Cost Minimization

The pattern at the heart of every variational algorithm: define a quantum cost function, then drive it to its minimum with a classical optimizer.

A minimal variational loop

import qalgora
from qalgora import spin

@qalgora.kernel
def ansatz(theta: float):
    q = qalgora.qubit()
    ry(theta, q)

cost_op = spin.z(0)

def cost(params):
    theta = params[0]
    return qalgora.observe(ansatz, cost_op, theta).expectation()

opt = qalgora.optimizers.COBYLA()
minimum, best = opt.optimize(dimensions=1, function=cost)
print("minimum <Z> =", minimum, "at theta =", best[0])   # expected optimum: <Z> = -1 at theta = π

Anatomy

• Ansatz — a parameterized kernel that prepares a trial state.
• Cost — an expectation value to minimize (energy, error, loss).
• Optimizer — a classical routine that proposes new parameters.