Takuya Machida

Associate Professor of College of Industrial Technology, Nihon University

E-mail: machida.takuya@nihon-u.ac.jp


Primary Research Area: Probability
Research Interests: Quantum walks

(See also) What are quantum walks?


EDUCATION:
Yokohama National University, Japan
Ph.D. in Engineering, March 2010
  Dissertation: "Limit theorems for the time-dependent coined quantum walk in one dimension"
  Dissertations Advisor: Professor Norio Konno
M.S. in Engineering, March 2007
B.S. in Engineering, March 2005


RESEARCH EXPERIENCE:

  • (4.2022 - Present) Associate professor of College of Industrial Technology, Nihon University
  • (4.2016 - 4.2022) Assistant professor of College of Industrial Technology, Nihon University
  • (8.2013 - 1.2015) Postdoctoral Scholar, Department of Mathematics, University of California, Berkeley
  • (4.2013 - 3.2016) Research Fellow, Japan Society for the Promotion of Science
  • (4.2010 - 3.2013) Postdoctoral Fellow, Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University


MEMBERSHIPS:

  • Japanese Society for Mathematical Biology (JSMB) (4.2010 - 3.2012)
  • Mathematical Society of Japan (4.2011 - Present)




  Papers
31 Takuya Machida,
A simple model of quantum walk with a gap in distribution,
arXiv:2503.08151.
30 Takuya Machida,
Phase transition of a continuous-time quantum walk on the half line,
Quantum Information Processing, Vol.23, 243 (2024), arXiv:2403.13576.
29 Takuya Machida,
Limit distribution of a continuous-time quantum walk with a spatially 2-periodic Hamiltonian,
Quantum Information Processing, Vol.22, 332 (2023), arXiv:2304.06464.
28 Takuya Machida,
Phase transition of an open quantum walk,
International Journal of Quantum Information, Vol.19, No.6, 2150028 (2021), arXiv:2103.01473.
27 Takuya Machida,
Limit distribution of a time-dependent quantum walk on the half line,
Quantum Information Processing, Vol.19, 296 (2020), arXiv:2003.01953.
26 Takuya Machida,
A limit distribution for a quantum walk driven by a five-diagonal unitary matrix,
Quantum Information and Computation, Vol.21 No.1&2, pp.19-36 (2021), arXiv:1903.07192.
25 Takuya Machida, F. Alberto Grünbaum,
Some limit laws for quantum walks with applications to a version of the Parrondo paradox,
Quantum Information Processing, Vol.17(9), 241 (2018), arXiv:1803.04522.
24 Takuya Machida,
A limit theorem for a splitting distribution of a quantum walk,
International Journal of Quantum Information, Vol.16, No.3, 1850023 (2018), arXiv:1704.04554.
23 Takuya Machida,
A quantum walk on the half line with a particular initial state,
Quantum Information Processing, Vol.15, No.8, pp. 3101-3119 (2016), arXiv:1604.02227.
22 Takuya Machida,
A localized quantum walk with a gap in distribution,
Quantum Information and Computation, Vol.16 No.5&6, pp.515-529 (2016), arXiv:1510.03046.
21 Takuya Machida, C. M. Chandrashekar,
Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice,
Physical Review A, 92, 062307 (2015), arXiv:1510.02885.
20 Takuya Machida,
A limit law of the return probability for a quantum walk on a hexagonal lattice,
International Journal of Quantum Information, Vol.13, No.7, 1550054 (2015), arXiv:1502.06453.
19 Takuya Machida, Etsuo Segawa,
Trapping and spreading properties of quantum walk in homological structure,
Quantum Information Processing, Vol.14, No.5, pp. 1539-1558 (2015), arXiv:1405.1487.
18 Yusuke Ide, Hirofumi Izuhara, Takuya Machida,
Turing instability in Reaction-Diffusion models on complex networks,
Physica A, 457(1), pp. 331-347 (2016), arXiv:1405.0642.
17 Takuya Machida,
Limit theorems of a 3-state quantum walk and its application for discrete uniform measures,
Quantum Information and Computation, Vol.15 No.5&6, pp.406-418 (2015), arXiv:1404.1522.
16 F. Alberto Grünbaum, Takuya Machida,
A limit theorem for a 3-period time-dependent quantum walk,
Quantum Information and Computation, Vol.15 No.1&2, pp.50-60 (2015), arXiv:1404.1509.
15 Takuya Machida, C. M. Chandrashekar, Norio Konno, Thomas Busch,
Limit distributions for different forms of four-state quantum walks on a two-dimensional lattice,
Quantum Information and Computation, Vol.15 No.13&14, pp.1248-1258 (2015), arXiv:1307.6288.
14 Vincenzo Nicosia, Takuya Machida, Richard Wilson, Edwin Hancock, Norio Konno, Vito Latora, Simone Severini,
Co-evolution of networks and quantum dynamics: a generalization of preferential attachment,
The Journal of Statistical Mechanics: Theory and Experiment, P08016 (2013), arXiv:1302.0887.
13 Yukio Hayashi, Takayuki Komaki, Yusuke Ide, Takuya Machida, Norio Konno,
Combinatorial and approximative analyses in spatially random division process,
Physica A, 392(9), pp.2212-2225 (2013), arXiv:1301.2369.
12 Carlo Di Franco, Michael Mc Gettrick, Takuya Machida, Thomas Busch,
Measurement-induced generation of spatial entanglement in a two-dimensional quantum walk with single-qubit coin,
Journal of Computational and Theoretical Nanoscience, Vol.10, No.7, pp.1613-1616 (2013), arXiv:1307.2993.
11 Takuya Machida,
Realization of the probability laws in the quantum central limit theorems by a quantum walk,
Quantum Information and Computation, Vol.13 No.5&6, pp.430-438 (2013), arXiv:1208.1005.
10 Takuya Machida,
A quantum walk with a delocalized initial state: contribution from a coin-flip operator,
International Journal of Quantum Information, Vol.11, No.5, 1350053 (2013), arXiv:1203.5396.
9 Takuya Machida,
Limit theorems for the interference terms of discrete-time quantum walks on the line,
Quantum Information and Computation, Vol.13 No.7&8, pp.661-671 (2013), arXiv:1112.4633.
8 Norio Konno, Takuya Machida, Tohru Wakasa,
The Heun differential equation and the Gauss differential equation related to quantum walks,
Yokohama Mathematical Journal, Vol.58, pp.53-63 (2012), arXiv:1109.2662.
7 Carlo Di Franco, Michael Mc Gettrick, Takuya Machida, Thomas Busch,
Alternate two-dimensional quantum walk with a single-qubit coin,
Physical Review A, 84, 042337 (2011), arXiv:1107.4400.
6 Yusuke Ide, Norio Konno, Takuya Machida,
Entanglement for discrete-time quantum walks on the line,
Quantum Information and Computation, Vol.11 No.9&10, pp.855-866 (2011), arXiv:1012.4164.
5 Yusuke Ide, Norio Konno, Takuya Machida, Etsuo Segawa,
Return probability of one-dimensional discrete-time quantum walks with final-time dependence,
Quantum Information and Computation, Vol.11 No.9&10, pp.761-773 (2011), arXiv:1103.1180.
4 Takuya Machida,
Limit distribution for a time-inhomogeneous 2-state quantum walk,
Journal of Computational and Theoretical Nanoscience, Vol.10, No.7, pp.1571-1578 (2013), arXiv:1010.3481.
3 Takuya Machida,
Limit theorems for a localization model of 2-state quantum walks,
International Journal of Quantum Information, Vol.9, No.3, pp.863-874 (2011), arXiv:1008.1116.
2 Norio Konno, Takuya Machida,
Limit theorems for quantum walks with memory,
Quantum Information and Computation, Vol.10, No.11&12, pp.1004-1017 (2010), arXiv:1004.0443.
1 Takuya Machida, Norio Konno,
Limit theorem for a time-dependent coined quantum walk on the line,
F. Peper et al. (Eds.): IWNC 2009, Proceedings in Information and Communications Technology, Vol.2, pp.226-235 (2010), arXiv:1004.0425.




  Books
5 Takuya Machida，
Chapter 7 "Limit theorem for a quantum walk by Fourier analysis" in the book "New development of quantum walks",
BAIFUKAN Co., Ltd., pp.133-146 (2019).
4 Takuya Machida, "Quantum Walk −Introduction and Fundamental Theory−", SHOKABO Co., Ltd. (2018).
3 Takuya Machida，
Chapter 2 "Quantum Walks" in the book "Research Advances in Quantum Dynamics",
InTech, pp.27-51 (2016). (web)
2 Takuya Machida, "Visual Guide Book of an Introduction to Quantum Walks", Morikita Publishing Co., Ltd. (2015).
1 Norio Konno and Takuya Machida, "Visual Guide Book of Complex Networks", Shuwa System (2008).




  Teachings
11 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Precalculus, Mathematical Tools for Physical Sciences (2023)
10 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Precalculus, Mathematical Tools for Physical Sciences (2022)
9 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Exercises in mathematics (2021)
8 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Exercises in mathematics, Precalculus (2020)
7 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Precalculus (2019)
6 College of Industrial Technology, Nihon University
Calculus, Linear algebra (2018)
5 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Probability and Statistics, Exercises in mathematics, Precalculus (2017)
4 College of Industrial Technology, Nihon University
Calculus, Linear algebra, Exercises in mathematics, Precalculus (2016)
3 College of Engineering Science, Yokohama National University
Linear algebra (2015)
2 College of Engineering Science, Yokohama National University
Linear algebra (2012)
1 Department of Information Technology, Kanagawa Industrial and Technical Junior College
Discrete mathematics (2009)




  Grants
4 Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) (23K03220), "A study of quantum walks driven by Weyl Hamiltonians", Principal Investigator (4.2023 - 3.2026)
3 Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C) (19K03625), "A study of duplications between quantum walks", Principal Investigator (4.2019 - 3.2023)
2 Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (B) (16K17648), "A study of limit theorems for quantum walks with gaps in distribution", Principal Investigator (4.2016 - 3.2019)
1 Japan Society for the Promotion of Science, Grants-in-Aid for JSPS Fellows (13J06287), "Quantum walks on stochastic graphs", Principal Investigator (4.2013 - 3.2016)




  Activities
5 Organizer of Mathematical Congress Of The Americas 2017 Special Session on Quantum Walks, Open Quantum Walks, Quantum Computation and Related Topics （The Centre Mont-Royal and McGill University, Montreal, Canada） （2017.7） (web)
4 Organizer of 2016 Joint Mathematics Meetings AMS Special Session on Quantum Walks, Quantum Markov Chains, Quantum Computation and Related Topics （Washington State Convention Center, Seattle, WA, America） （1.2016） (web)
3 Organizer of Workshop of Quantum Simulation and Quantum Walks 2015 （Yokohama National University, Yokohama, Kanagawa, Japan） （11.2015） (web)
2 Organizer of 2015 Joint Mathematics Meetings AMS Special Session on Quantum Markov Chains, Quantum Walks, and Related Topics (Henry B. Gonzalez Convention Center, San Antonio, TX, America) (1.2015) (web)
1 Organizer of 2014 Joint Mathematics Meetings AMS Special Session on Quantum Walks, Quantum Computation, and Related Topics (Baltimore Convention Center, Baltimore, MD, America) (1.2014) (web)




  Presentations in English (Invited talks)
12 Introduction to Quantum Walks
Rigorous Statistical Mechanics and Related Topics, RIMS, Kyoto University, Japan (2019.11)
11 Quantum walk on a half line
Mathematical Congress Of The Americas, The Centre Mont-Royal and McGill University, Montreal, Canada (2017.7)
10 Limit distribution of a quantum walk on a two-dimensional square lattice
Joint Mathematics Meetings, Washington State Convention Center, Seattle, WA, America (2016.1)
9 Limit distribution of a 3-period time-dependent quantum walk
Joint Mathematics Meetings, Henry B. Gonzalez Convention Center, San Antonio, TX, America (1.2015)
8 Limit distribution of a 2-state quantum walk on the line with a delocalized initial state
Joint Mathematics Meetings, The Baltimore Convention Center, Baltimore, MD, America (1.2014)
7 Limit distributions of a quantum walk and central limit theorems in quantum probability theory II
Probabilistic Operator Algebra Sem., University of California, Berkeley, Berkeley, CA, America (10.2013)
6 Limit distributions of a quantum walk and central limit theorems in quantum probability theory I
Probabilistic Operator Algebra Sem., University of California, Berkeley, Berkeley, CA, America (10.2013)
5 Limit theorem of a 2-state quantum walk with a non-localized initial state
Research Visit: Prof. Norio KONNO & Dr. Takuya MACHIDA, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan (4.2013)
4 Limit distributions of quantum walks and 2nd order linear ordinary differential equations
Joint Mathematics Meetings, San Diego Convention Center, San Diego, CA, America (1.2013)
3 Limit distributions of quantum walks and the Heun equation
The 7th Jikji Workshop: Infinite Dimensional Analysis and Quantum Probability, Chungbuk National University, Cheongju, Korea (7.2012)
2 Relationship between quantum walks and differential equations
Progress in Variational Problems-Variational Problems Interacting with Probability Theories, Kyoto University, Kyoto, Japan (6.2012)
1 The limit theorems for a time-dependent discrete-time quantum walk on the line
Seminar on Mathematical Sciences Based on Modeling, Analysis and Simulation, Meiji University, Kawasaki, Japan (4.2010)




  Presentations in English (Others)
3 Relation between a limit distribution of a quantum walk and the Heun equation
Workshop of Quantum Dynamics and Quantum Walks, Okazaki Conference Center, Aichi, Japan (11.2012)
2 Quantum walks and the Heun equation
2012 International Conference on Modeling, Analysis and Simulation, Meiji University, Tokyo, Japan (11.2012)
1 Limit theorem for a time-dependent coined quantum walk on the line
4th International Conference on Natural Computing, Himeji International Exchange Center, Hyogo, Japan (9.2009)




  International research collaborators
6 Norman Sheu (University of California, Berkeley) (web)
6 F. Alberto Grünbaum (University of California, Berkeley) (web)
5 C. M. Chandrashekar (The Institute of Mathematical Sciences) (web)
4 Simone Severini (University College London) (web)
3 Thomas Busch (Okinawa Institute of Science and Technology Graduate University) (web)
2 Michael Mc Gettrick (The National University of Ireland) (web)
1 Carlo Di Franco (Universidad del País Vasco / Euskal Herriko Unibertsitatea)




  Research visits
12 University of California, Berkeley, Berkeley, CA, USA (2023.8.9-2023.8.23)
11 University of California, Berkeley, Berkeley, CA, USA (2023.3.8-2023.3.22)
10 University of California, Berkeley, Berkeley, CA, USA (2019.8.2-2019.8.20)
9 University of California, Berkeley, Berkeley, CA, USA (2019.3.4-2019.3.21)
8 University of California, Berkeley, Berkeley, CA, USA (2018.8.6-2018.8.22)
7 University of California, Berkeley, Berkeley, CA, USA (2018.3.4-2018.3.21)
6 University of California, Berkeley, Berkeley, CA, USA (2017.8.7-2017.8.25)
5 University of California, Berkeley, Berkeley, CA, USA (2017.3.5-2017.3.19)
4 University of California, Berkeley, Berkeley, CA, USA (2016.8.9-2016.8.24)
3 University of California, Berkeley, Berkeley, CA, USA (2016.1.10-2016.1.18)
2 University of California, Berkeley, Berkeley, CA, USA (2015.9.14-2015.9.30)
1 University of California, Berkeley, Berkeley, CA, USA (2013.8.1-2015.1.31)


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