Hosts

Beijing Institute of Mathematical Sciences and Applications (BIMSA)

Organizers

Zhengfeng Ji (Tsinghua University)

Chunlan Jiang (Hebei Normal University)

Zhengwei Liu (Tsinghua University)

Shunlong Luo (Academy of Mathematics and Systems Science, CAS)

Jinsong Wu (BIMSA)

Contact

Email: qtot@bimsa.cn

Location: A6 Lecture Hall 101, BIMSA Campus.

Aug 25 is the Registration Day

Accommodation: Aloft Beijing Huairou (北京怀柔雅乐轩酒店)，Building No.3, Compound No.9, Yong Le North 2 Street, Huairou District, Beijing, China（北京怀柔区永乐北二街 9 号院 3 号楼）

BIMSA Campus: No. 544 Hefangkou Village, Huairou, Beijing北京市怀柔区河防口村544号金隅兴发科技园 101408

Lunch & Dinner: BIMSA Campus A4 Dinning Hall

Date	Lunch	Dinner
Aug. 26	12:00 ~ 13:00	18:10 ~ 19:00
Aug. 27	12:00 ~ 13:00	18:10 ~ 19:00
Aug. 28	12:00 ~ 13:00	18:10 ~ 19:00
Aug. 29	12:00 ~ 13:00	18:10 ~ 19:00
Aug. 30	12:00 ~ 13:00	18:10 ~ 19:00

Notices: To travel from the airport to the hotel, you have the option of taking a taxi, which typically costs around 120 to 180RMB. The hotel is conveniently located near Yanqi Lake, which is a popular sightseeing in Huairou, Beijing. Additionally, there is a daily bus service available from Aloft Beijing Huairou to the BIMSA campus, providing convenient transportation for your needs.

Registration Address

Aloft Beijing Huairou

北京怀柔雅乐轩酒店

Conference Venue

A6 Lecture Room, BIMSA Campus.

BIMSA Campus

No. 544 Hefangkou Village, Huairou, Beijing

北京市怀柔区河防口村544号金隅兴发科技园 101408

Daily bus service available from Aloft Huairou (雅乐轩) to the BIMSA campus, providing convenient transportation for your needs.

Date	Hotel —-> BIMSA A6	BIMSA A6 —-> Hotel
Aug. 26	8:40 ~ 9:00	12:40 ~ 13:00
	14:00 ~ 14:20	19:00 ~ 19:20
Aug. 27	9:00 ~ 9:20	12:40 ~ 13:00
	14:00 ~ 14:20	19:00 ~ 19:20
Aug. 28	9:00 ~ 9:20	12:40 ~ 13:00
	14:00 ~ 14:20	19:00 ~ 19:20
Aug. 29	9:00 ~ 9:20	12:40 ~ 13:00
	14:00 ~ 14:20	19:00 ~ 19:20
Aug. 30	9:00 ~ 9:20	12:40 ~ 13:00
	14:00 ~ 14:20	19:00 ~ 19:20

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Daily bus service available from Tsinghua to the BIMSA campus

Tsinghua(7:30)-Southeast Gate(7:35)- Wangjingxi(08:05)-BIMSA(9:15)From Tuesday to Friday

Tsinghua(7:10)-Southeast Gate(7:35)- Wangjingxi(08:05)-BIMSA(9:15)Every Monday

Tsinghua(9:30)-Southeast Gate(9:35)-Shuangqing Office(10:00)-BIMSA(11:10)

BIMSA(16:30)-Tsinghua( 18:00)

BIMSA(20:00)-Wangjingxi(21:00) -Shuangqing Office (21: 30) -Southeast Gate (21: 45) -Tsinghua(21: 50)

Aug 26, 2024

09:20 ~ 09:40		Open Ceremony
09:40 ~ 10:40	Huaxin Lin	Almost commuting self-adjoint operators and quantum measurements
Tea Break
10:50 ~ 11:50	Zhengwei Liu	Ising 3+1 TQFT and quantum invariants of 2-knots in smooth 4-manifolds
Lunch
14:30 ~ 15:30	Shaoming Fei	On theory of quantum information and related physics
Tea Break
15:50 ~ 16:50	Li Gao	Sufficiency of quantum Fisher information
17:00 ~ 18:00	Jianchao Wu	Borsuk-Ulam-type conjectures, local triviality dimension and noncommutative principal bundles

Aug 27, 2024

09:30 ~ 10:30	David Evans	Quantum Symmetries
Tea Break
11:00 ~ 12:00	Weihua Liu	Intermediate de Finetti type theorems for *-random variables in classical and free probability
Lunch
14:30 ~ 15:30	Huangjun Zhu	The Magic in qudit shadow estimation based on the Clifford group
Tea Break
15:50 ~ 16:50	Ke Li	Quantum Rényi divergence and its use in quantum information
17:00 ~ 18:00	Yi Wang	Some Remarks on the von Neumann's Inequality

Aug 28, 2024

09:30 ~ 10:30	Matteo Paris	Chiral quantum walks and applications
Tea Break
10:50 ~ 11:50	Ziwen Liu	Complexity and order in approximate quantum error-correcting codes
Lunch
14:30 ~ 15:30	Seung-Hyeok Kye	Bilinear forms and Choi matrices in quantum information theory
Tea Break
15:50 ~ 16:50	Yanqi Qiu	Harmonic analysis of Mandelbrot Cascades
17:00 ~ 18:00	Yuhei Suzuki	Crossed product splitting of intermediate operator algebras via 2-cocycles

Aug 29, 2024

09:30 ~ 10:30	Xu Zhang	Stochastic PDE control: progresses and open problems
Tea Break
10:50 ~ 11:50	Jin-Peng Liu	Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost
Lunch
Free Discussion on Great Wall

Aug 30, 2024

09:30 ~ 10:30	Dong Liu	Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition
Tea Break
10:50 ~ 11:50	Dongling Deng	Quantum adversarial machine learning: from theory to experiment
Lunch
14:30 ~ 15:30	Lihong Zhi	Noncommutative Real Algebraic Geometry and Nonlocal Games
Tea Break
15:50 ~ 16:50	Changpeng Shao	Testing quantum satisfiability
17:00 ~ 18:00	Shuang Ming	3 dimensional alterfold, characters and modular invariants.

Speaker:

Dongling Deng (Tsinghua University)

Title:

Quantum adversarial machine learning: from theory to experiment

Abstract:

Quantum adversarial machine learning is an emergent interdisciplinary research frontier that studies the vulnerability of quantum learning systems in adversarial scenarios and the development of potential countermeasures to enhance their robustness against adversarial perturbations. In this talk, I will first make a brief introduction to this field and review some recent progresses. I will show, through concrete examples, that typical quantum classifiers are extremely vulnerable to adversarial perturbations: adding a tiny amount of carefully crafted noises into the original legitimate samples may lead the classifiers to make incorrect predictions at a high confidence level. I will talk about possible defense strategies against adversarial attacks.

I will also talk about a recent experimental demonstration of quantum adversarial learning with programmable superconducting qubits.

Ref:
[1] S.-R. Lu, L. M. Duan, and D.-L. Deng, Phys. Rev. Research 2, 033212 (2020)
[2] W.-Y. Gong and D.-L. Deng, National Science Review 9, nwab130 (2022)
[3] W.-H. Ren et al., Nature Computational Science 2, 711 (2022)
[4] H.-L. Zhang et al., Nature Communications 13, 4993 (2022)

Speaker:

David Evans ( Cardiff University, UK)

Title:

Quantum Symmetries

Abstract:

This talk is part of a programme to understand quantum symmetries through subfactors and twisted equivariant K-theory and their applications in conformal field theory. Here I discuss the question of constructing actions of these quantum symmetries on the irrational rotation algebras and more generally noncommutative tori. This is based on joint work with Corey Jones.

Speaker:

Shaoming Fei (Capital Normal University)

Title:

On theory of quantum information and related physics

Abstract:

We introduce recent progresses in the theory of quantum information and related physics, including quantum coherence, quantum correlations, quantum uncertainty relations, as well as quantum measurement enhanced quantum battery capacity.

Speaker:

Li Gao (Wuhan University)

Title:

Sufficiency of quantum Fisher information

Abstract:

Fisher information is a measure of the amount of information that an observable random variable \(X\) carries about an unknown parameter \(\theta\). One important application of classical Fisher information is the sufficient statistic: a statistic \(T=T(X)\) is sufficient for \(X_\theta\) w.r.t the parameter \(\theta\) if and only if the Fisher information is preserved by \(T\). In this talk, I talk about the sufficiency about quantum Fisher information. It turns out that the sufficiency (i.e. the recoverability by a quantum channel) are not guaranteed by the preservation of SLD or RLD Fisher Information, which are the two most considered definitions in the literature. Nevertheless, the sufficiency is equivalent to the preservation of a large family of “regular” Fisher information, including BKM Fisher Information, just as the classical case.

Speaker:

Seung-Hyeok Kye (Seoul National University, Seoul, Korea)

Title:

Bilinear forms and Choi matrices in quantum information theory

Abstract:

We provide a unified approach with which we may explain several important notions arising from current quantum information theory. They include separability/entanglement and Schmidt numbers of bipartite states as well as various kinds of positive maps like k-superpositive maps, k-positive maps and completely positive maps. Recall that a linear map is 1-superpositive if and only if it is entanglement breaking if and only if its Choi matrices are separable.

Main tools for our approach are bi-linear pairings and Choi matrices. After we explain the above notions with the usual bi-linear pairings and Choi matrices, we find all bilinear pairings between mapping spaces and tensor products of matrices, which retains the duality between k-positivity and Schmidt number k. We also characterize all linear isomorphisms of Choi type from mapping spaces onto tensor products, which retains the correspondences between k-superpositivity and Schmidt number k, as well as Choi’s original correspondence between completely positive maps and positive (semi-definite) matrices.

Finally, we consider infinite dimensional analogues of Choi matrices. For this purpose, we assign two objects, bounded linear operators and trace class operators for a class of linear maps between von Neumann factors. With this approach, we extend the above mentioned notions for the type I factor acting on the infinite dimensional separable Hilbert space.

Speaker:

Ke Li (Harbin Institute of Technology)

Title:

Quantum Rényi divergence and its use in quantum information

Abstract:

In this talk, I will introduce the quantum generalization of Rényi’s information divergence and its use in quantum information theory. Due to the noncommutativity of quantum theory, the quantum version of Rényi divergence is not unique, and we still lack a full understanding of it. A proper formula of the quantum Rényi divergence should admit precise operational interpretation. Based on a series of recent works with coauthors, I will report: (1) how quantum Rényi divergence characterizes exactly the error exponents in quantum information, and (2) conversely, how the former operational characterization sheds light on the quantum generalization of Rényi’s information divergence.

Speaker:

Huaxin Lin (The Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS))

Title:

Almost commuting self-adjoint operators and quantum measurements

Abstract:

In quantum mechanics, macroscopic observables may be represented by bounded self-adjoint operators \(T_1\), \(T_2\), …, \(T_n\) on a Hilbert space \(H\). Commutators \(T_jT_i-T_iT_j\) are related to the uncertainty principle in their measurements and small commutators indicate more precise measurements. In his recent book, David Mumford proposed to study “near eigenvectors” for some set of human observables which are called “Approximately Macroscopically Unique” states. This talk will present some answers to Mumford’s questions.

Speaker:

Dong Liu (Tsinghua University)

Title:

Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition

Abstract:

The robustness of quantum memory against physical noises is measured by two methods: the exact and approximate quantum error correction (QEC) conditions for error recoverability, and the decoder-dependent error threshold which assesses if the logical error rate diminishes with system size. Here we unravel their relations and propose a unified framework to extract an intrinsic error threshold from the approximate QEC condition, which could upper bound other decoder-dependent error thresholds. Our proof establishes that relative entropy, effectively measuring deviations from exact QEC conditions, serves as the order parameter delineating the transition from asymptotic recoverability to unrecoverability. Consequently, we establish a unified framework for determining the error threshold across both exact and approximate QEC codes, addressing errors originating from noise channels as well as those from code space imperfections. This result sharpens our comprehension of error thresholds across diverse QEC codes and error models.

Speaker:

Jin-Peng Liu (Tsinghua University)

Title:

Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost

Abstract:

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

Ref:  [1] Dong An, Jin-Peng Liu, Lin Lin. Physical Review Letters, 131(15):150603, 2023.

Speaker:

Weihua Liu (Zhejiang University)

Title:

Intermediate de Finetti type theorems for *-random variables in classical and free probability

Abstract:

Firstly, we will introduce the notion of free independence, which comes from Voiculescu’s probabilistic method to attack the free group von Neumann algebra isomorphism problem. Then, we introduce free analogues of certain classical groups, which are compact quantum groups in the sense of Woronowicz. There is a canonical way to define symmetric invariants on operator algebras with faithful states from compact quantum groups. With those symmetric conditions, we are able to determine the relations between generators of given von Neumann algebras conditionally by Kostler, Speicher, Curran, etc. These results are called de Finetti type theorems. In my recent work, we will provide a full classification of de Finetti type theorems for non-selfadjoint generators in both the commutative and free case. If time permits, we will explain the possible symmetries between classical and free case.

Speaker:

Ziwen Liu (Tsinghua University)

Title:

Complexity and order in approximate quantum error-correcting codes

Abstract:

Quantum codes achieving approximate quantum error correction (AQEC) are useful, often fundamentally important, from both practical and physical perspectives but lack a systematic understanding. In this work, we establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) properties, covering both all-to-all and geometric scenarios including lattice systems. To this end, we introduce a type of code parameter that we call “subsystem variance”, which is closely related to the optimal AQEC precision. Our key finding is that if the subsystem variance is below an O(k/n) critical threshold then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial “phases” of codes. Based on our results, we propose O(k/n) as a boundary between subspaces that should and should not count as AQEC codes. Our theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems.

In addition to showcasing applications to a wide variety of AQEC codes arising from diverse contexts spanning computer science and physics, we also demonstrated how our theory offers new physical insights through the lens of both gapped and gapless systems. Specifically, it enables a long-sought rigorous understanding of the gap between strict definitions of gapped topological order and the widely-used long-range entanglement and topological entanglement entropy (TEE) signatures, as well as a discussion of how AQEC codes exhibiting physically significant power-law-error behavior emerge at low energies of conformal field theory (CFT), potentially advancing the understanding of quantum gravity through holography. We observe from various different perspectives that roughly O(1/n) represents a common, physically significant “scaling threshold” of subsystem variance for features associated with nontrivial quantum order.

Speaker:

Zhengwei Liu (Tsinghua university & BIMSA)

Title:

Ising 3+1 TQFT and quantum invariants of 2-knots in smooth 4-manifolds

Abstract:

We review the remarkable theory of 2+1 TQFT and its construction from spherical fusion categories. We introduce a unified framework to generalize the 2+1 theory to both non-semisimple and higher dimensional cases. We will construct the Ising 3+1 TQFT and a non-semisimple one by renormalization, which is the first non-trvial example in various ways. This quantum invariant detects 2-knots in smooth 4–manifolds.

Speaker:

Shuang Ming (BIMSA)

Title:

3 dimensional alterfold, characters and modular invariants.

Abstract:

Alterfold theory of dimension three, is a three dimensional generalization of Jones’ Planar algebra of finite depth. It has the advantage of describing/discovering/proving nontrivial equalities and inequalities in the theory of tensor categories and subfactors. In this talk, we will review the basic setting of the three dimensional alterfold theory, for a pair of Morita equivalent spherical fusion categories. In addition, if one of the category is braided, we show how modular invariant matrix can be read from the certain alterfold diagram. As a corollary, we show an obstruction for a modular invariant matrix to be physical.

Speaker:

Matteo Paris (University of Milan)

Title:

Chiral quantum walks and applications

Abstract:

Quantum walks are the quantum mechanical counterpart of classical random walks and provide a general and flexible tool to describe the quantum propagation of a particle or an excitation in a network, i.e. a discrete structure modeled as a graph. Besides the fundamental interest, quantum walks represent a valuable tool to describe, design and optimize energy transport in artificial or biological systems. Continuous-time quantum walks (CTQW) on graphs are traditionally defined as the quantum analogue of classical random walks (RW), by promoting the classical transfer matrix, i.e. the RW graph Laplacian, to an Hamiltonian. However, this association does not encompass all the possible quantum evolutions of a walker on a graph, thus strongly limiting the set of exploitable quantum Hamiltonians to achieve quantum enhancement in specific tasks. A question thus arises on whether it is possible to define more general quantum walks on a graph, by considering all Hermitian Hamiltonians compatible with a given graph topology, and how do these generalized QWs compare with their classical analogues.

In this talk, I present a systematic approach to chiral quantum walks, introducing a full characterization of all the possible Hamiltonians describing the time evolution over a given topology. As applications, we address the problem of optimally routing classical and quantum information encoded in the position of a quantum walker on the simplest graphs apt to this task, and prove that chirality may be exploited to achieve the quantum speed limit in search algorithms on graphs.

Speaker:

Yanqi Qiu (Hangzhou Institute of Advanced Study, UCAS)

Title:

Harmonic analysis of Mandelbrot Cascades

Abstract:

We will talk about the asymptotic decay of the Fourier coefficients of the Mandelbrot canonical cascade measure and more general cascade measures. Our method is to put the analysis of these Fourier series into the framework of vector-valued martingales, as well as to apply celebrated asymptotics of small moments of critical or super-critical branching random walks. This talk is based on recent joint works with Xinxin Chen, Yong Han and Zipeng Wang.

Speaker:

Changpeng Shao (Academy of Mathematics and Systems Science, CAS)

Title:

Testing quantum satisfiability

Abstract:

Quantum k-SAT (the problem of determining whether a k-local Hamiltonian is frustration-free) is known to be QMA_1-complete for k >= 3, and hence likely hard for quantum computers to solve. Building on a classical result of Alon and Shapira, we show that quantum k-SAT can be solved in randomised polynomial time given the ‘property testing’ promise that the instance is either satisfiable (by any state) or far from satisfiable by a product state; by ‘far from satisfiable by a product state’ we mean that n^k constraints must be removed before a product state solution exists, for some fixed > 0. The proof has two steps: we first show that for a satisfiable instance of quantum k-SAT, most subproblems on a constant number of qubits are satisfiable by a product state. We then show that for an instance of quantum k-SAT which is far from satisfiable by a product state, most subproblems are unsatisfiable by a product state. Given the promise, quantum k-SAT may therefore be solved by checking satisfiability by a product state on randomly chosen subsystems of constant size.

Speaker:

Yuhei Suzuki (Hokkaido University)

Title:

Crossed product splitting of intermediate operator algebras via 2-cocycles

Abstract:

We give a new complete description theorem of the intermediate operator algebras, which unifies the discrete Galois correspondence results and the crossed product splitting results. As an application, we obtain a Galois’s type result for Bisch—Haagerup type inclusions arising from isometrically shift-absorbing actions of compact-by-discrete groups.

Based on my preprint arxiv:2406.00304

Speaker:

Yi Wang (Chongqing University)

Title:

Some Remarks on the von Neumann’s Inequality

Abstract:

The von Neumann’s inequality says that for a contraction operator T on a Hilbert space and an analytic polynomial p. The norm of p(T) is controlled by the supreme norm of p on the unit disc. There are various proofs of this inequality. When it comes to multivariable. Ando showed that an analogous result holds for two contractions on the bidisc. However, Varopolous showed that it fails for three or more contractions. I would like to share a new proof of the von Neumann’s inequality and a method of generating counterexamples of the von Neumann’s inequality on the polydisc.

Speaker:

Jianchao Wu (Fudan University)

Title:

Borsuk-Ulam-type conjectures, local triviality dimension and noncommutative principal bundles

Abstract:

The classical Borsuk-Ulam theorem may be seen as a statement about the complexity of spheres as principal Z/2Z-bundles via the antipodal action. The truthfulness of analogous statements in the noncommutative setting for general compact groups, or even compact quantum groups, were proposed by Baum, Dąbrowski, and Hajac. For classical principal bundles, a dimensional notion called G-index plays a crucial role in this quest. I will talk about my joint work with Gardella, Hajac, and Tobolski, where we introduce the local triviality dimension, a generalization of G-index for noncommutative principal bundles that can be used to transfer Borsuk-Ulam-type results and ideas from the classical setting to the noncommutative setting.

Speaker:

Xu Zhang (Sichuan University)

Title:

Stochastic PDE control: progresses and open problems

Abstract:

In this talk, I will present some recent progresses and open problems on control theory for stochastic partial differential equations. I will explain the new phenomena and difficulties in the study of controllability and optimal control problems for these systems. In particular, I will show by some examples that both the formulation of corresponding stochastic control problems and the tools to solve them may differ considerably from their deterministic/finite-dimensional counterparts.

Speaker:

Lihong Zhi (Academy of Mathematics and Systems Science, CAS)

Title:

Noncommutative Real Algebraic Geometry and Nonlocal Games

Abstract:

Noncommutative inequalities and equalities arise in studying perfect strategies for nonlocal games. I will introduce recent results based on noncommutative Positivstellensatz and Nullstellensatz that provide algebraic characterizations of whether or not a nonlocal game has perfect quantum strategies. I also plan to discuss the algebraic reformulation of Connes’ embedding problem and a counter-example to the Nichtnegativstellensatz for polynomials in noncommuting variables.

Speaker:

Huangjun Zhu (Fudan University)

Title:

The Magic in qudit shadow estimation based on the Clifford group

Abstract:

The classical shadow estimation is a sample-efficient protocol for learning the properties of a quantum system through randomized measurements. For qubit systems, the efficiency of this approach is tied to the fact that the Clifford group forms a unitary 3-design. However, this property no longer holds for qudit systems, and it is substantially more difficult to understand the sample complexity of qudit shadow estimation. In this work, we show that qudit shadow estimation based on the Clifford group can achieve a similar performance as in qubit systems despite the crucial difference in the underlying group. Notably, the sample complexity of fidelity estimation is independent of the system size. Moreover, a single magic can significantly boost the efficiency and bridge the gap between qudit systems and qubit systems. These results may have profound implications for shadow estimation and quantum information processing based on qudits. Our work is based on a deep understanding of third moments of Clifford orbits, which is of independent interest.

Deng, Dongling (邓东灵)	Tsinghua University
Evans, David	Cardiff University
Fei, Shaoming (费少明)	Capital Normal University
Gao, Li (高力)	Wuhan University
Kye, Seung-Hyeok	Seoul National University
Li, Ke (李科)	Harbin Institute of Technology
Lin, Huaxin (林华新)	University of Oregon & SIMIS
Liu, Dong (刘东)	Tsinghua University
Liu, Weihua (刘伟华)	Zhejiang University
Liu, Jin-Peng (刘锦鹏)	Tsinghua University
Liu, Zhengwei (刘正伟)	Tsinghua University
Liu, Ziwen (刘子文)	Tsinghua University
Ming, Shuang (明爽)	BIMSA
Paris, Matteo	University of Milan
Qiu, Yanqi (邱彦奇)	Hanzhou Institute of Advanced Study, UCAS
Shao, Changpeng (邵长鹏)	Academy of Mathematics and Systems Science, CAS
Suzuki, Yuhei	Hokkaido University
Wang, Yi (王奕)	Chongqing University
Wu, Jianchao (吴健超)	Fudan University
Zhang, Xu (张旭)	Sichuan University
Zhi, Lihong (支丽红)	Academy of Mathematics and Systems Science, CAS
Zhu, Huangjun (朱黄俊)	Fudan University

The Quantum Theory and Operator Theory 2024 (QTOT2024) satellite conference, part of the International Congress of Basic Sciences, took place at the Beijing Institute of Mathematical Sciences and Applications from August 26 to August 30, 2024. During the event, twenty-two invited speakers from around the world delivered exceptional presentations. The speakers represented various countries, including the United Kingdom, Italy, Korea, and Japan.

We had 12 speakers focusing on quantum information, 3 on quantum symmetries, including quantum field theory, 5 on operator theory and operator algebra, and 2 on noncommutative analysis. The event attracted over 100 participants, who actively engaged in the discussions.

We extend our gratitude to Zhengfeng Ji from Tsinghua University, Chunlan Jiang from Hebei Normal University, Zhengwei Liu from Tsinghua University, Shunlong Luo from the Academy of Mathematics and Systems Science, CAS, and Jinsong Wu from BIMSA for bringing together such an outstanding group of speakers. We would also like to thank the quantum symmetry research group for their assistance and Hanru Jiang for maintaining the qlab website (https://qlab.bimsa.cn/events/qtot/2024/).

Special thanks to Ruihua Wang, Zhenyao Zhang and Aziza Abudula for delivering the workshop, and to Zeyin Li for coordinating the event. We would also like to thank Modi Hou and Jingxuan Peng for organizing the Mutianyu Great Wall climb, as well as Fan Liu for recording all the talks.