aqora

Walk/Zeta Correspondence

Takashi Komatsu, Norio Konno, Iwao Sato

arXiv:2104.10287Journal of Statistical PhysicsDec 19, 20229 citations

QW-search/zeta correspondence

Taisuke Hosaka, Norio Konno, Etsuo Segawa

arXiv:2402.17183Quantum Studies Mathematics and FoundationsMar 11, 20250 citations

Mahler/Zeta Correspondence

Takashi Komatsu, Norio Konno, Iwao Sato +1 more

arXiv:2202.05966Quantum Information ProcessingAug 20, 20223 citations

Walk/Zeta Correspondence for quantum and correlated random walks

Norio Konno, Shunya Tamura

In this paper, following the recent paper on Walk/Zeta Correspondence by the first author and his coworkers, we compute the zeta function for the three- and four-state quantum walk and correlated random walk, and the multi-state random walk on the one-dimensional torus by using the Fourier analysis. We deal with also the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we introduce a new class of models determined by the generalized Grover matrix bridging the gap between the Grover matrix and the positive-support of the Grover matrix. Finally, we give a generalized version of the Konno-Sato theorem for the new class. As a corollary, we calculate the zeta function for the generalized Grover matrix on the d-dimensional torus.In this paper, following the recent paper on Walk/Zeta Correspondence by the first author and his coworkers, we compute the zeta function for the three- and four-state quantum walk and correlated random walk, and the multi-state random walk on the one-dimensional torus by using the Fourier analysis. We deal with also the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we introduce a new class of models determined by the generalized Grover matrix bridging the gap between the Grover matrix and the positive-support of the Grover matrix. Finally, we give a generalized version of the Konno-Sato theorem for the new class. As a corollary, we calculate the zeta function for the generalized Grover matrix on the d-dimensional torus.

arXiv:2109.07664Sep 16, 20211 citation

IPS/Zeta correspondence

Takashi Komatsu, Norio Konno, Iwao Sato

Our previous works presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models including random walks, correlated random walks, quantum walks, and open quantum random walks. This paper introduces a new zeta function for multi-particle models with probabilistic or quantum interactions, called the interacting particle system (IPS). We compute the zeta function for some tensor-type IPSs.

arXiv:2105.04056Quantum Information and ComputationFeb 1, 20223 citations

Walk/Zeta correspondence for quantum walks on path graphs: a pre-geometric structure implied by a generalized reflection principle

Jiro Akahori, Riki Kitano, Norio Konno +1 more

We establish a local Konno-Sato correspondence for reflected random and Szegedy walks on a finite path graph. A generalized reflection principle, using explicit involutions rather than point reflections in the asymmetric case, yields exact zeta factorizations into a boundary factor and local factors indexed by the infinite dihedral group. After symmetrization, the classical and quantum local factors correspond for each group element. The identity contribution determines the normalized thermodynamic limits. In the symmetric case, diffusive and ballistic scalings recover the Gaussian Poisson summation formula and the Dirac comb identity, respectively. Under a double scaling of the asymmetry and spectral parameter, the quantum factorization yields a massive Dirac-type limit: nonidentity even words produce the periodic-orbit factor, the identity produces the free-field factor, and odd words together with the boundary produce a finite boundary correction.We establish a local Konno-Sato correspondence for reflected random and Szegedy walks on a finite path graph. A generalized reflection principle, using explicit involutions rather than point reflections in the asymmetric case, yields exact zeta factorizations into a boundary factor and local factors indexed by the infinite dihedral group. After symmetrization, the classical and quantum local factors correspond for each group element. The identity contribution determines the normalized thermodynamic limits. In the symmetric case, diffusive and ballistic scalings recover the Gaussian Poisson summation formula and the Dirac comb identity, respectively. Under a double scaling of the asymmetry and spectral parameter, the quantum factorization yields a massive Dirac-type limit: nonidentity even words produce the periodic-orbit factor, the identity produces the free-field factor, and odd words together with the boundary produce a finite boundary correction.

math.PRCross-listedarXiv:2610.05393Oct 6, 2026

Grover/Zeta Correspondence based on the Konno–Sato theorem

Related papers

Grover/Zeta Correspondence based on the Konno–Sato theorem

Related papers