Fuda, Toru; Funakawa, Daiju; Sasayama, Satoshi; Suzuki, Akito Eigenvalues and threshold resonances of a two-dimensional split-step quantum walk with strong shift. (English) Zbl 07899089 Quantum Stud. Math. Found. 10, No. 4, 483-496 (2023). MSC: 81-XX × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asahara, Keisuke; Funakawa, Daiju; Segawa, Etsuo; Suzuki, Akito; Teranishi, Noriaki Spectral mapping theorem of an abstract non-unitary quantum walk. (English) Zbl 07734073 Linear Algebra Appl. 676, 1-24 (2023). MSC: 47A25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Matsuzawa, Yasumichi; Suzuki, Akito; Tanaka, Yohei; Teranishi, Noriaki; Wada, Kazuyuki The Witten index for one-dimensional split-step quantum walks under the non-Fredholm condition. (English) Zbl 1522.47030 Rev. Math. Phys. 35, No. 6, Article ID 2350010, 41 p. (2023). MSC: 47A53 81Q35 81Q60 47B39 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mandal, Amrita; Sarma Sarkar, Rohit; Adhikari, Bibhas Localization of two dimensional quantum walks defined by generalized Grover coins. (English) Zbl 1519.81222 J. Phys. A, Math. Theor. 56, No. 2, Article ID 025303, 21 p. (2023). MSC: 81Q35 82B41 55P60 60J05 15B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fuda, Toru; Narimatsu, Akihiro; Saito, Kei; Suzuki, Akito Spectral analysis for a multi-dimensional split-step quantum walk with a defect. (English) Zbl 07899030 Quantum Stud. Math. Found. 9, No. 1, 93-112 (2022). MSC: 81-XX × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kiumi, Chusei; Saito, Kei Strongly trapped space-inhomogeneous quantum walks in one dimension. (English) Zbl 1506.81031 Quantum Inf. Process. 21, No. 9, Paper No. 330, 33 p. (2022). MSC: 81Q35 15A18 81P16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kiumi, Chusei Localization of space-inhomogeneous three-state quantum walks. (English) Zbl 1506.81030 J. Phys. A, Math. Theor. 55, No. 22, Article ID 225205, 14 p. (2022). MSC: 81Q35 15A18 81P16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kiumi, Chusei Localization in quantum walks with periodically arranged coin matrices. (English) Zbl 1510.81059 Int. J. Quantum Inf. 20, No. 5, Article ID 2250013, 14 p. (2022). MSC: 81Q05 35P15 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Maeda, Masaya Asymptotic stability of small bound state of nonlinear quantum walks. (English) Zbl 1507.81196 Physica D 439, Article ID 133408, 14 p. (2022). MSC: 81V45 60G50 35B35 35B32 35P15 81U05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Maeda, Masaya; Sasaki, Hironobu; Segawa, Etsuo; Suzuki, Akito; Suzuki, Kanako Dispersive estimates for quantum walks on 1D lattice. (English) Zbl 1485.35329 J. Math. Soc. Japan 74, No. 1, 217-246 (2022). Reviewer: Nelson Faustino (Alfeizerão) MSC: 35Q41 81U30 82B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ide, Yusuke; Konno, Norio; Segawa, Etsuo Eigenvalues of quantum walk induced by recurrence properties of the underlying birth and death process: application to computation of an edge state. (English) Zbl 1509.81486 Quantum Inf. Process. 20, No. 5, Paper No. 160, 17 p. (2021). MSC: 81Q35 81Q10 82B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asahara, Keisuke; Funakawa, Daiju; Seki, Motoki; Tanaka, Yohei An index theorem for one-dimensional gapless non-unitary quantum walks. (English) Zbl 1514.47020 Quantum Inf. Process. 20, No. 9, Paper No. 287, 26 p. (2021). MSC: 47A53 81Q10 81T35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kuriki, Shuji; Nirjhor, Md Sams Afif; Ohno, Hiromichi Parameterization of quantum walks on cycles. (English) Zbl 1509.81167 Quantum Inf. Process. 20, No. 1, Paper No. 28, 16 p. (2021). MSC: 81P45 81P16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Narimatsu, Akihiro; Ohno, Hiromichi; Wada, Kazuyuki Unitary equivalence classes of split-step quantum walks. (English) Zbl 1508.81852 Quantum Inf. Process. 20, No. 11, Paper No. 368, 23 p. (2021). MSC: 81Q35 81P45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tanaka, Yohei A constructive approach to topological invariants for one-dimensional strictly local operators. (English) Zbl 1460.81029 J. Math. Anal. Appl. 500, No. 1, Article ID 125072, 22 p. (2021). MSC: 81Q10 34L40 34C14 81Q35 82C20 47A53 34L05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Matsuzawa, Yasumichi An index theorem for split-step quantum walks. (English) Zbl 1508.81851 Quantum Inf. Process. 19, No. 8, Paper No. 227, 8 p. (2020). MSC: 81Q35 47A53 47N50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wada, Kazuyuki A weak limit theorem for a class of long-range-type quantum walks in 1d. (English) Zbl 1516.81081 Quantum Inf. Process. 19, No. 1, Paper No. 2, 17 p. (2020). MSC: 81Q10 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Suzuki, Akito; Tanaka, Yohei The Witten index for 1D supersymmetric quantum walks with anisotropic coins. (English) Zbl 1508.81924 Quantum Inf. Process. 18, No. 12, Paper No. 377, 36 p. (2019). MSC: 81S25 47N50 81Q35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Suzuki, Akito Supersymmetry for chiral symmetric quantum walks. (English) Zbl 1508.81331 Quantum Inf. Process. 18, No. 12, Paper No. 363, 23 p. (2019). MSC: 81P45 47A53 47N50 60K40 81Q35 × Cite Format Result Cite Review PDF Full Text: DOI
Segawa, Etsuo; Suzuki, Akito Spectral mapping theorem of an abstract quantum walk. (English) Zbl 1508.05149 Quantum Inf. Process. 18, No. 11, Paper No. 333, 24 p. (2019). MSC: 05C81 05C50 05C63 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Morioka, Hisashi; Segawa, Etsuo Detection of edge defects by embedded eigenvalues of quantum walks. (English) Zbl 1504.81010 Quantum Inf. Process. 18, No. 9, Paper No. 283, 18 p. (2019). MSC: 81P16 47A75 47A40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Morioka, Hisashi Generalized eigenfunctions and scattering matrices for position-dependent quantum walks. (English) Zbl 1476.81141 Rev. Math. Phys. 31, No. 7, Article ID 1950019, 37 p. (2019). MSC: 81U20 47A75 47A40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wada, Kazuyuki Absence of wave operators for one-dimensional quantum walks. (English) Zbl 1428.81130 Lett. Math. Phys. 109, No. 11, 2571-2583 (2019). MSC: 81U20 47A40 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Richard, S.; Suzuki, A.; Tiedra de Aldecoa, R. Quantum walks with an anisotropic coin. II: Scattering theory. (English) Zbl 1411.81215 Lett. Math. Phys. 109, No. 1, 61-88 (2019). MSC: 81U05 46N50 47A40 47B47 60F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Wang, Caishi; Wang, Ce; Tang, Yuling; Ren, Suling Quantum walk in terms of quantum Bernoulli noise and quantum central limit theorem for quantum Bernoulli noise. (English) Zbl 1404.81157 Adv. Math. Phys. 2018, Article ID 2507265, 9 p. (2018). MSC: 81S25 81R15 60G50 60F05 × Cite Format Result Cite Review PDF Full Text: DOI OA License
Ohno, Hiromichi Parameterization of translation-invariant two-dimensional two-state quantum walks. (English) Zbl 1401.81061 Acta Math. Vietnam. 43, No. 4, 737-747 (2018). MSC: 81S25 60G50 × Cite Format Result Cite Review PDF Full Text: DOI Link
Fuda, Toru; Funakawa, Daiju; Suzuki, Akito Localization for a one-dimensional split-step quantum walk with bound states robust against perturbations. (English) Zbl 1395.81143 J. Math. Phys. 59, No. 8, 082201, 13 p. (2018). MSC: 81S25 60G50 05C20 34E15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo Partition-based discrete-time quantum walks. (English) Zbl 1395.81086 Quantum Inf. Process. 17, No. 4, Paper No. 100, 35 p. (2018). MSC: 81P68 81Q35 60G50 05C81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luo, Xin; Tate, Tatsuya Up and down Grover walks on simplicial complexes. (English) Zbl 1384.05109 Linear Algebra Appl. 545, 174-206 (2018). MSC: 05C50 39A12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Higuchi, Yusuke; Segawa, Etsuo Quantum walks induced by Dirichlet random walks on infinite trees. (English) Zbl 1390.81271 J. Phys. A, Math. Theor. 51, No. 7, Article ID 075303, 21 p. (2018). MSC: 81S25 05C81 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Richard, S.; Suzuki, A.; Tiedra de Aldecoa, R. Quantum walks with an anisotropic coin. I: Spectral theory. (English) Zbl 1384.81033 Lett. Math. Phys. 108, No. 2, 331-357 (2018). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q10 47A10 47B47 46N50 60G50 35P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Portugal, Renato; Segawa, Etsuo Connecting coined quantum walks with Szegedy’s model. (English) Zbl 1470.81035 Interdiscip. Inf. Sci. 23, No. 1, 119-125 (2017). MSC: 81Q35 81P68 05C81 68Q25 81S25 82C10 82C41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Matsue, Kaname; Ogurisu, Osamu; Segawa, Etsuo A note on the spectral mapping theorem of quantum walk models. (English) Zbl 1470.81028 Interdiscip. Inf. Sci. 23, No. 1, 105-114 (2017). MSC: 81P68 81S40 60G50 05C81 47A70 81R25 16S35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Higuchi, Yusuke; Konno, Norio; Sato, Iwao; Segawa, Etsuo Periodicity of the discrete-time quantum walk on a finite graph. (English) Zbl 1470.81043 Interdiscip. Inf. Sci. 23, No. 1, 75-86 (2017). MSC: 81S25 60G50 81Q35 15B52 05C81 05C85 58J50 39A12 11R60 47A25 × Cite Format Result Cite Review PDF Full Text: DOI
Fuda, Toru; Funakawa, Daiju; Suzuki, Akito Localization of a multi-dimensional quantum walk with one defect. (English) Zbl 1387.81150 Quantum Inf. Process. 16, No. 8, Paper No. 203, 24 p. (2017). MSC: 81P68 81S25 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ohno, Hiromichi Unitary equivalence classes of one-dimensional quantum walks. II. (English) Zbl 1382.81059 Quantum Inf. Process. 16, No. 12, Paper No. 287, 17 p. (2017). MSC: 81P68 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License
Sasaki, Itaru; Suzuki, Akito Essential spectrum of the discrete Laplacian on a perturbed periodic graph. (English) Zbl 1348.05128 J. Math. Anal. Appl. 446, No. 2, 1863-1881 (2017). MSC: 05C50 05C63 05C80 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ohno, Hiromichi Unitary equivalent classes of one-dimensional quantum walks. (English) Zbl 1348.81173 Quantum Inf. Process. 15, No. 9, 3599-3617 (2016). MSC: 81P68 60G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv OA License