# Diagonal¶

class Diagonal(diag)[Quellcode]

Bases: 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.

Parameter

diag (Union[List, array]) – list of the 2^k diagonal entries (for a diagonal gate on k qubits).

Verursacht

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.

Rückgabetyp

List[AncillaQubit]

calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form

{‚gate_name‘: {(qubits, params): schedule}}

Rückgabetyp

dict

clbits

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

Rückgabetyp

List[Clbit]

data

Return the circuit data (instructions and context).

Rückgabe

a list-like object containing the CircuitInstructions for each instruction.

Rückgabetyp

QuantumCircuitData

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

Return the global phase of the circuit in radians.

Rückgabetyp

Union[ParameterExpression, float]

instances = 87

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.

Rückgabetyp

dict

num_ancillas

Return the number of ancilla qubits.

Rückgabetyp

int

num_clbits

Return number of classical bits.

Rückgabetyp

int

num_parameters

The number of parameter objects in the circuit.

Rückgabetyp

int

num_qubits

Return number of qubits.

Rückgabetyp

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.

Rückgabetyp

List[int]

Rückgabe

List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.

Verursacht

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])
])

Rückgabetyp

ParameterView

Rückgabe

The sorted Parameter objects in the circuit.

prefix = 'circuit'
qubits

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

Rückgabetyp

List[Qubit]