qiskit/test/python/circuit/library/test_functional_pauli_rotations.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2023.
#
# 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.

"""Test the functional Pauli rotations."""

import unittest
from collections import defaultdict
import numpy as np
from ddt import ddt, data, unpack

from qiskit import transpile
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import (
    LinearPauliRotations,
    LinearPauliRotationsGate,
    PolynomialPauliRotations,
    PolynomialPauliRotationsGate,
    PiecewiseLinearPauliRotations,
    PiecewiseLinearPauliRotationsGate,
    PiecewisePolynomialPauliRotations,
    PiecewisePolynomialPauliRotationsGate,
    ExactReciprocalGate,
    PiecewiseChebyshevGate,
)
from qiskit.quantum_info import Statevector
from test import QiskitTestCase  # pylint: disable=wrong-import-order


@ddt
class TestFunctionalPauliRotations(QiskitTestCase):
    """Test the functional Pauli rotations."""

    def assertFunctionIsCorrect(self, function_circuit, reference, num_ancilla_qubits=None):
        """Assert that ``function_circuit`` implements the reference function ``reference``."""
        if isinstance(function_circuit, QuantumCircuit):
            num_ancilla_qubits = function_circuit.num_ancillas

        num_state_qubits = function_circuit.num_qubits - 1 - num_ancilla_qubits

        circuit = QuantumCircuit(num_state_qubits + 1 + num_ancilla_qubits)
        circuit.h(list(range(num_state_qubits)))
        circuit.compose(function_circuit, list(range(function_circuit.num_qubits)), inplace=True)

        tqc = transpile(circuit, basis_gates=["u", "cx"])
        statevector = Statevector(tqc)
        probabilities = defaultdict(float)
        for i, statevector_amplitude in enumerate(statevector):
            i = bin(i)[2:].zfill(circuit.num_qubits)[num_ancilla_qubits:]
            probabilities[i] += np.real(np.abs(statevector_amplitude) ** 2)

        unrolled_probabilities = []
        unrolled_expectations = []
        for i, probability in probabilities.items():
            x, last_qubit = int(i[1:], 2), i[0]
            if last_qubit == "0":
                expected_amplitude = np.cos(reference(x)) / np.sqrt(2**num_state_qubits)
            else:
                expected_amplitude = np.sin(reference(x)) / np.sqrt(2**num_state_qubits)

            unrolled_probabilities += [probability]
            unrolled_expectations += [np.real(np.abs(expected_amplitude) ** 2)]

        np.testing.assert_almost_equal(unrolled_probabilities, unrolled_expectations)

    @data(
        ([1, 0.1], 3),
        ([0, 0.4, 2], 2),
        ([1, 0.5, 0.2, -0.2, 0.4, 2.5], 5),
    )
    @unpack
    def test_polynomial_function(self, coeffs, num_state_qubits):
        """Test the polynomial rotation."""

        def poly(x):
            res = sum(coeff * x**i for i, coeff in enumerate(coeffs))
            return res

        for use_gate in [True, False]:
            if use_gate:
                polynome = PolynomialPauliRotationsGate(
                    num_state_qubits, [2 * coeff for coeff in coeffs]
                )
                num_ancillas = 0
            else:
                with self.assertWarns(DeprecationWarning):
                    polynome = PolynomialPauliRotations(
                        num_state_qubits, [2 * coeff for coeff in coeffs]
                    )
                num_ancillas = None

            with self.subTest(use_gate=use_gate):
                self.assertFunctionIsCorrect(polynome, poly, num_ancillas)

    def test_polynomial_rotations_mutability(self):
        """Test the mutability of the linear rotations circuit."""

        with self.assertWarns(DeprecationWarning):
            polynomial_rotations = PolynomialPauliRotations()

        with self.subTest(msg="missing number of state qubits"):
            with self.assertRaises(AttributeError):  # no state qubits set
                _ = str(polynomial_rotations.draw())

        with self.subTest(msg="default setup, just setting number of state qubits"):
            polynomial_rotations.num_state_qubits = 2
            self.assertFunctionIsCorrect(polynomial_rotations, lambda x: x / 2)

        with self.subTest(msg="setting non-default values"):
            polynomial_rotations.coeffs = [0, 1.2 * 2, 0.4 * 2]
            self.assertFunctionIsCorrect(polynomial_rotations, lambda x: 1.2 * x + 0.4 * x**2)

        with self.subTest(msg="changing of all values"):
            polynomial_rotations.num_state_qubits = 4
            polynomial_rotations.coeffs = [1 * 2, 0, 0, -0.5 * 2]
            self.assertFunctionIsCorrect(polynomial_rotations, lambda x: 1 - 0.5 * x**3)

    @data(
        (2, 0.1, 0),
        (4, -2, 2),
        (1, 0, 0),
    )
    @unpack
    def test_linear_function(self, num_state_qubits, slope, offset):
        """Test the linear rotation arithmetic circuit."""

        def linear(x):
            return offset + slope * x

        for use_gate in [True, False]:
            if use_gate:
                linear_rotation = LinearPauliRotationsGate(num_state_qubits, slope * 2, offset * 2)
                num_ancillas = 0
            else:
                with self.assertWarns(DeprecationWarning):
                    linear_rotation = LinearPauliRotations(num_state_qubits, slope * 2, offset * 2)
                num_ancillas = None

            with self.subTest(use_gate=use_gate):
                self.assertFunctionIsCorrect(linear_rotation, linear, num_ancillas)

    def test_linear_rotations_mutability(self):
        """Test the mutability of the linear rotations circuit."""

        with self.assertWarns(DeprecationWarning):
            linear_rotation = LinearPauliRotations()

        with self.subTest(msg="missing number of state qubits"):
            with self.assertRaises(AttributeError):  # no state qubits set
                _ = str(linear_rotation.draw())

        with self.subTest(msg="default setup, just setting number of state qubits"):
            linear_rotation.num_state_qubits = 2
            self.assertFunctionIsCorrect(linear_rotation, lambda x: x / 2)

        with self.subTest(msg="setting non-default values"):
            linear_rotation.slope = -2.3 * 2
            linear_rotation.offset = 1 * 2
            self.assertFunctionIsCorrect(linear_rotation, lambda x: 1 - 2.3 * x)

        with self.subTest(msg="changing all values"):
            linear_rotation.num_state_qubits = 4
            linear_rotation.slope = 0.2 * 2
            linear_rotation.offset = 0.1 * 2
            self.assertFunctionIsCorrect(linear_rotation, lambda x: 0.1 + 0.2 * x)

    @data(
        (1, [0], [1], [0]),
        (2, [0, 2], [-0.5, 1], [2, 1]),
        (3, [0, 2, 5], [1, 0, -1], [0, 2, 2]),
        (2, [1, 2], [1, -1], [2, 1]),
        (3, [0, 1], [1, 0], [0, 1]),
    )
    @unpack
    def test_piecewise_linear_function(self, num_state_qubits, breakpoints, slopes, offsets):
        """Test the piecewise linear rotations."""

        def pw_linear(x):
            for i, point in enumerate(reversed(breakpoints)):
                if x >= point:
                    return offsets[-(i + 1)] + slopes[-(i + 1)] * (x - point)
            return 0

        slopes2 = [2 * slope for slope in slopes]
        offsets2 = [2 * offset for offset in offsets]

        for use_gate in [False, True]:
            if use_gate:
                pw_linear_rotations = PiecewiseLinearPauliRotationsGate(
                    num_state_qubits, breakpoints, slopes2, offsets2
                )
                # ancilla for the comparator bit
                num_ancillas = int(len(breakpoints) > 1)
            else:
                with self.assertWarns(DeprecationWarning):
                    pw_linear_rotations = PiecewiseLinearPauliRotations(
                        num_state_qubits, breakpoints, slopes2, offsets2
                    )
                num_ancillas = None  # automatically deducted

            with self.subTest(use_gate=use_gate):
                self.assertFunctionIsCorrect(pw_linear_rotations, pw_linear, num_ancillas)

    def test_piecewise_linear_rotations_mutability(self):
        """Test the mutability of the linear rotations circuit."""

        with self.assertWarns(DeprecationWarning):
            pw_linear_rotations = PiecewiseLinearPauliRotations()

        with self.subTest(msg="missing number of state qubits"):
            with self.assertRaises(AttributeError):  # no state qubits set
                _ = str(pw_linear_rotations.draw())

        with self.subTest(msg="default setup, just setting number of state qubits"):
            pw_linear_rotations.num_state_qubits = 2
            self.assertFunctionIsCorrect(pw_linear_rotations, lambda x: x / 2)

        with self.subTest(msg="setting non-default values"):
            pw_linear_rotations.breakpoints = [0, 2]
            pw_linear_rotations.slopes = [-1 * 2, 1 * 2]
            pw_linear_rotations.offsets = [0, -1.2 * 2]
            self.assertFunctionIsCorrect(
                pw_linear_rotations, lambda x: -1.2 + (x - 2) if x >= 2 else -x
            )

        with self.subTest(msg="changing all values"):
            pw_linear_rotations.num_state_qubits = 4
            pw_linear_rotations.breakpoints = [1, 3, 6]
            pw_linear_rotations.slopes = [-1 * 2, 1 * 2, -0.2 * 2]
            pw_linear_rotations.offsets = [0, -1.2 * 2, 2 * 2]

            def pw_linear(x):
                if x >= 6:
                    return 2 - 0.2 * (x - 6)
                if x >= 3:
                    return -1.2 + (x - 3)
                if x >= 1:
                    return -(x - 1)
                return 0

            self.assertFunctionIsCorrect(pw_linear_rotations, pw_linear)

    @data(
        (1, [0], [[1]]),
        (2, [0, 1], [[1, 2], [0, 1]]),
        (3, [0, 5], [[1, 0, -1], [0, 2, 2]]),
    )
    @unpack
    def test_piecewise_polynomial_function(self, num_state_qubits, breakpoints, coeffs):
        """Test the piecewise linear rotations."""

        def pw_poly(x):
            for i, point in enumerate(reversed(breakpoints)):
                if x >= point:
                    return sum(coeff / 2 * x**d for d, coeff in enumerate(coeffs[~i]))
            return 0

        for use_gate in [False, True]:
            if use_gate:
                pw_poly_rotations = PiecewisePolynomialPauliRotationsGate(
                    num_state_qubits, breakpoints, coeffs
                )
                # ancilla for the comparator bit
                num_ancillas = int(len(breakpoints) > 1)
            else:
                with self.assertWarns(DeprecationWarning):
                    pw_poly_rotations = PiecewisePolynomialPauliRotations(
                        num_state_qubits, breakpoints, coeffs
                    )
                num_ancillas = None  # automatically deducted

            with self.subTest(use_gate=use_gate):
                self.assertFunctionIsCorrect(pw_poly_rotations, pw_poly, num_ancillas)

    @data((1, 0.01), (5, 0.02))
    @unpack
    def test_exact_reciprocal(self, num_state_qubits, scaling):
        """Test the exact reciprocal."""

        def reference(x):
            if x == 0:
                return 0

            value = scaling * 2**num_state_qubits / x
            if value >= 1 - 1e-5:
                return np.pi / 2

            return np.arcsin(value)

        gate = ExactReciprocalGate(num_state_qubits, scaling)
        self.assertFunctionIsCorrect(gate, reference, num_ancilla_qubits=0)

    def test_piecewise_chebyshev(self):
        """Test the piecewise Chebyshev function."""

        with self.subTest(msg="constant"):
            gate = PiecewiseChebyshevGate(0.123, num_state_qubits=3, degree=0)
            ref = lambda x: 0.123 / 2
            self.assertFunctionIsCorrect(gate, ref, num_ancilla_qubits=0)

        with self.subTest(msg="linear"):
            target = lambda x: x
            gate = PiecewiseChebyshevGate(target, num_state_qubits=3, degree=1)
            self.assertFunctionIsCorrect(gate, target, num_ancilla_qubits=0)

        with self.subTest(msg="poly"):
            target = lambda x: x**3 - x
            gate = PiecewiseChebyshevGate(target, num_state_qubits=5, degree=3)
            self.assertFunctionIsCorrect(gate, target, num_ancilla_qubits=0)

        with self.subTest(msg="pw poly"):

            def target(x):  # pylint: disable=function-redefined
                if hasattr(x, "__len__"):  # support single-value inputs and arrays
                    return np.array([target(xi) for xi in x])

                if x < 3:
                    return x
                elif x < 6:
                    return x**2

                return x**3

            gate = PiecewiseChebyshevGate(
                target, num_state_qubits=3, degree=3, breakpoints=[0, 3, 6]
            )
            self.assertFunctionIsCorrect(gate, target, num_ancilla_qubits=1)

    def test_piecewise_chebyshev_invalid(self):
        """Test giving the function in an invalid format."""

        def constant_noarg():
            return 1

        with self.assertRaises(TypeError):
            _ = PiecewiseChebyshevGate(constant_noarg, 2, 0)

        def constant(_x):
            return 1

        with self.assertRaises(TypeError):
            _ = PiecewiseChebyshevGate(constant, 2, 0)

        as_lambda = lambda x: x**3 if x <= 1 else x
        with self.assertRaises(TypeError):
            _ = PiecewiseChebyshevGate(as_lambda, 2, 1, breakpoints=[1])


if __name__ == "__main__":
    unittest.main()