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class qiskit.circuit.library.Diagonal(diag)

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Bases: QuantumCircuit

Diagonal circuit.

Circuit symbol:

     │           │
q_1:1 Diagonal ├
     │           │

Matrix form:

DiagonalGate q0,q1,..,qn1=(D[0]000D[1]0000D[n1])\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}

Diagonal gates are useful as representations of Boolean functions, as they can map from {0,1}2n\{0,1\}^{2^n} to {0,1}2n\{0,1\}^{2^n} space. For example a phase oracle can be seen as a diagonal gate with {1,1}\{1, -1\} on the diagonals. Such an oracle will induce a +1+1 or :math`-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 2n×2n2^n \times 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.


[1] Shende et al., Synthesis of Quantum Logic Circuits, 2009 arXiv:0406176(opens in a new tab)


diag (Sequence[complex(opens in a new tab)]) – List of the 2k2^k diagonal entries (for a diagonal gate on kk qubits).


CircuitError – if the list of the diagonal entries or the qubit list is in bad format; if the number of diagonal entries is not 2k2^k, where kk denotes the number of qubits.



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


Return calibration dictionary.

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


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


Return the circuit data (instructions and context).


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

Return type



Default value: 'include "";'


Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'


Default value: 167


Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.


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 the number of ancilla qubits.


Return number of classical bits.


The number of parameter objects in the circuit.


Return number of qubits.


Return a list of operation start times.

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


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


AttributeError(opens in a new tab) – When circuit is not scheduled.


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.


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 unintuitive 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()
>>> 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
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])


The sorted Parameter objects in the circuit.


Default value: 'circuit'


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

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