonalOperator(layout, variable_index, coefficient=1.0, name='local_square_value_diagonal')

Bases: BaseLocalOperator

Diagonal operator proportional to one squared variable value.

coefficient * config[variable_index] ** 2

For spin-1 variables m in {-1, 0, +1}, this represents coefficient * (S^z)^2 in the S^z product basis.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='local_square_value_diagonal')

class qlinks.operators.LocalSumDiagonalOperator(layout, variable_indices, weights=None, coefficient=1.0, name='local_sum_diagonal')

Bases: BaseLocalOperator

Diagonal operator

coefficient * sum_i weights[i] * config[variable_indices[i]]

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

weights: ndarray[tuple[Any, ...], dtype[int64]] | None

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_indices, weights=None, coefficient=1.0, name='local_sum_diagonal')

class qlinks.operators.LocalUpdateAction(coefficient, variable_indices, new_values)

Bases: object

Compact operator action.

Instead of storing the full output configuration, store only

variable_indices new_values

The optimized sparse builder will reuse a scratch array:

scratch[:] = config scratch[variable_indices] = new_values

coefficient: complex

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

new_values: ndarray[tuple[Any, ...], dtype[int64]]

__init__(coefficient, variable_indices, new_values)

class qlinks.operators.LocalUpdateOperator(*args, **kwargs)

Bases: Protocol

Optimized local-operator protocol.

This protocol does not return a full new configuration. It returns only local updates.

layout: VariableLayout

name: str

affected_variables()

apply_update(config)

__init__(*args, **kwargs)

class qlinks.operators.LocalValueDiagonalOperator(layout, variable_index, coefficient=1.0, name='local_value_diagonal')

Bases: BaseLocalOperator

Diagonal operator proportional to one variable value.

coefficient * config[variable_index]

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='local_value_diagonal')

class qlinks.operators.MultiNegationFlipOperator(layout, variable_indices, coefficient=1.0, name='multi_negation_flip')

Bases: BaseLocalOperator

Simultaneously apply v -> -v to several variables.

Useful as a simple QLM-like plaquette flip when the link variables are represented as {-1, +1}.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

apply(config)

__init__(layout, variable_indices, coefficient=1.0, name='multi_negation_flip')

class qlinks.operators.NegationFlipOperator(layout, variable_index, coefficient=1.0, name='negation_flip')

Bases: BaseLocalOperator

Flip one sign variable v -> -v.

Useful for internal integer representation of spin-1/2 flux variables with values {-1, +1}.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

apply(config)

__init__(layout, variable_index, coefficient=1.0, name='negation_flip')

class qlinks.operators.OperatorAction(coefficient, config)

Bases: object

One operator action on one computational configuration.

coefficient:

Matrix element contributed by this action.

config:

Resulting configuration after the operator acts. For diagonal operators, this is usually a copy of the input config.

coefficient: complex

config: ndarray[tuple[Any, ...], dtype[int64]]

__init__(coefficient, config)

class qlinks.operators.OperatorSum(terms, name='operator_sum')

Bases: object

Formal sum of local operators.

This is still only an action-level object. Sparse matrix construction is handled by the next layer.

terms: tuple[LocalOperator, ...]

name: str

classmethod from_terms(terms, name='operator_sum')

affected_variables()

apply(config)

__init__(terms, name='operator_sum')

class qlinks.operators.PXPSpinFlipOperator(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='pxp_spin_flip')

Bases: BaseLocalOperator

Constrained spin flip for PXP/Rydberg-blockade models.

The spin at site_id is flipped only if all neighboring sites are not occupied.

With binary variables:

0 <-> 1

and usually:

occupied_value = 1

layout: VariableLayout

lattice: LatticeGraph

site_id: int

coefficient: complex

occupied_value: int

name: str

property site_variable: int

property neighbor_sites: ndarray[tuple[Any, ...], dtype[int64]]

property neighbor_variables: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='pxp_spin_flip')

class qlinks.operators.PatternDiagonalOperator(layout, variable_indices, pattern, coefficient=1.0, name='pattern_diagonal')

Bases: BaseLocalOperator

Diagonal projector-like operator.

If selected variables match pattern, return coefficient * config. Otherwise return no action.

Example

A flippability counter for a plaquette can be represented as a sum of pattern diagonal operators.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

pattern: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, variable_indices, pattern, coefficient=1.0, name='pattern_diagonal')

class qlinks.operators.PlaquettePatternOperator(layout, lattice, plaquette_id, transitions, name='plaquette_pattern')

Bases: BaseLocalOperator

General plaquette transition operator.

It reads the plaquette’s link variables in the lattice plaquette order. If the current values match one of the allowed transition patterns, it returns the corresponding new configuration.

This is suitable for QDM plaquette flips, constrained ring exchanges, and other local loop moves.

layout: VariableLayout

lattice: LatticeGraph

plaquette_id: int

transitions: tuple[PlaquettePatternTransition, ...]

name: str

classmethod qdm_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

Standard binary dimer plaquette flip:

1010 <-> 0101

The order is the plaquette link order supplied by the lattice.

classmethod alternating_binary_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

classmethod alternating_flux_flip(layout, lattice, plaquette_id, coefficient=1.0)

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, plaquette_id, transitions, name='plaquette_pattern')

class qlinks.operators.PlaquettePatternTransition(initial, final, coefficient=1.0)

Bases: object

One allowed plaquette pattern transition.

initial:

Values on plaquette links before the operator acts.

final:

Values on plaquette links after the operator acts.

coefficient:

Matrix element for this transition.

initial: ndarray[tuple[Any, ...], dtype[int64]]

final: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

__init__(initial, final, coefficient=1.0)

class qlinks.operators.SetVariablesOperator(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='set_variables')

Bases: BaseLocalOperator

General local transition operator.

If

config[variable_indices] == initial_values

then produce a new config with

new_config[variable_indices] = final_values

Otherwise return no action.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

initial_values: ndarray[tuple[Any, ...], dtype[int64]]

final_values: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

apply(config)

__init__(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='set_variables')

class qlinks.operators.SingleLocalUpdateOperator(*args, **kwargs)

Bases: LocalUpdateOperator, Protocol

Local update operator with at most one action per input config.

single_update(config)

class qlinks.operators.SpinOneXYBondOperator(layout, lattice, link_id, coefficient=1.0, name='spin_one_xy_bond')

Bases: BaseLocalOperator

Spin-1 XY bond operator on sites i,j.

H_ij = J_xy * (S^x_i S^x_j + S^y_i S^y_j)

= J_xy/2 * (S^+_i S^-_j + S^-_i S^+_j)

The computational basis is the S^z product basis with values:

m_i in {-1, 0, +1}

layout: VariableLayout

lattice: ChainLattice

link_id: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, link_id, coefficient=1.0, name='spin_one_xy_bond')

class qlinks.operators.SpinOneXYPairOperator(layout, site_i, site_j, coefficient=1.0, name='spin_one_xy_pair')

Bases: BaseLocalOperator

Hermitian spin-1 XY exchange on an arbitrary ordered site pair.

The operator uses the same matrix-element convention as SpinOneXYBondOperator for real couplings,

0.5 * (t S_i^+ S_j^- + t^* S_i^- S_j^+).

Consequently an allowed |0,0> -> |+,- > transition has matrix element t. Complex t gives a Hermitian Peierls-phase exchange.

layout: VariableLayout

site_i: int

site_j: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, site_i, site_j, coefficient=1.0, name='spin_one_xy_pair')

class qlinks.operators.ToricCodePlaquetteFluxOperator(layout, lattice, plaquette_id, coefficient=-1.0, name='toric_code_plaquette_flux')

Bases: BaseLocalOperator

Toric-code plaquette operator B_p in the Z basis.

It is diagonal:

B_p |z> = prod_{l in boundary(p)} z_l |z>

layout: VariableLayout

lattice: SquareLattice

plaquette_id: int

coefficient: complex

name: str

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

diagonal_value(config)

apply(config)

__init__(layout, lattice, plaquette_id, coefficient=-1.0, name='toric_code_plaquette_flux')

class qlinks.operators.ToricCodeStarFlipOperator(layout, lattice, site_id, coefficient=-1.0, name='toric_code_star_flip')

Bases: BaseLocalOperator

Toric-code star operator A_v in the Z basis.

It flips all links incident on site v.

layout: VariableLayout

lattice: SquareLattice

site_id: int

coefficient: complex

name: str

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply(config)

__init__(layout, lattice, site_id, coefficient=-1.0, name='toric_code_star_flip')

class qlinks.operators.TransposedBasisOperator(parent, conjugate=False)

Bases: object

Transpose or adjoint view of BasisOperator.

parent: BasisOperator

conjugate: bool = False

property shape: tuple[int, int]

property T: BasisOperator | TransposedBasisOperator

property H: BasisOperator

matvec(vector)

Compute A.T @ vector or A.H @ vector.

rmatvec(vector)

Compute vector @ A.T or vector @ A.H.

__init__(parent, conjugate=False)

class qlinks.operators.UpdateBinaryFlipOperator(layout, variable_index, coefficient=1.0, name='update_binary_flip')

Bases: BaseLocalUpdateOperator

Optimized binary flip 0 <-> 1.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_site(layout, site_id, coefficient=1.0)

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_index, coefficient=1.0, name='update_binary_flip')

class qlinks.operators.UpdateMultiNegationFlipOperator(layout, variable_indices, coefficient=1.0, name='update_multi_negation_flip')

Bases: BaseLocalUpdateOperator

Optimized simultaneous sign flip on several variables.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_indices, coefficient=1.0, name='update_multi_negation_flip')

class qlinks.operators.UpdateNegationFlipOperator(layout, variable_index, coefficient=1.0, name='update_negation_flip')

Bases: BaseLocalUpdateOperator

Optimized sign flip v -> -v.

layout: VariableLayout

variable_index: int

coefficient: complex

name: str

classmethod on_link(layout, link_id, coefficient=1.0)

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_index, coefficient=1.0, name='update_negation_flip')

class qlinks.operators.UpdateOperatorSum(terms, name='update_operator_sum')

Bases: object

Sum of update-level local operators.

terms: tuple[LocalUpdateOperator, ...]

name: str

classmethod from_terms(terms, name='update_operator_sum')

affected_variables()

apply_update(config)

__init__(terms, name='update_operator_sum')

class qlinks.operators.UpdatePXPSpinFlipOperator(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='update_pxp_spin_flip')

Bases: BaseLocalUpdateOperator

Optimized PXP constrained spin flip.

Flip site_id only if all neighbors are not occupied.

layout: VariableLayout

lattice: LatticeGraph

site_id: int

coefficient: complex

occupied_value: int

name: str

property site_variable: int

property neighbor_sites: ndarray[tuple[Any, ...], dtype[int64]]

property neighbor_variables: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, lattice, site_id, coefficient=1.0, occupied_value=1, name='update_pxp_spin_flip')

class qlinks.operators.UpdatePlaquettePatternOperator(layout, lattice, plaquette_id, transitions, name='update_plaquette_pattern')

Bases: BaseLocalUpdateOperator

Optimized plaquette-pattern transition operator.

This is the update-action version of PlaquettePatternOperator.

layout: VariableLayout

lattice: LatticeGraph

plaquette_id: int

transitions: tuple[UpdatePlaquettePatternTransition, ...]

name: str

classmethod qdm_flip(layout, lattice, plaquette_id, coefficient=1.0, reverse_coefficient=None)

property link_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

property supports_single_update: bool

single_update(config)

apply_update(config)

__init__(layout, lattice, plaquette_id, transitions, name='update_plaquette_pattern')

class qlinks.operators.UpdatePlaquettePatternTransition(initial, final, coefficient=1.0)

Bases: object

One local plaquette pattern transition for update operators.

initial

Source local pattern.

Type:

numpy.ndarray[tuple[Any, …], numpy.dtype[numpy.int64]]

final

Target local pattern.

Type:

numpy.ndarray[tuple[Any, …], numpy.dtype[numpy.int64]]

coefficient

Transition coefficient.

Type:

complex

initial: ndarray[tuple[Any, ...], dtype[int64]]

final: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

__init__(initial, final, coefficient=1.0)

class qlinks.operators.UpdateSetVariablesOperator(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='update_set_variables')

Bases: BaseLocalUpdateOperator

Optimized version of SetVariablesOperator.

If config[variable_indices] == initial_values, return a local update setting those variables to final_values.

layout: VariableLayout

variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

initial_values: ndarray[tuple[Any, ...], dtype[int64]]

final_values: ndarray[tuple[Any, ...], dtype[int64]]

coefficient: complex

name: str

affected_variables()

single_update(config)

apply_update(config)

__init__(layout, variable_indices, initial_values, final_values, coefficient=1.0, name='update_set_variables')

class qlinks.operators.UpdateSpinOneXYBondOperator(layout, lattice, link_id, coefficient=1.0, name='update_spin_one_xy_bond')

Bases: BaseLocalUpdateOperator

Update-action version of SpinOneXYBondOperator.

The operator returns only local two-site updates instead of allocating full output configurations. It is intended for OptimizedSparseHamiltonianBuilder.

layout: VariableLayout

lattice: ChainLattice

link_id: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply_update(config)

__init__(layout, lattice, link_id, coefficient=1.0, name='update_spin_one_xy_bond')

class qlinks.operators.UpdateSpinOneXYPairOperator(layout, site_i, site_j, coefficient=1.0, name='update_spin_one_xy_pair')

Bases: BaseLocalUpdateOperator

Update-action version of SpinOneXYPairOperator.

layout: VariableLayout

site_i: int

site_j: int

coefficient: complex

name: str

property site_ids: ndarray[tuple[Any, ...], dtype[int64]]

property variable_indices: ndarray[tuple[Any, ...], dtype[int64]]

affected_variables()

apply_update(config)

__init__(layout, site_i, site_j, coefficient=1.0, name='update_spin_one_xy_pair')

qlinks.operators.alternating_binary_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return binary flippability projectors for one plaquette.

Parameters:

• layout (VariableLayout) – Variable layout.

• lattice (LatticeGraph) – Lattice containing the plaquette.

• plaquette_id (int) – Plaquette id.

• coefficient (complex) – Diagonal coefficient for each projector.

Returns:

Pair of diagonal projectors onto the two alternating binary patterns.

Return type:

tuple[PatternDiagonalOperator, PatternDiagonalOperator]

qlinks.operators.alternating_binary_patterns(length)

Return the two binary alternating patterns on an even plaquette.

Parameters:

length (int) – Plaquette cycle length.

Returns:

Pair of arrays like 1010... and 0101....

Return type:

tuple[ndarray, ndarray]

qlinks.operators.alternating_flux_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return flux flippability projectors for one plaquette.

Parameters:

• layout (VariableLayout) – Variable layout.

• lattice (LatticeGraph) – Lattice containing the plaquette.

• plaquette_id (int) – Plaquette id.

• coefficient (complex) – Diagonal coefficient for each projector.

Returns:

Pair of diagonal projectors onto the two alternating flux patterns.

Return type:

tuple[PatternDiagonalOperator, PatternDiagonalOperator]

qlinks.operators.alternating_flux_patterns(length)

Return the two {-1, +1} alternating flux patterns.

Parameters:

length (int) – Plaquette cycle length.

Returns:

Pair of opposite alternating flux arrays.

Return type:

tuple[ndarray, ndarray]

qlinks.operators.as_basis_operator(basis, operators, **kwargs)

Convenience constructor.

qlinks.operators.combine_duplicate_actions(actions, *, atol=0.0)

Combine actions that produce the same output configuration.

This is useful before sparse assembly when two terms lead to the same row/column matrix element.

qlinks.operators.qdm_flippability_projectors(layout, lattice, plaquette_id, coefficient=1.0)

Return diagonal projectors onto the two flippable QDM plaquette patterns:

1010 and 0101

The potential term V * P_p^2 in a QDM-like model can be represented using these diagonal projectors.

qlinks.operators.spin_one_lower_amplitude(m)

Spin-1 S^- amplitude.

S^- |m> = sqrt(S(S+1) - m(m-1)) |m-1>

for S=1 and m in {-1, 0, 1}.

qlinks.operators.spin_one_raise_amplitude(m)

Spin-1 S^+ amplitude.

S^+ |m> = sqrt(S(S+1) - m(m+1)) |m+1>

for S=1 and m in {-1, 0, 1}.