Quantum Theory and Operator Theory

Welcome to the Quantum Theory and Operator Theory satellite conference (QTOT) of the International Congress of Basic Science, taking place in the beautiful city of Beijing from July 10th to 14th, 2023. This emerging event brings together leading experts and researchers from diverse backgrounds, fostering the exchange of innovative ideas, breakthroughs, and research findings in the areas of quantum and operator theories. As two of the most fundamental pillars of modern physics and mathematics, this interdisciplinary conference provides an unparalleled opportunity to explore their intersections, applications, and impact on our understanding of the universe.

Quantum theory, the cornerstone of modern physics, has revolutionized our comprehension of the atomic and subatomic worlds. It describes the strange and counterintuitive behavior of particles at the quantum scale, explaining phenomena such as superposition, entanglement, and wave-particle duality. Operator theory, on the other hand, is a branch of mathematics that deals with the study of linear operators on function spaces. It has played a crucial role in the development of quantum mechanics, as well as various other fields such as functional analysis, differential equations, and mathematical physics.

The conference will feature a diverse array of presentations, panel discussions, and workshops led by esteemed experts from around the globe. Attendees will have the opportunity to engage with the latest research findings, theoretical advancements, and computational methods in quantum theory and operator theory, as well as their applications in other disciplines. The event promises to spark stimulating conversations and collaborations that will propel our understanding of these complex subjects to new heights.

Apart from the academic program, the conference will also provide ample opportunities for networking and socializing. Set against the backdrop of Beijing, a city with a rich history and vibrant culture, attendees can explore iconic landmarks such as the Great Wall of China, the Forbidden City, and the Temple of Heaven, as well as immerse themselves in local arts, cuisine, and traditions. The conference organizers have meticulously planned a series of guided tours, cultural events, and receptions to ensure that participants have a memorable and enriching experience while in the city.

In summary, the International Conference on Quantum Theory and Operator Theory promises to be a landmark event in the fields of physics and mathematics. We warmly invite you to join us in Beijing and contribute your expertise to this exciting intellectual journey. Together, we will push the boundaries of knowledge and foster new connections that will shape the future of quantum and operator theories for years to come.

Hosts

Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA)

Morningside Center of Mathematics, Chinese Academy of Sciences (MCM)

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)

Local Organizers

Meng Cao (BIMSA)

Song Cheng (BIMSA)

Zhuofeng He (BIMSA)

Hanru Jiang (BIMSA)

Yilong Wang (BIMSA)

Yu Wang (BIMSA)

Administrative Organizer

Modi Hou (BIMSA)

Contact

Email: qtot@bimsa.cn

Registration Address

Zhongjian Yanqi Lakeview Hotel (北京中建雁栖湖景酒店)

Conference Venue:

A6 Lecture Hall, 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

Accommodation:

Zhongjian Yanqi Lakeview Hotel (北京中建雁栖湖景酒店)，No. 1 Yanxiu Road, Huairou, Beijing（北京市怀柔区雁栖湖雁秀路1号）.

Lunch & Dinner:

BIMSA Campus A4 Dinning Hall

Date	Lunch	Dinner
Jul. 11	12:00 ~ 13:00	17:00 ~ 18:00
Jul. 12	12:00 ~ 13:00	17:45 ~ 18:45
Jul. 13	12:00 ~ 13:00	17:45 ~ 18:45
Jul. 14	12:00 ~ 13:00	17:00 ~ 18:00

Transportation and Shuttle Bus

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 中建湖景 to the BIMSA campus, providing convenient transportation for your needs.

Date	Hotel —-> BIMSA A6	BIMSA A6 —-> Hotel
Jul. 11	8:40 ~ 9:00	18:00 ~ 18:20
Jul. 12	9:00 ~ 9:20	18:45 ~ 19:05
Jul. 13	9:00 ~ 9:20	18:45 ~ 19:05
Jul. 14	9:00 ~ 9:20	18:00 ~ 18:20

Warm Tips:

During the program, the weather in Beijing will be mainly sunny, with the highest temperature around 35 degrees Celsius. Please pay attention to sun protection.

Please pay attention to your personal and financial safety during your stay at the hotel and keep your personal belongings properly.

If you need any help during the program, please contact the relevant staff of the program team.

Jul 10, 2023

Registration

Jul 11, 2023

09:10 ~ 09:30		Opening Ceremony
09:30 ~ 10:30	Nicolai Reshetikhin	Quantum integrable systems on a classical integrable background.
Tea Break
10:45 ~ 11:45	Shuang Ming	Tensor categories and bi-colored three manifolds
Lunch
13:30 ~ 14:30	Jinwei Yang	Ribbon categories arising from vertex operator algebras
14:30 ~ 15:30	Bingzhe Hou	Analytic automorphisms, composition operators and the representation of analytic functions
Tea Break
15:45 ~ 16:45	Xin Wang	Estimate distillable entanglement and quantum capacity

Jul 12, 2023

09:30 ~ 10:30	Guihua Gong	On the classification of noncommutative spaces
Tea Break
10:45 ~ 11:45	Zheng-Cheng Gu	Classification and construction of crystalline topological superconductors and insulators in interacting fermion systems
Lunch
13:30 ~ 14:30	Bin Gui	Reflection positivity in conformal blocks
14:30 ~ 15:30	Jianchao Wu	Order zero maps and noncommutative dimensions
Tea Break
15:45 ~ 16:45	Dongsheng Wang	Universal quantum computing models and quantum resources
16:45 ~ 17:45	Xiao Yuan	Virtual quantum resource distillation

Jul 13, 2023

09:30 ~ 10:30	Feng Xu	Rigorous results about entropies in QFT
Tea Break
10:45 ~ 11:45	Dylan Thurston	Towards the quantum exceptional series
Lunch
13:30 ~ 14:30	Hang Wang	Delocalized $l^2$-Betti numbers and higher Kazhdan projections
14:30 ~ 15:30	Cupjin Huang	Randomized benchmarking beyond groups
Tea Break
15:45 ~ 16:45	Yinan Li	Combinatorial theory of matrix spaces and its applications in quantum information
16:45 ~ 17:45	Quan Chen	K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

Jul 14, 2023

09:30 ~ 10:30	Pan Zhang	qecGPT: decoding Quantum Error Correction codes with Generative Pre-trained Transformers
Tea Break
10:45 ~ 11:45	Liang Kong	Topological orders and higher categories
Lunch
13:30 ~ 14:30	Tianxiang Yue	HASM quantum machine learning
14:30 ~ 15:30	Jiehang Zhang	Quantum information with a high-connectivity processor
Tea Break
15:45 ~ 16:45	Zhaohui Wei	All pure bipartite entangled states can be semi-self-tested with only one measurement setting on each party

Speaker:

Quan Chen (Vanderbilt University (Fall 2023))

Title:

K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

Abstract:

We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C*-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on unital AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on AF-algebras.

Speaker:

Guihua Gong (University of Puerto Rico & Hebei Normal University)

Title:

On the classification of noncommutative spaces

Abstract:

C*-algebras as noncommutative spaces have deep application in differential geometry and mathematical physics. I this talk, I will brief discuss the basic ideas in non-commutative geometry and present my joint work with Huaxin Lin (and part of them are also with George Elliott and Zhuang Niu) on the classification of simple separable C*-algebras with finite nuclear dimensions.

Speaker:

Zheng-Cheng Gu (Chinese University of Hong Kong)

Title:

Classification and construction of crystalline topological superconductors and insulators in interacting fermion systems

Abstract:

The construction and classication of crystalline symmetry protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Crystalline SPT phases are not only of conceptual importance, but also provide us great opportunities towards experimental realization since space group symmetries naturally exist for any realistic material. In this talk, I will discuss how to construct and classify crystalline topological superconductors (TSC) and topological insulators (TI) in interacting fermion systems. I will also discuss the relationship between internal symmetry protected SPT phases and crystalline symmetry protected SPT Phases.

Speaker:

Bin Gui (Tsinghua University)

Title:

Reflection positivity in conformal blocks

Abstract:

Conformal blocks associated to a vertex operator algebras (VOA) V and a Riemann surface are chiral halves of 2d conformal field theory in the sense of Segal. It is the key ingredient of the tensor category of VOA modules Mod(V). Assume that the VOA V and its modules are unitary. Then on the space of conformal blocks one can define (algebraically) a non-degenerate Hermitian product. If this Hermitian product is positive definite (which is expected to be always true) then Mod(V) is a unitary modular tensor category. In this talk, I will explain how to understand this Hermitian product geometrically in terms of the complex conjugate structures of Riemann surfaces. This geometric understanding will help us prove the positive definiteness for certain examples that cannot be proved using other methods.

Speaker:

Bingzhe Hou (Jilin University)

Title:

Analytic automorphisms, composition operators and the representation of analytic functions

Abstract:

In this talk, we focus on the weighted Hardy spaces of polynomial growth, which cover the classical Hardy space, weighted Bergman spaces, weighted Dirichlet spaces and much broader. We discuss the boundedness of the composition operators with symbols of analytic automorphisms of unit open disk (finite Blaschke product and analytic functions on the unit closed disk) acting on weighted Hardy spaces of polynomial growth. Moreover, we study the norms, spectra and (semi-)Fredholmness of composition operators induced by disc automorphisms. Furthermore, the Jordan decomposition theorem and similar classification for the representation of analytic functions on the unit closed disk as multiplication operators are obtained.

Speaker:

Cupjin Huang (Quantum Laboratory, DAMO Academy (DAMO-QL))

Title:

Randomized benchmarking beyond groups

Abstract:

Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations but this can be problematic. For example, Clifford circuits need up to O(n^2) gates and thus Clifford RB cannot scale to larger devices. Attempts to remedy this include new schemes such as linear cross-entropy benchmarking (XEB), cycle benchmarking, and nonuniform RB but they do not fall within the group-based RB framework. In this work, we formulate the universal randomized benchmarking (URB) framework, which does away with the group structure and also replaces the recovery-gate-plus-measurement component with a general “post-processing” positive operator-valued measurement (POVM). Not only does this framework cover most of the existing benchmarking schemes but it also gives the language for and helps inspire the formulation of new schemes. We specifically consider a class of URB schemes called twirling schemes. For twirling schemes, the post-processing POVM approximately factorizes into an intermediate channel, inverting maps, and a final measurement. This leads us to study the twirling map corresponding to the gate ensemble specified by the scheme. We prove that if this twirling map is strictly within unit distance of the Haar twirling map in induced diamond norm, the probability of measurement as a function of gate length is a single exponential decay up to small error terms. The core technical tool we use is the matrix perturbation theory of linear operators on quantum channels. As an application, we investigate the theoretical foundation of the linear XEB, and propose a variant using Clifford circuits, that allows efficient classical post-processing and supports holistic benchmarking of over 1,000 qubits.

Speaker:

Liang Kong (SIQSE, Southern University of Science and Technology)

Title:

Topological orders and higher categories

Abstract:

I will explain why topological defects in an (\(n+1\))-D topological order form a fusion n-category with a trivial \(E_1\)-center. I will present some basic results on separable \(n\)-categories, \({ E_m}\)-monoidal fusion \(n\)-categories, \(E_n\)-centers and their physical applications obtained in arXiv:2011.02859 and arXiv:2107.03858.

Speaker:

Yinan Li (Wuhan University)

Title:

Combinatorial theory of matrix spaces and its applications in quantum information

Abstract:

I will explain why topological defects in an n+1D topological order form a fusion n-category with a trivial E_1-center. I will present some basic results on separable n-categories, \(E_m\)-monoidal fusion n-categories, \(E_n\)-centers and their physical applications obtained in arXiv:2011.02859 and arXiv:2107.03858.

Speaker:

Shuang Ming (Yanqi Lake Beijing Institute of Mathematical Sciences and Applications(BIMSA))

Title:

Tensor categories and bi-colored three manifolds

Abstract:

In this talk, I will introduce a partition function defined on bi-colored three-manifolds decorated by tensor diagrams from a spherical fusion category C. This partition function yields three-manifold invariants and three-dimensional topological quantum field theories (TQFTs). I will discuss how well-known invariants and TQFTs, such as Turaev-Viro theory and Reshetikhin-Turaev theory, can be naturally embedded within our framework. Furthermore, our bi-colored theory provides topological interpretations for fundamental concepts in tensor categories, including the Drinfeld center and Frobenius-Schur indicators.

Speaker:

Nicolai Reshetikhin (Tsinghua University & BIMSA)

Title:

Quantum integrable systems on a classical integrable background.

Abstract:

The talk will be focused on examples and some general features of Hybrid quantum-classical integrable systems. In this systems classical inferable dynamics, commuting flows is lifted to a quantum “fibers” resulting in a geometric structure similar to a flat connection on a vector bundle.

Speaker:

Dylan Thurston (Indiana University)

Title:

Towards the quantum exceptional series

Abstract:

Each of the two classical series of Lie groups, SL(n) and OSp(n), gives a two-parameter quantum invariant of knots (and suitable graphs). There is also a conjectural third classical series, the exceptional series, containing all the exceptional Lie groups (and thus having only finitely many points). We look at the quantum version of this third series, and show that it satisfies a simple quantum Jacobi relation, giving a (conjectural) skein-theoretic description for a third two-parameter quantum exceptional polynomial invariant. We can unconditionally use these to compute previously out-of-reach knot polynomials (for particular exceptional groups) for all knots with 12 or fewer crossings.

Speaker:

Dongsheng Wang (Institute of Theoretical Physics, Chinese Academy of Sciences)

Title:

Universal quantum computing models and quantum resources

Abstract:

Unravelling the source of quantum computing power has been a major goal in the field of quantum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require investigation. The so-called universal quantum computing model (UQCM), e.g., the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum computers etc. In this work, we combine the study of UQCM together with QRT. We find, on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among resources and classify them.

We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum of UQCMs and the corresponding universal resources. Depending on a hierarchical structure of resource theories, we find models can be classified into families. In this talk, I will present four natural families of UQCMs: the amplitude family, the quasi-probability family, the Hamiltonian family, and the evolution family. They include some well known models, like the measurement-based model and adiabatic model, and also inspire new models such as the contextual model and von Neumann architecture we introduce. Each family contains at least a triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture to investigate resources and design models. It also provides a rigorous framework to resolve puzzles, such as the role of entanglement vs. interference, and unravel resource-theoretic features of quantum algorithms.

See arXiv:2303.03715, arXiv:2304.03460.

Speaker:

Hang Wang (East China Normal University)

Title:

Delocalized \(l^2\)-Betti numbers and higher Kazhdan projections

Abstract:

Higher Kazhdan projections were introduced by Li-Nowak-Pooya, associated to higher degree group cohomology, in comparision to the classical Kazhdan projection appeared in the degree zero cohomology. In the joint work with Sanaz Pooya, we explicitly describe the K-theory class of the higher Kazhdan projections of certain free product groups and their Cartesian products. The explicit description enables us to obtain new calculations of Lott’s delocalized l^2-Betti numbers, which are generalizations of the classical Betti numbers and l^2-Betti numbers. In particular, we establish the first non-vanishing results for infinite groups.

Speaker:

Xin Wang (Hong Kong University of Science and Technology (Guangzhou))

Title:

Estimate distillable entanglement and quantum capacity

Abstract:

Entanglement distillation is crucial in quantum information processing. But it remains challenging to estimate the distillable entanglement and its closely related essential quantity, the quantum capacity of a noisy quantum channel. This work proposes methods for evaluating these two central quantities in quantum Shannon theory. We also apply our methods to investigate purifying the maximally entangled states under practical noises and notably establish improvements. Our bounds also offer useful benchmarks for evaluating the quantum capacities of basic quantum channels of interest, including the Pauli channels and the random mixed unitary channels.

Speaker:

Zhaohui Wei (Tsinghua University)

Title:

All pure bipartite entangled states can be semi-self-tested with only one measurement setting on each party

Abstract:

It has been known that all bipartite pure quantum state can be self-tested, i.e., any such state can be certified completely by first measuring both subsystems of this state by proper local quantum measurements and then observing that the correlation between the choices of measurements and their outcomes satisfies certain condition, where the conclusion can be reliable even if the involved quantum measurements are untrusted. In such protocols, quantum nonlocality is crucial and plays a central role, which means that each party has to conduct at least two different quantum measurements to produce a desirable correlation. Here, we prove that when the underlying Hilbert space dimension is known beforehand, any d x d bipartite pure state can be pinned down completely (up to local transformations) by a certain correlation generated by only one measurement setting on each subsystem, where each measurement produces only 3d outcomes. In our protocol, there is no any quantum nonlocality involved.

Speaker:

Jianchao Wu (Fudan University)

Title:

Order zero maps and noncommutative dimensions

Abstract:

The standard notion of morphisms between operator algebras is (*-)homomorphisms. A more general notion called c.p.c. order zero maps was introduced by W. Winter and J. Zacharias. Extensive theories have been built on top of this notion, including various dimensions for C*-algebras and C*-dynamical systems (even with quantum group actions). It has played a pivotal role in the classification program of C*-algebras and is seeing more applications to C*-dynamical systems and quantum principal bundles. I will survey some of the ideas and results around this notion.

Speaker:

Feng Xu (University of Califonia, Riverside)

Title:

Rigorous results about entropies in QFT

Abstract:

I will discuss some recent results about relative entropies in QFT, with particular emphasis on the singular limits of such entropies.

Speaker:

Jinwei Yang ( Shanghai Jiao Tong University)

Title:

Ribbon categories arising from vertex operator algebras

Abstract:

In this talk, we will give a sufficient condition for the existence of tensor category structure on the representation categories of vertex operator algebras, and consequently provide a few examples of tensor categories. We will also discuss how to prove rigidity of such tensor categories.

Speaker:

Xiao Yuan (Peking University)

Title:

Virtual quantum resource distillation

Abstract:

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted “free” operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call virtual resource distillation, provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.

Speaker:

Tianxiang Yue (Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences)

Title:

HASM quantum machine learning

Abstract:

Moore’s law states that the number of transistors on a microprocessor chip will double every two years or so. It was worldwide acknowledged that Moore’s law was nearing its end. In other words, the miniaturization of transistors has been an essential progress in computers mainly to speed up their computation. Such miniaturization has approached its fundamental limits. Fortunately, the development of quantum computing brings light to solve this problem. The method for high accuracy surface modelling (HASM) is an approach to reinforced machine learning. It can be transformed into a large sparse linear system and combined with the Harrow-Hassidim-Lloyd (HHL) quantum algorithm, by which a HASM-HHL algorithm was developed for quantum machine learning. HASM has been successfully operated on classical computers to conduct spatial interpolation, upscaling, downscaling, data fusion and model-data assimilation of eco-environmental surfaces, such as digital terrain models, climate change, carbon stocks, CO2 concentrations, soil properties, COVID-19, species diversity, and ecosystems. In all of these applications, HASM has produced more accurate results than other methods, thereby foreshadowing the advantages that would likely follow the adoption and use of HASM-HHL for such applications. Ideally, HASM-HHL can maintain the high accuracy of classical algorithms, and meanwhile it can achieve exponential speedup compared to the classical algorithms, which has been demonstrated by several case-studies in Poyang Lake Basin.

Speaker:

Jiehang Zhang (University of Science and Technology of China)

Title:

Quantum information with a high-connectivity processor

Abstract:

Trapped atomic ions is among the leading platforms in building a scalable quantum computer. By encoding naturally identical qubits in the atoms, we entangle them by a controlled laser drive. We show how to tailor the inter-qubit couplings to perform quantum simulations of non-equilibrium physics. Combining global interactions and individual single qubit addressing, a universal quantum computer can be realized.

Building upon these tools, we show how numerical optimizations can aid the design of qubit couplings in higher dimensions, even when the physical system is one-dimensional. We discuss further potentials of building a graph-model based quantum computer.

Speaker:

Pan Zhang (Institute of Theoretical Physics, Chinese Academy of Sciences)

Title:

qecGPT: decoding Quantum Error Correction codes with Generative Pre-trained Transformers

Abstract:

In this talk, Pan Zhang will introduce a general framework for decoding quantum error correction codes using generative modeling. The model learns the joint probability of logical operators of multiple logical qubits and all syndromes using autoregressive neural networks, specifically with casual transformers. The training is in an unsupervised way without requiring any labeled training data, so is termed as pre-training, after which, the model offers fast computation of the likelihood of the logical operators, and directly generates the most-likely logical operators for all logical qubits in the manner of maximum likelihood decoding, for all syndromes. Based on the pre-trained model, Pan Zhang will futher introduce refinement to compute a more accurate likelihood of logical operators for a given syndrome by using reinforcement learning and by directly sampling the stabilizer operators. The framework is general, it applies to arbitrary error models and applies in the same way to quantum codes with different topologies such as surface code and general quantum LDPC code. It also utilizes the parallelization power of GPUs to decode a large number of syndromes simultaneously. The approach sheds like on the efficient decoding of quantum error correction codes using generative artificial intelligence and modern computational power.