Diagonal¶

class Diagonal(diag)[source]¶

Bases: qiskit.circuit.quantumcircuit.QuantumCircuit

Diagonal circuit.

Circuit symbol:

     ┌───────────┐
q_0: ┤0          ├
     │           │
q_1: ┤1 Diagonal ├
     │           │
q_2: ┤2          ├
     └───────────┘

Matrix form:

\[\begin{split}\text{DiagonalGate}\ q_0, q_1, .., q_{n-1} = \begin{pmatrix} D[0] & 0 & \dots & 0 \\ 0 & D[1] & \dots & 0 \\ \vdots & \vdots & \ddots & 0 \\ 0 & 0 & \dots & D[n-1] \end{pmatrix}\end{split}\]

Diagonal gates are useful as representations of Boolean functions, as they can map from {0,1}^2**n to {0,1}^2**n space. For example a phase oracle can be seen as a diagonal gate with {+1, -1} on the diagonals. Such an oracle will induce a +1 or -1 phase on the amplitude of any corresponding basis state.

Diagonal gates appear in many classically hard oracular problems such as Forrelation or Hidden Shift circuits.

Diagonal gates are represented and simulated more efficiently than a dense 2**n x 2**n unitary matrix.

The reference implementation is via the method described in Theorem 7 of [1]. The code is based on Emanuel Malvetti’s semester thesis at ETH in 2018, supervised by Raban Iten and Prof. Renato Renner.

Reference:

[1] Shende et al., Synthesis of Quantum Logic Circuits, 2009 arXiv:0406176

Create a new Diagonal circuit.

Parameters: diag (Union[List, array]) – list of the 2^k diagonal entries (for a diagonal gate on k qubits).
Raises: CircuitError – if the list of the diagonal entries or the qubit list is in bad format; if the number of diagonal entries is not 2^k, where k denotes the number of qubits

Attributes

ancillas¶

Returns a list of ancilla bits in the order that the registers were added.

Return type: List[AncillaQubit]

calibrations¶

Return calibration dictionary.

The custom pulse definition of a given gate is of the form: {‘gate_name’: {(qubits, params): schedule}}

Return type: dict

clbits¶

Returns a list of classical bits in the order that the registers were added.

Return type: List[Clbit]

data¶

Return the circuit data (instructions and context).

Returns: a list-like object containing the CircuitInstructions for each instruction.
Return type: QuantumCircuitData

extension_lib = 'include "qelib1.inc";'¶

global_phase¶

Return the global phase of the circuit in radians.

Return type: Union[ParameterExpression, float]

header = 'OPENQASM 2.0;'¶

instances = 87¶

metadata¶

The user provided metadata associated with the circuit

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

Return type: dict

num_ancillas¶

Return the number of ancilla qubits.

Return type: int

num_clbits¶

Return number of classical bits.

Return type: int

num_parameters¶

The number of parameter objects in the circuit.

Return type: int

num_qubits¶

Return number of qubits.

Return type: int

op_start_times¶

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

Return type: List[int]
Returns: List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises: AttributeError – When circuit is not scheduled.

parameters¶

The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.

Examples

The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unituitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])

Return type: ParameterView
Returns: The sorted Parameter objects in the circuit.

prefix = 'circuit'¶

qubits¶

Returns a list of quantum bits in the order that the registers were added.

Return type: List[Qubit]