Quantum imaginary-time evolution

import numpy as np

# One QITE step. The two measurement functions are the parts that come
# from a device or simulator; they are stood in for here with the
# analytic values of a single-qubit RY ansatz under H = -Z, so the whole
# file runs as written. Replace them with real measurements to use it.
def measure_metric(theta):
    return np.array([[0.25]])  # Fubini-Study metric of RY(theta) on one qubit

def measure_imaginary_time_force(theta):
    # -d<H>/dtheta / 2 for H = -Z, where <H> = -cos(theta), so the step
    # descends toward theta = 0 (the ground state) rather than away from it.
    return np.array([-0.5 * np.sin(theta[0])])

theta = np.array([0.3])
dt = 0.05
metric = measure_metric(theta)
force = measure_imaginary_time_force(theta)
velocity = np.linalg.solve(metric + 1e-8 * np.eye(len(theta)), force)
theta = theta + dt * velocity
print('theta after one imaginary-time step:', theta)

RESULT = {'theta': [float(v) for v in theta], 'velocity': [float(v) for v in velocity]}