def test_iswap_matrix():
cirq.testing.assert_allclose_up_to_global_phase(cirq.ISwapGate().matrix(),
np.array([[1, 0, 0, 0],
[0, 0, 1j, 0],
[0, 1j, 0, 0],
[0, 0, 0, 1]]),
atol=1e-8)
def test_iswap_decompose():
a = cirq.NamedQubit('a')
b = cirq.NamedQubit('b')
original = cirq.ISwapGate(exponent=0.5)
decomposed = cirq.Circuit.from_ops(original.default_decompose([a, b]))
cirq.testing.assert_allclose_up_to_global_phase(
original.matrix(), decomposed.to_unitary_matrix(), atol=1e-8)
assert decomposed.to_text_diagram() == """
a: ───@───H───X───T───X───T^-1───H───@───
│ │ │ │
b: ───X───────@───────@──────────────X───
""".strip()
def fermi_fourier_trans_2(p: cirq.QubitId, q: cirq.QubitId) -> cirq.OP_TREE:
"""The 2-mode fermionic Fourier transformation can be implemented
straightforwardly by the √iSWAP gate. The √iSWAP gate can be readily
implemented with the gmon qubits using the XX + YY Hamiltonian. The matrix
representation of the 2-qubit fermionic Fourier transformation is:
[1 0 0 0],
[0 1/√2 1/√2 0],
[0 1/√2 -1/√2 0],
[0 0 0 -1]
The square root of the iSWAP gate is:
[1, 0, 0, 0],
[0, 0.5 + 0.5j, 0.5 - 0.5j, 0],
[0, 0.5 - 0.5j, 0.5 + 0.5j, 0],
[0, 0, 0, 1]
Args:
p: the id of the first qubit
q: the id of the second qubit
"""
yield cirq.Z(p)**1.5
yield cirq.ISwapGate(exponent=0.5).on(q, p)
yield cirq.Z(p)**1.5
def bogoliubov_trans(p, q, theta):
"""The 2-mode Bogoliubov transformation is mapped to two-qubit operations.
We use the identity X S^\dag X S X = Y X S^\dag Y S X = X to transform
the Hamiltonian XY+YX to XX+YY type. The time evolution of the XX + YY
Hamiltonian can be expressed as a power of the iSWAP gate.
Args:
p: the first qubit
q: the second qubit
theta: The rotational angle that specifies the Bogoliubov
transformation, which is a function of the kinetic energy and
the superconducting gap.
"""
# The iSWAP gate corresponds to evolve under the Hamiltonian XX+YY for
# time -pi/4.
expo = -4 * theta / np.pi
yield cirq.X(p)
yield cirq.S(p)
yield cirq.ISwapGate(exponent=expo).on(p, q)
yield cirq.S(p)**1.5
yield cirq.X(p)
