We thank all the speakers and participants

**Dates:**21st - 24th, June, 2021**Style:**The presentation will be delivered via Zoom.

Before and after the presentation time, free discussion will be organized via Remo.**Organizing committee:**Masahito Hayashi (Chair, SUSTech/Nagoya Univ.),

Hiroaki Kanno (Nagoya Univ.), Shintarou Yanagida (Nagoya Univ.), Man-Hong Yung (SUSTech)**Contact:**sustechnagoya2021 [at] gmail.com

- Francesco Buscemi (Nagoya Univ.)
- Oscar Dahlsten (SUSTech)
- Masahito Hayashi (SUSTech/Nagoya Univ.)
- Liang Kong (SUSTech)
- Francois Le Gall (Nagoya Univ.)
- Zi-Wen Liu (Perimeter Inst.)
- Tomoki Nakanishi (Nagoya Univ.)
- Harumichi Nishimura (Nagoya Univ.)
- Shinichiroh Matsuo (Nagoya Univ.)
- Hitoshi Moriyoshi (Nagoya Univ.)
- Seunghoan Song (Nagoya Univ.)
- Shintarou Yanagida (Nagoya Univ.)
- Man-Hong Yung (SUSTech)
- Hao Zheng (Peking Univ.)

For the participation, please mail to
**sustechnagoya2021 [at] gmail.com**

with the following information:
**your name, affiliation and e-mail address**.

We will send the Zoom and Remo addresses later.

Talks were also streamed by koushare and YouTube.

CST (UTC+8) | JST (UTC+9) | 6/21(Mon) | 6/22(Tue) | 6/23(Wed) | 6/24(Thu) | |
---|---|---|---|---|---|---|

09:50-09:55 | 10:50-10:55 | Opening | Free discussion | |||

10:00-10:50 | 11:00-11:50 | Matsuo | Song | |||

11:00-11:50 | 12:00-12:50 | Zheng | Dahlsten | Hayashi | ||

14:00-14:50 | 15:00-15:50 | Nakanishi | Nishimura | Free discussion | Yanagida | |

15:00-15:50 | 16:00-16:50 | Kong | Yung | Liu | ||

16:00-16:50 | 17:00-17:50 | Moriyoshi | Le Gall | Buscemi | ||

16:50-16:55 | 17:50-17:55 | Closing | ||||

We will organize free discussion by Remo in the following time.

- 6/21, 11:50--14:00 (CST), 12:50--15:00 (JST).
- 6/21, 16:50--19:20 (CST), 17:50--20:20 (JST).
- 6/22, 11:50--14:00 (CST), 12:50--15:00 (JST).
- 6/22, 16:50--19:20 (CST), 17:50--20:20 (JST).
- 6/23, 09:20--16:30 (CST), 10:20--17:30 (JST).
- 6/24, 11:50--14:00 (CST), 12:50--15:00 (JST).
- 6/24, 16:50--19:20 (CST), 17:50--20:20 (JST).

**6/21 (Mon)**- 10:00-10:50 (CST) 11:00-11:50 (JST)

**Shinichiroh Matsuo**(Graduate School of Mathematics, Nagoya University)

**The APS index theorem, domain-wall fermions, and global anomaly inflow**slide

Inspired by global anomaly inflow and bulk-edge correspondence in physics, we introduced a new formulation of the Atiyah-Patodi-Singer index using domain-wall fermion Dirac operators. In this talk, we will explain our new formulation and its equivalence to the traditional one. We will also mention a generalisation to mod-two index. - 11:00-11:50 (CST) 12:00-12:50 (JST)

**Hao Zheng**(School of Mathematical Sciences, Peking University)

**Categorical computation**

We show that computation based on topological materials is a categorification of quantum computation. This is a joint work with Liang Kong. - 14:00-14:50 (CST) 15:00-15:50 (JST)

**Tomoki Nakanishi**(Graduate School of Mathematics, Nagoya University)

**Cluster algebras**

Cluster algebras, introduced by Fomin and Zelevinsky around 2000, are a class of commutative algebras originated in Lie theory. They are nowadays recognized as a common underlying algebraic/combinatorial structure diversely appearing in mathematics. Naturally, they also appear in various subjects of mathematical physics, such as, T-systems and Y-systems in conformal field theory, Stokes phenomenon in WKB analysis, Faddeev’s quantum dilogarithms, and mirror symmetry in string theory. In this talk I will explain the most basic notions of cluster algebras, namely, seeds and mutations. - 15:00-15:50 (CST) 16:00-16:50 (JST)

**Liang Kong**(Shenzhen Institute for Quantum Science and Engineering, SUSTech)

**Boundary-bulk relations in topological orders**

The relation between the physics of the bulk and that of a boundary plays an important role in quantum field theories, quantum gravity and condensed matter physics. In this talk, I will review a manifestation of this relation that can be summarized as a short statement: "the bulk is the center of a boundary". I will explain the meaning of "center" and provide a formal proof of this statement (arXiv:1702.00673). By including higher codimensional domain walls between boundaries, the boundary-bulk relation can be formulated mathematically as a higher functor. In lower dimensional cases, it becomes precise mathematical theorems. In the end, I will discuss the significances of this relation in the study of topological orders and topological phase transitions. - 16:00-16:50 (CST) 17:00-17:50 (JST)

**Hitoshi Moriyoshi**(Graduate School of Mathematics, Nagoya University)

**The Ginsparg-Wilson index theorem for Quantum walk on the integer lattice**

The Atiyah-Singer index theorem is one of the most celebrated mathematical formula in the 20th century, which can be rephrased with relevance to Plank's law of black-body radiation. In Lattice Gauge theory physicists are trying to discretize the index theorem by introducing modified Dirac operators, one of which is called the Ginsparg-Wilson operator. In this talk, we first set up a discretized index theorem on the integer lattice by exploiting the coin and shift operators, which are fundamental ingredients in Quantum random walk. We then formulate the Ginsparg-Wilson index theorem and clarify the relation to the earliest index theorem, which is due to F. Noether in 1920.

- 10:00-10:50 (CST) 11:00-11:50 (JST)
**6/22 (Tue)**- 10:00-10:50 (CST) 11:00-11:50 (JST)

**Seunghoan Song**(Graduate School of Mathematics, Nagoya University)

**Quantum private information retrieval**slide

In quantum private information retrieval (QPIR), a user retrieves aclassical file from multiple servers by downloading quantum systems without leaking the identity of the retrieved file to the servers. The QPIR capacity is the maximal achievable ratio of the size of the retrieved file to the total download size. The QPIR capacity is derived for various settings: on the non-communicating servers, colluding servers, and distributed storage. The tight upper bound of the QPIR capacity is proved by entropic inequalities. The lower bound is proved by constructing capacity-achieving protocols with stabilizer quantum codes. - 11:00-11:50 (CST) 12:00-12:50 (JST)

**Oscar Dahlsten**(Department of Physics, SUSTech)

**Universal bound on energy cost of bit reset in finite time**

We consider how the energy cost of bit reset scales with the time duration of the protocol. Bit reset necessarily takes place in finite time, where there is an extra penalty on top of the quasistatic work cost derived by Landauer. This extra energy is dissipated as heat in the computer, inducing a fundamental limit on the speed of irreversible computers. We formulate a hardware-independent expression for this limit. We derive a closed-form lower bound on the work penalty as a function of the time taken for the protocol and bit reset error. It holds for discrete as well as continuous systems, assuming only that the master equation respects detailed balance. This is a join work with Yizheng Zhen, Dario Egloff and Kavan Modi arXiv:2106.00580. - 14:00-14:50 (CST) 15:00-15:50 (JST)

**Harumichi Nishimura**(Graduate School of Informatics, Nagoya University)

**SMP model, PSM protocols, and their quantum analogues**slide

Communication complexity is one of major complexity measures in theoretical computer science. There are several computation models for studying communication complexity. The simultaneous message passing (SMP) model is the most simplest one. In this model, k parties, P_1, P_2, ..., P_k have their inputs x_1, x_2, ..., x_n, and another party R (called the referee) does not know their inputs. The goal is that R computes the function value f(x_1, x_2, ..., x_n) by possibly shorter messages from P_1, P_2, ..., P_k while the communication is non-interactive: P_1, P_2, ..., P_k send their messages once, and then R must output the function value. The private simultaneous message (PSM) protocols are the protocols in the SMP model but satisfy some kind of "zero-knowledge" condition. Namely, R is required not to know any information from the messages except f(x_1, x_2,..., x_n).

In this talk, I first explain the SMP model and PSM protocols. After that, I explain the quantum versions of SMP models and PSM protocols, called the private simultaneous quantum message (PSQM) protocols, and present several known results and the results obtained by Akinori Kawachi (Mie U.) and me. Finally, I give several open questions about PSQM models.

This talk is based on arXiv:2105.07120. - 15:00-15:50 (CST) 16:00-16:50 (JST)

**Man-Hong Yung**(Department of Physics, SUSTech)

**Quantum Software Engineering for NISQ**

Quantum computing is now emerging as a rapidly-growing industry on a global scale. This is mainly because of the many technological breakthroughs achieved over the last few years. Remarkably, it was experimentally demonstrated that the status of computational advantage (also known as quantum supremacy) can be reached with only 53 noisy qubits. The next step is to demonstrate how near-term chips can solve practical problems better than any classical means. For this purpose, hardware improvement is not enough; what is perhaps more important might be the algorithm and/or software part. In this talk, I will share my experience over the last few years in trying to push forward this direction. - 16:00-16:50 (CST) 17:00-17:50 (JST)

**Francois Le Gall**(Graduate School of Mathematics, Nagoya University)

**Quantum Communication Complexity of Distribution Testing**slide

The classical communication complexity of testing closeness of discrete distributions has recently been studied by Andoni, Malkin and Nosatzki (ICALP'19). In this problem, two players each receive samples from one distribution over {1,2,...,n}, and the goal is to decide whether their two distributions are equal, or are far apart in the l1-distance. In this talk I will discuss the quantum communication complexity of this problem, and present a quantum protocol that gives a quadratic improvement over the classical communication complexity obtained by Andoni, Malkin and Nosatzki when the distributions have low l2-norm. I will also explain how to prove tight lower bounds. Note that in our setting, the samples received by each of the parties are classical, and it is only the communication between them that is quantum. Our results thus give one setting where quantum protocols overcome classical protocols for a testing problem with purely classical samples. This talk is based on arXiv:2006.14870.

- 10:00-10:50 (CST) 11:00-11:50 (JST)
**6/24 (Thu)**- 11:00-11:50 (CST) 12:00-12:50 (JST)
- 14:00-14:50 (CST) 15:00-15:50 (JST)

**Shintarou Yanagida**(Graduate School of Mathematics, Nagoya University)

**Probability distribution expressed by Racah hypergeometric orthogonal polynomial**slide

This talk is based on the collaboration arXiv:2104.12635 with Masahito Hayashi (SUSTech/Nagoya) and Akihito Hora (Hokkaido).

Considering the irreducible decomposition of a certain distinguished vector in the tensor space of the classical SU(2)-S_n Schur-Weyl duality, we obtained a discrete probability distribution equipped with four parameters. Surprisingly, this distribution can be expressed by Racah polynomial, which sits in the top line of Askey scheme of hypergeometric orthogonal polynomials. Moreover, the cumulative distribution function is expressed by a 4F3-hypergeometric polynomial. I would like to give an overview of this distribution, and also explain some relevant mathematical topics such as Schur-Weyl duality, zonal spherical functions, and hypergeometric summation formulas. - 15:00-15:50 (CST) 16:00-16:50 (JST)

**Zi-Wen Liu**(Perimeter Institute for Theoretical Physics)

**No-go theorems for quantum resource purification: Universal theories and practical applications**slide

The manipulation of quantum "resources" such as entanglement and coherence lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are highly susceptible to noises and thus often lose their power or become unreliable for direct usage. Here, we establish a theory of the universal limitations on the accuracy and efficiency of resource purification tasks which apply to any well-behaved resource theory, for both state (static) and channel (dynamical) resources. Our general results bring new insights and imply various forms of fundamental limits to a broad range of problems of great theoretical and practical importance, including magic state distillation and fault tolerant quantum computing, quantum error correction, quantum Shannon theory, and quantum circuit synthesis. Among the above I shall talk more about covariant quantum error correction, also in relation to quantum metrology, for which we have some recent progress. - 16:00-16:50 (CST) 17:00-17:50 (JST)

**Francesco Buscemi**(Graduate School of Informatics, Nagoya University)

**The "thermodynamic reverse bound" and the role of retrodiction in statistical mechanics**slide

In this talk I will present some recent work about the role that statistical retrodiction and the theory of approximate reversibility play in statistical mechanics, in particular, fluctuation relations and the second law of thermodynamics, for classical and quantum systems.

References:

[1] F. Buscemi, D. Fujiwara, N. Mitsui, and M. Rotondo. Thermodynamic reverse bounds for general open quantum processes. Physical Review A, vol.102, 032210 (2020).

[2] F. Buscemi and V. Scarani. Fluctuation relations from Bayesian retrodiction. Physical Review E, vol. 103, 052111 (2021).

**Masahito Hayashi**(Shenzhen Institute for Quantum Science and Engineering, SUSTech / Graduate School of Mathematics, Nagoya University)

**Estimation of group action with energy constraint and its application to uncertainty relations on S1 and S3**slide

In this talk, we will discuss the estimation of group action. We show an interesting relation between Fourier transform and this estimation problem. Then, applying this relation, we optimize our estimation method under various condition including the energy constraint. Finally, we apply obtained result to uncertainty relation related to compact groups.- 11:00-11:50 (CST) 12:00-12:50 (JST)

Last update 2021/07/04.