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
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 tuples for the circuit’s data.
Each tuple is in the format (instruction, qargs, cargs), where instruction is an Instruction (or subclass) object, qargs is a list of Qubit objects, and cargs is a list of Clbit objects.
Return type
QuantumCircuitData
extension_lib
Default value: 'include "qelib1.inc";'
global_phase
Return the global phase of the circuit in radians.
Return type
Union[ParameterExpression, float]
header
Default value: 'OPENQASM 2.0;'
instances
Default value: 9
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
Convenience function to get the number of parameter objects in the circuit.
Return type
int
num_qubits
Return number of qubits.
Return type
int
parameters
Convenience function to get the parameters defined in the parameter table.
Return type
ParameterView
prefix
Default value: 'circuit'
qubits
Returns a list of quantum bits in the order that the registers were added.
Return type
List[Qubit]