# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 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.
"""Instantaneous quantum polynomial circuit."""
from __future__ import annotations
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.exceptions import CircuitError
[docs]class IQP(QuantumCircuit):
r"""Instantaneous quantum polynomial (IQP) circuit.
The circuit consists of a column of Hadamard gates,
a column of powers of T gates,
a sequence of powers of CS gates (up to
:math:`\frac{n^2-n}{2}` of them),
and a final column of Hadamard gates, as introduced in [1].
The circuit is parameterized by an n x n interactions matrix.
The powers of each T gate are given by the diagonal elements
of the interactions matrix. The powers of the CS gates are
given by the upper triangle of the interactions matrix.
**Reference Circuit:**
.. plot::
from qiskit.circuit.library import IQP
A = [[6, 5, 3], [5, 4, 5], [3, 5, 1]]
circuit = IQP(A)
circuit.draw('mpl')
**Expanded Circuit:**
.. plot::
from qiskit.circuit.library import IQP
from qiskit.tools.jupyter.library import _generate_circuit_library_visualization
A = [[6, 5, 3], [5, 4, 5], [3, 5, 1]]
circuit = IQP(A)
_generate_circuit_library_visualization(circuit.decompose())
**References:**
[1] M. J. Bremner et al. Average-case complexity versus approximate
simulation of commuting quantum computations,
Phys. Rev. Lett. 117, 080501 (2016).
`arXiv:1504.07999 <https://arxiv.org/abs/1504.07999>`_
"""
def __init__(self, interactions: list | np.ndarray) -> None:
"""Create IQP circuit.
Args:
interactions: input n-by-n symmetric matrix.
Raises:
CircuitError: if the inputs is not as symmetric matrix.
"""
num_qubits = len(interactions)
interactions = np.array(interactions)
if not np.allclose(interactions, interactions.transpose()):
raise CircuitError("The interactions matrix is not symmetric")
a_str = np.array_str(interactions)
a_str.replace("\n", ";")
name = "iqp:" + a_str.replace("\n", ";")
circuit = QuantumCircuit(num_qubits, name=name)
circuit.h(range(num_qubits))
for i in range(num_qubits):
for j in range(i + 1, num_qubits):
if interactions[i][j] % 4 != 0:
circuit.cp(interactions[i][j] * np.pi / 2, i, j)
for i in range(num_qubits):
if interactions[i][i] % 8 != 0:
circuit.p(interactions[i][i] * np.pi / 8, i)
circuit.h(range(num_qubits))
super().__init__(*circuit.qregs, name=circuit.name)
self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)