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

Table 2

Comparison of eigenvalues obtained numerically and through Abrams-Lloyd quantum algorithm sequentially. The approximate eigenvector is obtained by orthogonalization of eigenstate of 3 qubits. The single qubit orthogonalization operator is 𝑖𝜎_𝑦. The index register of 5 qubits (𝑀=32) is measured as 𝑝.

Numerical			Abrams-Lloyd
eigenvalue of		p	eigenvalue of
H	U		U	H
−2	−0.4162+0.9093𝑖	22	−0.3827+0.9239𝑖	−1.9635
−1	0.5403+0.8415𝑖	27	0.5556+0.8315𝑖	−0.9818
1	0.5403−0.8415𝑖	5	0.5556−0.8315𝑖	0.9818
0	1	0	1	0
0	1	0	1	0
0	1	0	1	0