qiskit_dynamics.backend.parse_backend_hamiltonian_dict#

parse_backend_hamiltonian_dict(hamiltonian_dict, subsystem_list=None)[source]#

Convert Pulse backend Hamiltonian dictionary into concrete array format with an ordered list of corresponding channels.

The Pulse backend Hamiltonian dictionary, hamiltonian_dict, must have the following keys:

'h_str': List of Hamiltonian terms in string format (see below).
'qub': Dictionary giving subsystem dimensions. Keys are subsystem labels, values are their dimensions.
'vars': Dictionary whose keys are the variables appearing in the terms in the h_str list, and values being the numerical values of the variables.

The optional argument subsystem_list specifies a subset of subsystems to keep when parsing. If None, all subsystems are kept. If subsystem_list is specified, then terms including subsystems not in the list will be ignored.

Entries in the list hamiltonian_dict['h_str'] must be formatted as a product of constants (either numerical constants or variables in hamiltonian_dict['vars'].keys()) with operators. Operators are indicated with a capital letters followed by an integer indicating the subsystem the operator acts on. Accepted operator strings are:

'X': If the target subsystem is two dimensional, the Pauli \(X\) operator, and if greater than two dimensional, returns \(a + a^\dagger\), where \(a\) and \(a^\dagger\) are the annihiliation and creation operators, respectively.
'Y': If the target subsystem is two dimensional, the Pauli \(Y\) operator, and if greater than two dimensional, returns \(-i(a - a^\dagger)\), where \(a\) and \(a^\dagger\) are the annihiliation and creation operators, respectively.
'Z': If the target subsystem is two dimensional, the Pauli \(Z\) operator, and if greater than two dimensional, returns \(I - 2 * N\), where \(N\) is the number operator.
'a', 'A', or 'Sm': If two dimensional, the sigma minus operator, and if greater, generalizes to the annihilation operator.
'C', or 'Sp': If two dimensional, sigma plus operator, and if greater, generalizes to the creation operator.
'N', or 'O': The number operator.
'I': The identity operator.

In addition to the above, a term in hamiltonian_dict['h_str'] can be associated with a channel by ending it with a string of the form '||Sxx', where S is a valid channel label, and 'xx' is an integer. Accepted channel labels are:

'D' or 'd' for drive channels.
'U' or 'u' for control channels.
'M' or 'm' for measurement channels.
'A' or 'a' for acquire channels.

Finally, summations of terms of the above form can be indicated in hamiltonian_dict['h_str'] via strings with syntax '_SUM[i, lb, ub, aa||S{i}]', where:

i is the summation variable.
lb and ub are the summation endpoints (inclusive).
aa is a valid operator string, possibly including the string {i} to indicate operators acting on subsystem i.
S{i} is the specification of a channel indexed by i.

For example, the following hamiltonian_dict specifies a single transmon with 4 levels:

hamiltonian_dict = {
    "h_str": ["v*np.pi*O0", "alpha*np.pi*O0*O0", "r*np.pi*X0||D0"],
    "qub": {"0": 4},
    "vars": {"v": 2.1, "alpha": -0.33, "r": 0.02},
}

The following example specifies a two transmon system, with single system terms specified using the summation format:

hamiltonian_dict = {
    "h_str": [
        "_SUM[i,0,1,wq{i}/2*(I{i}-Z{i})]",
        "_SUM[i,0,1,delta{i}/2*O{i}*O{i}]",
        "_SUM[i,0,1,-delta{i}/2*O{i}]",
        "_SUM[i,0,1,omegad{i}*X{i}||D{i}]",
        "jq0q1*Sp0*Sm1",
        "jq0q1*Sm0*Sp1",
        "omegad1*X0||U0",
        "omegad0*X1||U1"
    ],
    "qub": {"0": 4, "1": 4},
    "vars": {
        "delta0": -2.111793476400394,
        "delta1": -2.0894421352015744,
        "jq0q1": 0.010495754104003914,
        "omegad0": 0.9715458990879812,
        "omegad1": 0.9803812537440838,
        "wq0": 32.517894442809514,
        "wq1": 33.0948996120196,
    },
}

Parameters:

hamiltonian_dict (dict) – Pulse backend Hamiltonian dictionary.
subsystem_list (Optional[List[int]]) – List of subsystems to include in the model. If None all are kept.

Returns:

Model converted into concrete arrays - the static Hamiltonian, a list of Hamiltonians corresponding to different channels, a list of channel labels corresponding to the list of time-dependent Hamiltonians, and a dictionary with subsystem dimensions whose keys are the subsystem labels.

Return type:

Tuple