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197 | class GKPQubit(BosonicQubit):
"""
GKP Qubit Class.
"""
name = "gkp"
def _params_validation(self):
super()._params_validation()
if "delta" not in self.params:
self.params["delta"] = 0.25
self.params["l"] = 2.0 * jnp.sqrt(jnp.pi)
s_delta = jnp.sinh(self.params["delta"] ** 2)
self.params["epsilon"] = s_delta * self.params["l"]
def _gen_common_gates(self) -> None:
"""
Overriding this method to add additional common gates.
"""
super()._gen_common_gates()
# phase space
self.common_gates["x"] = (
self.common_gates["a_dag"] + self.common_gates["a"]
) / jnp.sqrt(2.0)
self.common_gates["p"] = (
1.0j * (self.common_gates["a_dag"] - self.common_gates["a"]) / jnp.sqrt(2.0)
)
# finite energy
self.common_gates["E"] = jqt.expm(
-(self.params["delta"] ** 2)
* self.common_gates["a_dag"]
@ self.common_gates["a"]
)
self.common_gates["E_inv"] = jqt.expm(
self.params["delta"] ** 2
* self.common_gates["a_dag"]
@ self.common_gates["a"]
)
# axis
x_axis, z_axis = self._get_axis()
y_axis = x_axis + z_axis
# gates
X_0 = jqt.expm(1.0j * self.params["l"] / 2.0 * z_axis)
Z_0 = jqt.expm(1.0j * self.params["l"] / 2.0 * x_axis)
Y_0 = 1.0j * X_0 @ Z_0
self.common_gates["X_0"] = X_0
self.common_gates["Z_0"] = Z_0
self.common_gates["Y_0"] = Y_0
self.common_gates["X"] = self._make_op_finite_energy(X_0)
self.common_gates["Z"] = self._make_op_finite_energy(Z_0)
self.common_gates["Y"] = self._make_op_finite_energy(Y_0)
# symmetric stabilizers and gates
self.common_gates["Z_s_0"] = self._symmetrized_expm(
1.0j * self.params["l"] / 2.0 * x_axis
)
self.common_gates["S_x_0"] = self._symmetrized_expm(
1.0j * self.params["l"] * z_axis
)
self.common_gates["S_z_0"] = self._symmetrized_expm(
1.0j * self.params["l"] * x_axis
)
self.common_gates["S_y_0"] = self._symmetrized_expm(
1.0j * self.params["l"] * y_axis
)
@staticmethod
def _q_quadrature(q_points, n):
q_points = q_points.T
F_0_init = jnp.ones_like(q_points)
F_1_init = jnp.sqrt(2) * q_points
def scan_body(n, carry):
F_0, F_1 = carry
F_n = (jnp.sqrt(2 / n) * lax.mul(q_points, F_1) - jnp.sqrt(
(n - 1) / n) * F_0)
new_carry = (F_1, F_n)
return new_carry
initial_carry = (F_0_init, F_1_init)
final_carry = lax.fori_loop(2, jnp.max(jnp.array([n + 1, 2])),
scan_body, initial_carry)
q_quad = lax.select(n == 0, F_0_init,
lax.select(n == 1, F_1_init,
final_carry[1]))
q_quad = jnp.pi ** (-0.25) * lax.mul(
jnp.exp(-lax.pow(q_points, 2) / 2), q_quad)
return q_quad
@staticmethod
def _compute_gkp_basis_z(delta, dim, mu, series_trunc=100):
"""
Args:
mu: state index (0 or 1)
Returns:
GKP basis state
Adapted from code by Lev-Arcady Sellem <lev-arcady.sellem@inria.fr>
"""
# We choose the truncation of our series summation such that we
# capture 6 sigmas of the envelope for a value of delta of 0.02.
# delta * (truncat_series*2*sqrt(pi)) = 6
q_points = jnp.sqrt(jnp.pi) * (2 * jnp.arange(series_trunc) + mu)
def compute_pop(n):
quadvals = GKPQubit._q_quadrature(q_points, n)
return jnp.exp(-(delta ** 2) * n) * (
2 * jnp.sum(quadvals) - (1 - mu) * quadvals[0])
psi_even = vmap(compute_pop)(jnp.arange(0, dim, 2))
psi = jnp.zeros(2 * psi_even.size, dtype=psi_even.dtype)
psi = psi.at[::2].set(psi_even)
psi = jqt.Qarray.create(jnp.array(psi)[:dim])
return psi.unit()
def _get_basis_z(self) -> Tuple[jqt.Qarray, jqt.Qarray]:
"""
Construct basis states |+-z>.
"""
delta = self.params["delta"]
dim = self.params["N"]
if delta<0.02:
warnings.warn("State preparation with delta values lower than 0.02 might lead to loss of accuracy.")
jitted_compute_gkp_basis_z = jit(self._compute_gkp_basis_z,
static_argnames=("dim",))
plus_z = jitted_compute_gkp_basis_z(delta, dim, 0)
minus_z = jitted_compute_gkp_basis_z(delta, dim, 1)
return plus_z, minus_z
# utils
# ======================================================
def _get_axis(self):
x_axis = self.common_gates["x"]
z_axis = -self.common_gates["p"]
return x_axis, z_axis
def _make_op_finite_energy(self, op):
return self.common_gates["E"] @ op @ self.common_gates["E_inv"]
def _symmetrized_expm(self, op):
return (jqt.expm(op) + jqt.expm(-1.0 * op)) / 2.0
# gates
# ======================================================
@property
def x_U(self) -> jqt.Qarray:
return self.common_gates["X"]
@property
def y_U(self) -> jqt.Qarray:
return self.common_gates["Y"]
@property
def z_U(self) -> jqt.Qarray:
return self.common_gates["Z"]
|