// H = a*Z + b*X with a=1, b=0.5. Lower eigenvalue is -sqrt(a^2+b^2).
const a = 1, b = 0.5;
const r = Math.sqrt(a*a + b*b);
// Eigenvector for eigenvalue -r: [b, -(a+r)], then normalize.
let v0 = b, v1 = -(a + r);
const norm = Math.hypot(v0, v1);
v0 /= norm; v1 /= norm;
// RY(theta)|0> = cos(theta/2)|0> + sin(theta/2)|1>; match the eigenvector.
const theta = 2 * Math.atan2(v1, v0);
const c = circuit(1);
c.ry(theta, 0);
return c;