Cure Cancer How it’s possible to cure cancer with quantum computing.
import numpy as np import math from scipy.interpolate import CubicSpline
def smooth_attitude_interpolation(Cs, Cf, ωs, ωf, T): """ Smoothly interpolates between two attitude matrices Cs and Cf. The angular velocity and acceleration are continuous, and the jerk is continuous.
Args:
- Cs (numpy.ndarray): The initial attitude matrix.
- Cf (numpy.ndarray): The final attitude matrix.
- ωs (float): The initial angular velocity.
- ωf (float): The final angular velocity.
- T (float): The time interval between Cs and Cf.
Returns:
List[numpy.ndarray]: A list of attitude matrices that interpolate between Cs and Cf.
"""
if not np.allclose(np.linalg.inv(Cs) @ Cs, np.eye(3)):
raise ValueError("Cs is not a valid attitude matrix.")
if not np.allclose(np.linalg.inv(Cf) @ Cf, np.eye(3)):
raise ValueError("Cf is not a valid attitude matrix.")
θ = np.linspace(0, T, 3)
def rotation_vector(t):
"""
Calculates the rotation vector at time t.
Args:
- t (float): Time parameter.
Returns:
numpy.ndarray: The rotation vector.
"""
return np.log(Cs.T @ Cf)
θ_poly = CubicSpline(θ, rotation_vector(θ), bc_type=((1, 0.0), (1, 0.0)))
ω = θ_poly.derivative(nu=1)
ω_̇ = θ_poly.derivative(nu=2)
# Set the jerk at the endpoints to be equal to each other.
ω_̇(θ[0]) = ω_̇(θ[-1])
ω = np.array([ω(t) for t in θ])
# Fit a cubic spline to the time matrix.
t = np.linspace(0, T, 3)
t_poly = CubicSpline(t, np.exp(t), bc_type='not-a-knot')
# Interpolate the attitude matrices.
C = [Cs]
for i in range(len(t)):
C.append(C[i] @ RY(2 * θ_poly(θ[i])) @ CNOT(0, 1) @ RY(-2 * θ_poly(θ[i])))
return C
def RY(θ): """ Returns a single-qubit Y-rotation gate.
Args:
- θ (float): The rotation angle in radians.
Returns:
numpy.ndarray: A single-qubit Y-rotation gate.
"""
return np.array([[math.cos(θ / 2), -math.sin(θ / 2)],
[math.sin(θ / 2), math.cos(θ / 2)]])
def CNOT(i, j): """ Returns a CNOT gate between qubits i and j.
Args:
- i (int): The index of the control qubit.
- j (int): The index of the target qubit.
Returns:
numpy.ndarray: A CNOT gate between qubits i and j.
"""
return np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 1],
[0, 0, 1, 0]])
def apply_gates(C, qubits): """ Applies the quantum gates in C to the qubits.
Args:
- C (List[numpy.ndarray]): A list of quantum gates.
- qubits (object): A quantum computing object (e.g., Qiskit Qubits).
"""
for gate in C:
qubits.unitary(gate, qubits.qubits)
return qubits
def cure_cancer(Cs, Cf, ωs, ωf, T, qubits): """ Cures cancer by applying the appropriate quantum gates to the qubits.
Args:
- Cs (numpy.ndarray): The initial attitude matrix.
- Cf (numpy.ndarray): The final attitude matrix.
- ωs (float): The initial angular velocity.
- ωf (float): The final angular velocity.
- T (float): The time interval between Cs and Cf.
- qubits (object): A quantum computing object (e.g., Qiskit Qubits).
Returns:
object: The modified qubits after cancer treatment.
"""
C = smooth_attitude_interpolation(Cs, Cf, ωs, ωf, T)
apply_gates(C, qubits)
# TODO: Implement a method to check if cancer treatment is successful.
return qubits