# Source code for qiskit.extensions.quantum_initializer.diagonal

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
# The structure of the code is based on Emanuel Malvetti's semester thesis at ETH in 2018,
# which was supervised by Raban Iten and Prof. Renato Renner.
# pylint: disable=missing-param-doc
# pylint: disable=missing-type-doc
"""
Decomposes a diagonal matrix into elementary gates using the method described in Theorem 7 in
"Synthesis of Quantum Logic Circuits" by Shende et al. (https://arxiv.org/pdf/quant-ph/0406176.pdf).
"""
import cmath
import math
import numpy as np
from qiskit.circuit import Gate
from qiskit.circuit.quantumcircuit import QuantumCircuit, QuantumRegister
from qiskit.exceptions import QiskitError
_EPS = 1e-10 # global variable used to chop very small numbers to zero
class DiagonalGate(Gate):
"""
diag = list of the 2^k diagonal entries (for a diagonal gate on k qubits). Must contain at
least two entries.
"""
def __init__(self, diag):
"""Check types"""
# Check if diag has type "list"
if not isinstance(diag, list):
raise QiskitError("The diagonal entries are not provided in a list.")
# Check if the right number of diagonal entries is provided and if the diagonal entries
# have absolute value one.
num_action_qubits = math.log2(len(diag))
if num_action_qubits < 1 or not num_action_qubits.is_integer():
raise QiskitError("The number of diagonal entries is not a positive power of 2.")
for z in diag:
try:
complex(z)
except TypeError as ex:
raise QiskitError(
"Not all of the diagonal entries can be converted to " "complex numbers."
) from ex
if not np.abs(z) - 1 < _EPS:
raise QiskitError("A diagonal entry has not absolute value one.")
# Create new gate.
super().__init__("diagonal", int(num_action_qubits), diag)
def _define(self):
diag_circuit = self._dec_diag()
gate = diag_circuit.to_instruction()
q = QuantumRegister(self.num_qubits)
diag_circuit = QuantumCircuit(q)
diag_circuit.append(gate, q[:])
self.definition = diag_circuit
def validate_parameter(self, parameter):
"""Diagonal Gate parameter should accept complex
(in addition to the Gate parameter types) and always return build-in complex."""
if isinstance(parameter, complex):
return complex(parameter)
else:
return complex(super().validate_parameter(parameter))
def inverse(self):
"""Return the inverse of the diagonal gate."""
return DiagonalGate([np.conj(entry) for entry in self.params])
def _dec_diag(self):
"""
Call to create a circuit implementing the diagonal gate.
"""
q = QuantumRegister(self.num_qubits)
circuit = QuantumCircuit(q)
# Since the diagonal is a unitary, all its entries have absolute value one and the diagonal
# is fully specified by the phases of its entries
diag_phases = [cmath.phase(z) for z in self.params]
n = len(self.params)
while n >= 2:
angles_rz = []
for i in range(0, n, 2):
diag_phases[i // 2], rz_angle = _extract_rz(diag_phases[i], diag_phases[i + 1])
angles_rz.append(rz_angle)
num_act_qubits = int(np.log2(n))
contr_qubits = q[self.num_qubits - num_act_qubits + 1 : self.num_qubits]
target_qubit = q[self.num_qubits - num_act_qubits]
circuit.ucrz(angles_rz, contr_qubits, target_qubit)
n //= 2
circuit.global_phase += diag_phases[0]
return circuit
# extract a Rz rotation (angle given by first output) such that exp(j*phase)*Rz(z_angle)
# is equal to the diagonal matrix with entires exp(1j*ph1) and exp(1j*ph2)
def _extract_rz(phi1, phi2):
phase = (phi1 + phi2) / 2.0
z_angle = phi2 - phi1
return phase, z_angle
def diagonal(self, diag, qubit):
"""Attach a diagonal gate to a circuit.
The decomposition is based on Theorem 7 given in "Synthesis of Quantum Logic Circuits" by
Shende et al. (https://arxiv.org/pdf/quant-ph/0406176.pdf).
Args:
diag (list): list of the 2^k diagonal entries (for a diagonal gate on k qubits).
Must contain at least two entries
qubit (QuantumRegister|list): list of k qubits the diagonal is
acting on (the order of the qubits specifies the computational basis in which the
diagonal gate is provided: the first element in diag acts on the state where all
the qubits in q are in the state 0, the second entry acts on the state where all
the qubits q[1],...,q[k-1] are in the state zero and q[0] is in the state 1,
and so on)
Returns:
QuantumCircuit: the diagonal gate which was attached to the circuit.
Raises:
QiskitError: 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
"""
if isinstance(qubit, QuantumRegister):
qubit = qubit[:]
# Check if q has type "list"
if not isinstance(qubit, list):
raise QiskitError(
"The qubits must be provided as a list " "(also if there is only one qubit)."
)
# Check if diag has type "list"
if not isinstance(diag, list):
raise QiskitError("The diagonal entries are not provided in a list.")
num_action_qubits = math.log2(len(diag))
if not len(qubit) == num_action_qubits:
raise QiskitError(
"The number of diagonal entries does not correspond to" " the number of qubits."
)
return self.append(DiagonalGate(diag), qubit)
QuantumCircuit.diagonal = diagonal
```