Algorithm 6 VQE solving SVP.

Input:  the lattice basis $\mathbf{B}={[{\mathbf{b}}_1,\dots ,{\mathbf{b}}_m]}^T\in {\mathbb{Z}}^{(m+1)\times (m+1)}$. Output:  short vector $\mathbf{x}$.  1:Perform BKZ-reduction on $\mathbf{B}$.  2:The SVP problem is encoded to the ground state of the Hamiltonian operator H.  3:Construct parameterized quantum circuits.  4:Repeat preparing an ansatz state $|\mathsf{\Psi }(\mathit{\theta })\rangle$ from the parameterized quantum circuit and measuring it in Pauli-Z basis. Calculate the expectation value $C(\mathit{\theta })$.  5:Pass $C(\mathit{\theta })$ and parameters to a classical optimizer. Update the parameter $\mathit{\theta }$ and go to step 4 until the expectation value converges.