Operators

Generic operators

class qtealeaves.operators.TNOperators(set_names='default', mapping_func=None)[source]

Generic class to write operators. This class contains no pre-defined operators. It allows you to start from scratch if no other operator class fulfills your needs.

Arguments

set_nameslist of str, optional: Name of the operators sets. Default to default
mapping_funccallable (or None), optional: Mapping the site index to an operator. Arguments site_idx must be accepted. Default to None (default mapping to only operator set)

check_alternative_op(set_name, key)[source]

Check entry for alternative operators, i.e., the sigma_x squared is the identity.

Arguments

set_namestr: Search in this set name of operators. (Set names allow different Hilbert spaces on different sites.)
keystr: Operator represented as key. Check if there is an alternative key for this key.

Returns

alternative_keyNone | str: If None, no alternative key is given or the corresponding dictionary for checking is not set. If str, then this operator has the same representation as key.

generate_products_2nd_order(left_conj=False, left_transpose=False, right_conj=False, right_transpose=False)[source]

Generate all possible multiplications (matrix-matrix multiplications) of the operator set, i.e., [A, B, …] generators [A*A, A*B, B*A, B*B, …]. Transformation can be taken into account on top.

Arguments

left_conjBoolean: Tells if the left operator needs to be complex conjugated. Default is False.
right_transposeBoolean: Tells if the left operator needs to be transposed. Default is False.
right_conjBoolean: Tells if the right operator needs to be complex conjugated. Default is False.
right_transposeBoolean: Tells if the right operator needs to be transposed. Default is False.

Returns

None (in-place update of the operator dictionary)

get_local_links(num_sites, params)[source]

Extract the local links from the operators.

Arguments

num_sitesinteger: Number of sites.
paramsdict: Dictionary with parameterization of the simulation.

get_operator(site_idx_1d, operator_name, params)[source]

Provide a method to return any operator, either defined via a callable or directly as a matrix.

Arguments

site_idx_1dint, str: If int, site where we need the operator. Mapping will evaluate what to return. If str, name of operator set.
operator_namestr: Tag/identifier of the operator.
paramsdict: Simulation parameters as a dictionary; dict is passed to callable.

items()[source]: Iterate throught all (key, value) pairs of all operators sets.

property mapping_func: Mapping function for site to operator set name.

property one_unique: Flag if only one operators set exists (True) or multiple (False).

property set_names: Return operator set names as list of strings.

transform(transformation, **kwargs)[source]

Generate a new TNOperators by transforming the current instance.

Arguments

transformationcallable: Accepting key and value as arguments plus potential keyword arguments.
**kwargskey-word arguments: Will be passed to transformation

Spin 1/2 operators

class qtealeaves.operators.TNSpin12Operators[source]

Operators specifically targeted at spin 1/2 systems. The operators id, sx, sz, n``= 1/2*(1-``sz), and nz = 1/2*(1+``sz``) are provided by default.

Arguments

folder_operatorsstr, optional: The name of the subfolder inside the input folder, where we store operators. Default to SPIN12

Qudit operators

class qtealeaves.operators.TN3levelsOperators[source]

Operators defined for Lambda-like three-level systems, e.g., used in the case of Rydberg systems.

Arguments

folder_operatorsstr, optional: The name of the subfolder inside the input folder, where we store operators. Default to 3levels

Details

The three levels are labeled as: |0>, |1> and |r>. The following operators are defined: n0, n1, nr, sx01, sy01, sz01, n01, n10, n1r, nr1, sx1r. The identity id is defined as well.

class qtealeaves.operators.TN4levelsOperators[source]

Operators defined for a 4-level system, e.g., targeting Rydberg systems with two low-energy states, one Rydberg state |r>, and one additional state |d> allowing a decay from |r> to |d>.

Arguments

folder_operatorsstr, optional: The name of the subfolder inside the input folder, where we store operators. Default to 4levels

Details

The following operators are defined: n0, n1, nr, nd, sx01, and sx1r. The identity id is defined as well.

Bosonic operators

class qtealeaves.operators.TNBosonicOperators[source]

Operators specifically targeted at bosonic systems. The operators id, b, bdagger, n, and nint are provided by default.

Details

The truncation of the Fock-space can be set via the keys fock_space_nmin and fock_space_nmax. By default, the local dimension is four including the levels 0, 1, 2, and 3.

static get_b(params)[source]: Define the bosonic annihilation operator.

static get_bdagger(params)[source]: Define the bosonic creation operator.

static get_id(params)[source]: Define the identity operator.

static get_n(params)[source]: Define the number operator.

static get_nint(params)[source]: Define the on-site interaction operator 0.5 * n * (n - 1).

Combined operators

class qtealeaves.operators.TNCombinedOperators(ops_a, ops_b)[source]

Combine operators for system a and b.

Arguments

ops_ainstance of TNOperators: Set of operators for system a.
ops_binstance of TNOperators: Set of operators for system b.
folder_operatorsstr, optional: The name of the subfolder inside the input folder, where we store operators. Default to CombinedOps

Details

The key of the operators after merging will be ops_a.ops_b.

get_any_operator_function(key_a, key_b)[source]

Get function to compute kronecker product between set of operators a and b.

Parameters

key_astr: Operator name of class a.
key_bstr: Operator name of class b.

merge_ops()[source]: Merge set of operators.