User controlled rotation with arcBall
After some research I found that it's slightly more efficient to get the half quaternion directly from the double quaternion:

QVector3D rotaxis = QVector3D::crossProduct (vec1, vec2);
double cos = QVector3D::dotProduct (vec1, vec2);

// rotaxis and cos describe the double quat
// add 1 to cos so normalizing will 0.5 lerp between the null quat and the double quat
QQuaternion quat (1+cos,rotaxis);
quat.normalize ();


This saves the normalization of the bisector.

The rotation matrix can be constructed from a non-unit quaternion without first normalizing it. You do have to provide your own function to do so because the Qt algorithm assumes a unit quaternion:

inline QMatrix4x4 quatToMat(QQuaternion q)
{
    //based on algorithm on wikipedia
    // http://en.wikipedia.org/wiki/Rotation_matrix#Quaternion
    float w = q.scalar ();
    float x = q.x();
    float y = q.y();
    float z = q.z();

    float n = q.lengthSquared();
    float s =  n == 0?  0 : 2 / n;
    float wx = s * w * x, wy = s * w * y, wz = s * w * z;
    float xx = s * x * x, xy = s * x * y, xz = s * x * z;
    float yy = s * y * y, yz = s * y * z, zz = s * z * z;

    float m[16] = { 1 - (yy + zz),         xy + wz ,         xz - wy ,0,
                         xy - wz ,    1 - (xx + zz),         yz + wx ,0,
                         xz + wy ,         yz - wx ,    1 - (xx + yy),0,
                               0 ,               0 ,               0 ,1  };
    QMatrix4x4 result =  QMatrix4x4(m,4,4);
    result.optimize ();
    return result;
}


Using that eliminates all normalization from in mouseMoveEvent except to get the arcballVectors themselves.