Typo in docstring for GPI2 gate

[oschwarze]

There seems to be a typo in the docstring for the GPI2 gate:

Cirq/cirq-ionq/cirq_ionq/ionq_native_gates.py

Lines 101 to 156 in ab96766

	@cirq.value.value_equality
	class GPI2Gate(cirq.Gate):
	r"""The GPI2 gate is a single qubit gate representing a pi/2 pulse.
	The unitary matrix of this gate is
	$$
	\frac{1}{\sqrt{2}}
	\begin{bmatrix}
	1 & -i e^{-i \phi} \\
	-i e^{-i \phi} & 1
	\end{bmatrix}
	$$
	See [IonQ best practices](https://ionq.com/docs/getting-started-with-native-gates){:external}.
	"""
	def __init__(self, *, phi):
	self.phi = phi
	def _unitary_(self) -> np.ndarray:
	top = -1j * cmath.exp(self.phase * 2 * math.pi * -1j)
	bot = -1j * cmath.exp(self.phase * 2 * math.pi * 1j)
	return np.array([[1, top], [bot, 1]]) / math.sqrt(2)
	@property
	def phase(self) -> float:
	return self.phi
	def __str__(self) -> str:
	return 'GPI2'
	def _circuit_diagram_info_(
	self, args: 'cirq.CircuitDiagramInfoArgs'
	) -> Union[str, 'protocols.CircuitDiagramInfo']:
	return protocols.CircuitDiagramInfo(wire_symbols=(f'GPI2({self.phase!r})',))
	def _num_qubits_(self) -> int:
	return 1
	def __repr__(self) -> str:
	return f'cirq_ionq.GPI2Gate(phi={self.phi!r})'
	def _json_dict_(self) -> Dict[str, Any]:
	return cirq.obj_to_dict_helper(self, ['phi'])
	def _value_equality_values_(self) -> Any:
	return self.phi
	def __pow__(self, power):
	if power == 1:
	return self
	if power == -1:
	return GPI2Gate(phi=self.phi + 0.5)
	return NotImplemented

according to https://ionq.com/docs/getting-started-with-native-gates, the 10-component int the matrix should be $-i \exp{i \phi}$ and not $-i\exp(-i \phi)$

[dstrain115]

Cirq cycn: Ionq folks, can you comment whether this should be positive or negative signed?

[pavoljuhas]

TODO(@pavoljuhas) - contact ionq folks about this

[pavoljuhas]

The suggestion looks good given the unitary matrix below - however the docstring seems to be missing the 2π factor.

Cirq/cirq-ionq/cirq_ionq/ionq_native_gates.py

Lines 120 to 123 in f5566b6

	def _unitary_(self) -> np.ndarray:
	top = -1j * cmath.exp(self.phase * 2 * math.pi * -1j)
	bot = -1j * cmath.exp(self.phase * 2 * math.pi * 1j)
	return np.array([[1, top], [bot, 1]]) / math.sqrt(2)

@Cynocracy or @splch - can you please confirm?

[Cynocracy]

@pavoljuhas can confirm, updating the comment to match the unitary function* sgtm.

The 2pi factor comes from, aiui, the phase argument being expressed in units of turns, and should be present in the doc string as well, if phi there is intended to be the phase argument

[pavoljuhas]

@Cynocracy - thanks for a quick response. Can you PTAL at #6694?