Preparation of Approximate Eigenvector by Unitary Operations on Eigenstate in Abrams-Lloyd Quantum Algorithm

Table 1

Some single qubit orthogonalisation operators suitable for various types of eigenvectors.

|𝑣⟩	⟨𝑣|𝑖𝜎𝑦|𝑣⟩	⟨𝑣|𝜎𝑥|𝑣⟩	⟨𝑣|(𝜎𝑥−𝜎𝑦)/√2|𝑣⟩
0.97493; 0.22252	0	−0.43388	−0.30680
0.97493; 0.22252𝑖	−0.43388	0	−0.30680
0.87838+0.42301𝑖; −0.22252	−0.3909𝑖	−0.18825	0.1433
0.87838+0.42301𝑖; 0.19271−0.11126𝑖	−0.35869𝑖	0.24441	0.42632