Table of Links

Main Procedure

Applications

Discussion and Conclusion

Acknowledgements, Declarations, Data Availability Statement, and References

Appendix

Appendix A: Review of Chebyshev Approach

Here we make a review of Chebyshev approach that was employed in [2], which is essentially built upon quantum walk technique [6, 8]. What we will describe below is more or less a summary of Section 4 in Ref. [2], the result of which was used in our main text.

The so-called walk operator is defined as:

Let |λ⟩ and λ be eigenvector and eigenvalue of A/d (note that the scaling by d doesn’t have further systematic problem, as the spectrum remains the same, only eigenvalues got scaled by a factor). Within the subspace spanned by T |λ⟩ and ST |λ⟩, W admits the following block form:

The proof can be found in Lemma 15 of [2]. The above form of W possess the following remarkable property (Lemma 16 of [2]),