Diagonal
class Diagonal(diag)
Bases: qiskit.circuit.quantumcircuit.QuantumCircuit
Diagonal circuit.
Circuit symbol:
┌───────────┐
q_0: ┤0 ├
│ │
q_1: ┤1 Diagonal ├
│ │
q_2: ┤2 ├
└───────────┘Matrix form:
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
data
Return the circuit data (instructions and context).
Returns
a list-like object containing the CircuitInstructions for each instruction.
Return type
QuantumCircuitData
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 2308
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
Default value: 'circuit'