  It is a challenging problem to construct an efficient quantum algorithm which
can compute the Jones' polynomial for any knot or link obtained from platting
or capping of a $2n$-strand braid. We recapitulate the construction of
braid-group representations from vertex models. We present the eigenbases and
eigenvalues for the braiding generators and its usefulness in direct evaluation
of Jones' polynomial. The calculation suggests that it is possible to associate
a series of unitary operators for any braid word. Hence we propose a quantum
algorithm using these unitary operators as quantum gates acting on a $2n$ qubit
state. We show that the quantum computation gives Jones' polynomial for achiral
knots and links.
