from __future__ import annotations
import jax
from rydopt.protocols import GateSystem, PulseAnsatzLike
from rydopt.simulation.evolve import evolve
from rydopt.types import ParamsFloatLike
[docs]
def process_fidelity(gate: GateSystem, pulse: PulseAnsatzLike, params: ParamsFloatLike, tol: float = 1e-7) -> jax.Array:
r"""The function provides the process fidelity of the unitary resulting from a gate pulse :math:`U(T)` w.r.t. the
target unitary :math:`U_{\mathrm{targ}}`:
.. math::
F_{pro} = \frac{| \mathrm{tr}(U_{\mathrm{targ}}^{\dagger} U(T)) |^2}{d^2},
where :math:`d` is the dimension of the Hilbert space.
Note that if both :math:`U(T)` and :math:`U_{\mathrm{targ}}` are diagonal, the process fidelity is equivalent to
the generalized N-qubit Bell state fidelity
:math:`F_{+} = |\! \langle +|^{\otimes N} U_{\mathrm{targ}}^{\dagger} U(T) |+\rangle^{\otimes N}\!|^2`. For the
Rydberg gates that are currently implemented in RydOpt, this is the case.
Example:
>>> import rydopt as ro
>>> import numpy as np
>>> gate = ro.gates.TwoQubitGate(
... phi=None,
... theta=np.pi,
... Vnn=float("inf"),
... decay=0,
... )
>>> pulse = ro.pulses.PulseAnsatz(
... detuning_ansatz=ro.pulses.Const(),
... phase_ansatz=ro.pulses.SinCrab(2),
... )
>>> params = ro.pulses.PulseParams(7.61140652, [0.07842706], [1.80300902, -0.61792703], [])
>>> fidelity = ro.simulation.process_fidelity(gate, pulse, params)
Args:
gate: RydOpt Gate object.
pulse: RydOpt PulseAnsatz object.
params: Pulse parameters.
tol: Precision of the ODE solver, default is 1e-7.
Returns:
State fidelity :math:`F_{pro}`.
"""
final_states = evolve(gate, pulse, params, tol)
return gate.process_fidelity_helper(final_states)
[docs]
def average_gate_fidelity(
gate: GateSystem, pulse: PulseAnsatzLike, params: ParamsFloatLike, tol: float = 1e-7
) -> jax.Array:
r"""The function provides the average gate fidelity calculated from the process fidelity:
.. math::
F_{avg} = \frac{d \cdot F_{pro} + 1}{d+1},
where :math:`d` is the dimension of the Hilbert space.
Example:
>>> import rydopt as ro
>>> import numpy as np
>>> gate = ro.gates.TwoQubitGate(
... phi=None,
... theta=np.pi,
... Vnn=float("inf"),
... decay=0,
... )
>>> pulse = ro.pulses.PulseAnsatz(
... detuning_ansatz=ro.pulses.Const(),
... phase_ansatz=ro.pulses.SinCrab(2),
... )
>>> params = ro.pulses.PulseParams(7.61140652, [0.07842706], [1.80300902, -0.61792703], [])
>>> fidelity = ro.simulation.average_gate_fidelity(gate, pulse, params)
Args:
gate: RydOpt Gate object.
pulse: RydOpt PulseAnsatz object.
params: Pulse parameters.
tol: Precision of the ODE solver, default is 1e-7.
Returns:
Fidelity :math:`F_{avg}`.
"""
# The average gate fidelity is calculated from the process fidelity (which is also known as the entanglement
# fidelity) as described by https://arxiv.org/abs/quant-ph/0205035, equation (3), and
# https://quantum.cloud.ibm.com/docs/en/api/qiskit/quantum_info#average_gate_fidelity.
return (gate.dim() * process_fidelity(gate, pulse, params, tol) + 1.0) / (gate.dim() + 1.0)