Beijing Institute of Mathematical Sciences and Applications

25th August, 2025

09:40-10:30 Chongying Dong

Symmetries beyond group actions

I will discuss our recent investigation into the generalized symmetries of algebras in modular tensor categories, based on a joint work with Siu-Hung NG, Li Ren and Feng Xu.

10:50-11:40 Zhengwei Liu

Construct Planar Algebras by Classical and Quantum Computers

We propose a new program to effectively construct planar algebras and tensor categories by classical and quantum computer. Several brand new examples are discovered.

13:30-14:20 Xiongfeng Ma

Measurement-Assisted Quantum Circuits: Circuit Complexity and Entanglement Generation

Measurement-assisted quantum circuits offer a powerful approach to quantum computing by “trading measurement and space for circuit depth,” a key advantage for mitigating noise in shallow architectures. Yet, their resource requirements and fundamental limits has remained elusive, hindering systematic optimization. This talk introduces a unified embedded complexity framework to characterize such circuits. We prove that for states generated by general measurement-assisted circuits, embedded complexity is lower-bounded by circuit volume, extending the linear growth theorem and showing that intermediate measurements and ancillas cannot drastically reduce the cost of generic state preparation. This delineates the intrinsic limits of measurement-assisted protocols and informs applications such as random circuit sampling and quantum shadow tomography. For specific targets, we present a variational optimization scheme using parameterized measurements and efficient gradient estimation to avoid “barren plateaus,” enabling high-fidelity preparation of long-range entangled states at shallow depths and outperforming conventional circuits. These results map the capability boundaries and implementation pathways of measurement-assisted circuits, providing new foundations for fault-tolerant quantum computing and resource optimization. This work is published in [PRL 134, 170601 (2025); arXiv:2408.16602].

14:30-15:20 Li Ren

Reverse categories and reconstruction program

The reconstruction program posits that every modular category can be realized as a module category of a rational vertex operator algebra. In category theory, each modular category has an associated reverse category. In this talk, I will explore how to realize the reverse of a modular category through the framework of vertex operator algebras.

15:50-16:40 Kun Fang

Generalized quantum asymptotic equipartition and its applications

We establish a generalized quantum asymptotic equipartition property (AEP) beyond the i.i.d. framework where the random samples are drawn from two sets of quantum states. In particular, under suitable assumptions on the sets, we prove that all operationally relevant divergences converge to the quantum relative entropy between the sets. More specifically, both the smoothed min- and max-relative entropy approach the regularized relative entropy between the sets. Notably, the asymptotic limit has explicit convergence guarantees and can be efficiently estimated through convex optimization programs, despite the regularization, provided that the sets have efficient descriptions. We give four applications of this result: <ul><li>(i) The generalized AEP directly implies a new generalized quantum Stein’s lemma for conducting quantum hypothesis testing between two sets of quantum states. </li><li>(ii) We introduce a quantum version of adversarial hypothesis testing where the tester plays against an adversary who possesses internal quantum memory and controls the quantum device and show that the optimal error exponent is precisely characterized by a new notion of quantum channel divergence, named the minimum output channel divergence. </li><li>(iii) We derive a relative entropy accumulation theorem stating that the smoothed min-relative entropy between two sequential processes of quantum channels can be lower bounded by the sum of the regularized minimum output channel divergences. </li><li>(iv) We apply our generalized AEP to quantum resource theories and provide improved and efficient bounds for entanglement distillation, magic state distillation, and the entanglement cost of quantum states and channels. At a technical level, we establish new additivity and chain rule properties for the measured relative entropy which we expect will have more applications.</li></ul>

16:50-17:40 Zishuo Zhao

Bimodule Markov semigroups

This talk introduces bimodule quantum Markov semigroups, which describe the dynamics of symmetric quantum systems within the framework of quantum Fourier analysis. The symmetry is mathematically encoded by a finite index inclusion of von Neumann algebras. We generalize the classical notions of equilibrium and detailed balance, revealing new structures. When this condition is met, the fixed points of the channel form a von Neumann subalgebra. Furthermore, we demonstrate that the evolution of densities under these semigroups acts as a gradient flow for relative entropy with respect to a “hidden density” derived from the system’s underlying symmetries. This perspective allows for the establishment of several key functional inequalities in the bimodule setting, including the Poincaré, logarithmic Sobolev, and Talagrand inequalities.

26th August, 2025

09:30-10:20 Naihuan Jing

Local unitary equivalence and hypermatrix algebra

Entanglement is a key phenomenon in quantum theory and is invariant under local unitary (LOU) transformations. We will discuss the correspondence of LOU and simultaneous orthogonal equivalence for quantum bipartite states, and formulate a complete set of LOU invariants for tripartite states using techniques of hypermatrix algebra and Futorny-Horn-Sergeichuk’s Specht identities for quiver equivalence. We will also discuss possible generalization to multipartite quantum states.

10:50-11:40 You Zhou

Robust and efficient estimation of global quantum properties under realistic noise

Measuring global quantum properties—such as the fidelity to complex multipartite states—is both an essential and experimentally challenging task. Classical shadow estimation offers favorable sample complexity, but typically relies on many-qubit circuits that are difficult to realize on current platforms. We propose the robust phase shadow scheme, a measurement framework based on random circuits with controlled-$Z$ as the unique entangling gate type, tailored to architectures such as trapped ions and neutral atoms. Leveraging tensor diagrammatic reasoning, we rigorously analyze the induced circuit ensemble and show that phase shadows match the performance of full Clifford-based ones. Importantly, our approach supports a noise-robust extension via purely classical post-processing, enabling reliable estimation under realistic, gate-dependent noise where existing techniques often fail. Additionally, by exploiting structural properties of random stabilizer states, we design an efficient post-processing algorithm that resolves a key computational bottleneck in previous shadow protocols. Our results enhance the practicality of shadow-based techniques, providing a robust and scalable route for estimating global properties in noisy quantum systems. (arxiv: 2507.13237)

13:30-14:20 Li Gao

Convex Splitting: tight analysis and multipartite case

Convex splitting is a powerful tool in quantum information that has been used in many information-processing protocols such as quantum state redistribution and quantum channel coding. In this talk, we will present some near optimal one-shot estimates for convex splitting which yields matched second-order asymptotics as well as error and strong converse exponent. Moreover, using an interesting decomposition, our error exponent estimate also applies to multipartite case, which leads to the resolution of Quantum Broadcast Channel Simulation. This talk is based on joint works with Hao-Chung Cheng and Mario Berta.

14:30-15:20 Dong An

Quantum algorithms for matrix eigenvalue transformation

Quantum computers are expected to simulate unitary dynamics (i.e., Hamiltonian simulation) much faster than classical computers. However, most scientific computing applications involve non-unitary eigenvalue transformations. In this talk, we will discuss quantum algorithms for implementing those non-unitary eigenvalue transformations. The first algorithm is based on the Laplace transform and a recently proposed linear combination of Hamiltonian simulation formalism, and the second algorithm is based on a contour integral formalism. We will present several applications of the algorithms, including matrix inverses and solving differential equations of different forms.

15:50-16:40 Lingyan Hung

A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation in SymTO/SymTFT

In this talk, we introduce a “CFT factory”: a novel algorithm of methodically generating 2D lattice models that would flow to 2D conformal fixed points in the infrared. These 2D models are realised by giving critical boundary conditions to 3D topological orders (symTOs/symTFTs) described by string-net models, often called the strange correlators. We engineer these critical boundary conditions by introducing a commensurate amount of non-commuting anyon condensates. The non-invertible symmetries preserved at the critical point can be controlled by studying a novel ``refined condensation tree’’. Our structured method generates an infinite family of critical lattice models, including the A-series minimal models, and uncovers previously unknown critical points. Notably, we find at least three novel critical points ($c\approx 1.3$, $1.8$ and $2.5$ respectively) preserving the Haagerup symmetries, in addition to recovering previously reported ones. The condensation tree, together with a generalised Kramers-Wannier duality, predicts precisely large swathes of phase boundaries, fixes almost completely the global phase diagram, and sieves out second order phase transitions. This is not only illustrated in well-known examples (such as the 8-vertex model related to the $A_5$ category) but also further verified with precision numerics, using our improved (non-invertible) symmetry-preserving tensor-network RG, in novel examples involving the Haagerup symmetries. We show that critical couplings can be precisely encoded in the categorical data (Frobenius algebras and quantum dimensions in unitary fusion categories), thus establishing a powerful, systematic route to discovering and potentially classifying new conformal field theories

16:50-17:40 Ningfeng Wang

Quon classical simulation: a new way to understand quantum advantage

We establish Quon Classical Simulation (QCS), answering a long standing open question on unifying efficient classical simulations of both Clifford and Matchgates quantum circuits. QCS unifies various methods on classical simulations of hybrid-Clifford-Matchgate quantum circuits and tensor networks, based on the 3D Quon picture language which is a topological quantum field theory. It provides new insights to explore quantum advantage. This is joint work with Zixuan Feng, Zhengwei Liu and Fan Lu. https://arxiv.org/abs/2505.07804v2

27th August, 2025

09:30-10:20 Davide Girolami

Crossing the Entanglement Frontier

In this talk, I discuss recent results on theoretically and experimentally quantifying Entanglement. In particular, newfound quantum laws dictate that classical information (the outcome of a measurement) can freely spread into the Universe, while broadcasting quantum information (the wavefunction of a system) is subject to limitations, as local Entanglement in systems of many particles is inevitably suppressed. Refs:<ul><li>Npj Quantum Information 10 (1), 60 (2024);</li><li>Physical review letters 129 (1), 010401 (2022);</li><li>Physical review letters 128 (1), 010401 (2022)</li></ul>

10:50-11:40 Nan Li

Quantum coherence and basis-dependent correlations

Since both coherence and quantum correlations arise from the superposition principle and can be regarded as resources in quantum information tasks, it is of significance to investigate the interplay between them from different perspectives. In this work we focus on the basis-dependent correlations in a bipartite state defined by the coherence difference between global state and local state relative to a local basis and characterize bipartite states with vanishing basis-dependent correlations. Using the relative entropy of coherence, the structure of such states has been determined by Yadin et al. [Phys. Rev. X 6, 041028 (2016)], which we call block-diagonal product states here. We demonstrate that the set of block-diagonal product states can also be characterized by the property of possessing vanishing basis-dependent correlations using the coherence measure based on quantum Fisher information. In this sense, bipartite states with vanishing basis-dependent correlations can be characterized by the property of possessing no correlations contributing to the enhancement of parameter estimation precision, and thus are of metrological meanings. As a by-product of this result, we describe the structure of quantum ensembles saturating the convexity inequality in the resource theory of coherence using the coherence measure based on quantum Fisher information, which may be of independent interest.

13:30-14:20 Changpeng Shao

Quantum singular value transformation without block encodings: Near-optimal complexity with minimal ancilla

We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block encoding, incurring an intrinsic $O(\log L)$ ancilla overhead and circuit depth $\tilde(O)()Ld\lambda$ for polynomial transformations of a Hamiltonian $H=\sum^L_{k=1}H_k$, where $d$ is the polynomial degree and $\lambda=\sum_k\Vert H_k\Vert$. We introduce a simple yet powerful approach that utilizes only basic Hamiltonian simulation techniques, namely, Trotter methods, to: (i) eliminate the need for block encoding, (ii) reduce the ancilla overhead to only a single qubit, and (iii) still maintain near-optimal complexity. Our method achieves a circuit depth of $\tilde{O}(L(d\lambda_{comm})^{1+o(1)})$, without requiring any complicated multi-qubit controlled gates. Moreover, $\lambda_{comm}$ depends on the nested commutators of the terms of $H$ and can be substantially smaller than $\lambda$ for many physically relevant Hamiltonians, a feature absent in standard QSVT. To achieve these results, we make use of Richardson extrapolation in a novel way, systematically eliminating errors in any interleaved sequence of arbitrary unitaries and Hamiltonian evolution operators, thereby establishing a general framework that encompasses QSVT but is more broadly applicable. As applications, we develop end-to-end quantum algorithms for solving linear systems and estimating ground state properties of Hamiltonians, both achieving near-optimal complexity without relying on oracular access. Overall, our results establish a new framework for quantum algorithms, significantly reducing hardware overhead while maintaining near-optimal performance, with implications for both near-term and fault-tolerant quantum computing.

14:30-15:20 Yukai Wu

Quantum simulation and quantum error correction with two-dimensional ion crystals

Ion trap is one of the leading physical platforms for quantum information processing, with long coherence time, high quantum-gate fidelity, and long-range qubit connectivity. Recently, two-dimensional (2D) ion crystals have become a promising approach to scale up the ionic qubit number. In this talk, I will introduce our recent progress on quantum simulation and quantum error correction with 2D ion crystals. To utilize the phonon-mediated long-range interaction between the ions for quantitative quantum simulation tasks, we develop an efficient and precise scheme to learn the all-to-all-connected Ising model Hamiltonian through the experimentally available global laser and microwave manipulation together with single-shot measurement of the ions, and demonstrate this scheme for up to 300 ionic qubits. As for quantum error correction, we analyze the effect of crosstalk errors between parallel entangling gates due to this long-range interaction, and optimize the parallelism level to balance the crosstalk error and the idling error during the execution of the gates. We further examine the spatial dependence of the crosstalk error, and show that a logical error rate below $10^{-10}$ can be achieved in different parameter regimes by increasing the code distance.

15:50-16:40 Xiaofei Qi

Entanglement negativity for bipartite fermionic systems

Quantum entanglement plays a fundamental and important role in quantum information theory. In this talk, we discuss the behavior of physical positive linear maps in fermionic systems, and then propose the phase partial transpose and the phase entanglement negativity. We prove that the phase entanglement negativity is an entanglement monotone.

16:50-17:40 Fuchuan Wei

Long-range nonstabilizerness from quantum codes, orders, and correlations

We investigate long-range magic (LRM), defined as nonstabilizerness that cannot be (approximately) erased by shallow local unitary circuits. In doing so, we prove a robust generalization of the Bravyi-König theorem. By establishing connections to the theory of fault-tolerant logical gates on quantum error-correcting codes, we show that certain families of topological stabilizer code states exhibit LRM. Then, we show that all ground states of topological orders that cannot be realized by topological stabilizer codes, such as Fibonacci topological order, exhibit LRM, which yields a “no lowest-energy trivial magic” result. Building on our considerations of LRM, we discuss the classicality of short-range magic from e.g. preparation and learning perspectives, and put forward a “no low-energy trivial magic” (NLTM) conjecture that has key motivation in the quantum PCP context. Our study leverages and sheds new light on the interplay between quantum resources, error correction and fault tolerance, complexity theory, and many-body physics.

28th August, 2025

09:30-10:20 Ke Li

From Operator Space to Quantum Rényi Information: Additivity and Operational Interpretation

The connection between operator theory and quantum entropies dates back to the early days of the 20th century, when von Neumann formulated the mathematical foundation of quantum mechanics. I will talk about the recent development of this connection. From the perspective of operator space theory, we discuss the definitions and properties of the sandwiched quantum Rényi divergence and its induced information quantities. In particular, we show how tools from operator space theory help us prove the additivity of quantum Rényi information, which is crucial in establishing its operational meaning.

10:50-11:40 Yinan Li

Rigorous QROM Security Proofs for Some Post-Quantum Signature Schemes Based on Group Actions

Group action based cryptography was formally proposed in the seminal paper of Brassard and Yung (Crypto ’90) and recently further developed by Ji et al. (TCC ’19) and Alamati et al. (AsiaCrypt ’19). Based on a one-way group action, Three submissions to the NIST’s call for additional post-quantum digital signatures, such as ALTEQ and MEDS. These schemes can be shown to be secure in the quantum random oracle model (QROM) modulo certain assumptions on the group actions, thanks to the progress on the QROM security of the Fiat–Shamir transformation (Liu–Zhandry and Don et al., Crypto ’19). One approach to proving the QROM security for such group action based schemes uses the perfect unique response property introduced by Unruh (Eurocrypt ’12; AsiaCrypt ’17). In the contexts of ALTEQ and MEDS, this means that a random element does not have a non-trivial automorphism. Before this work, only computational evidence for small dimensions (Bläser et al., PQCrypto ’24; Reijnders–Samardjiska–Trimoska, Des. Codes Cryptogr. ’24) or subexponential bounds (Li–Qiao, FOCS ’17) are known. In this work, we formally prove that the average order of stabilizer groups is asymptotically trivial. As a result, when the dimension is large enough, all but an exponentially small fraction of alternating trilinear forms or matrix codes have the trivial stabilizer, confirming the assumptions for alternating trilinear forms (ALTEQ) and matrix codes (MEDS). Our approach is to examine the fixed points of the induced action of an invertible matrix over a finite field on trilinear forms.

13:30-14:20 Tian Yang

Turaev-Viro invariant from $U_qsl(2;\mathbb{R})$

We define a family of Turaev-Viro type invariants of hyperbolic 3-manifolds with totally geodesic boundary from the 6j-symbols of the modular double of $U_q sl(2;\mathbb{R})$ and prove that these invariants decay exponentially with the rate the hyperbolic volume of the manifolds and with the 1-loop term the adjoint twisted Reidemeister torsion of the double of the manifolds. This is a joint work with Tianyue Liu, Shuang Ming, Xin Sun and Baojun Wu.

14:30-15:20 Qi Zhao

Quantum entanglement accelerates quantum simulation

Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In our recent work [Nature Physics 25, QIP 2025], we investigate the relationship between quantum entanglement and quantum simulation, showing that product-formula approximations can perform better for entangled systems, tending to the average-performance [PRL 129 (27), 270502, QIP22 talk]. We establish a tighter upper bound for algorithmic error in terms of entanglement entropy and develop an adaptive simulation algorithm incorporating measurement gadgets to estimate the algorithmic error. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum simulation algorithms.

15:50-16:40 Penghui Yao

Nonlocal Games and Self-tests in the Presence of Noise

Self-tests are a fundamental class of nonlocal games, which allow one to uniquely determine the underlying quantum state and measurement operators used by the players, based solely on their observed input-output correlations. Motivated by the limitations of current quantum devices, we study self-testing in the high-noise regime, where the two players are restricted to sharing many copies of a noisy entangled state with an arbitrary constant noise rate. In this setting, many existing self-tests fail to certify any nontrivial structure. We first characterize the maximal winning probabilities of the CHSH game, the Magic Square game, and the 2-out-of-$n$ CHSH game as functions of the noise rate, under the assumption that players use traceless binary observables. These results enable the construction of device-independent protocols for estimating the noise rate. Building on this analysis, we show that these three games—together with an additional test enforcing the tracelessness of binary observables—can self-test one, two, and $n$ pairs of anticommuting Pauli operators, respectively. These are the first known self-tests that are robust in the high-noise regime and remain sound even when the players’ measurements are noisy. Our proofs rely on Sum-of-Squares (SoS) decompositions and Pauli analysis techniques developed in the contexts of quantum proof systems and quantum learning theory. This is a joint work with Honghao Fu, Minglong Qin and Haochen Xu.

29th August, 2025

09:30-10:20 Yuxiang Yang

Compression of many-copy and shallow-circuit states

Shallow quantum circuits feature not only computational advantage over their classical counterparts but also cutting-edge applications. Storing quantum information generated by shallow circuits is a fundamental question of both theoretical and practical importance that remained largely unexplored. In this work, we show that $N$ copies of an unknown $n-$qubit state generated by a fixed-depth circuit can be compressed into a hybrid memory of $O(n\log N)$ (qu)bits, which achieves the optimal scaling of memory cost. Our work shows that the computational complexity of resources can significantly impact the rate of quantum information processing, offering a unique and unified view of quantum Shannon theory and quantum computing in the NISQ era. Based on: Phys. Rev. Lett. 134, 010603 (2025; https://arxiv.org/abs/2404.11177)

10:50-11:40 Linghang Kong

Benchmarking fault-tolerant quantum computing hardware via QLOPS

It is widely recognized that quantum computing has profound impacts on multiple fields, including but not limited to cryptography, machine learning, materials science, etc. To run quantum algorithms, it is essential to develop scalable quantum hardware with low noise levels and to design efficient fault-tolerant quantum computing (FTQC) schemes. Currently, various FTQC schemes have been developed for different hardware platforms. However, a comprehensive framework for the analysis and evaluation of these schemes is still lacking. In this work, we propose Quantum Logical Operations Per Second (QLOPS) as a metric for assessing the performance of FTQC schemes on quantum hardware platforms. This benchmarking framework will integrate essential relevant factors, e.g., the code rates of quantum error-correcting codes, the accuracy, throughput, and latency of the decoder, and reflect the practical requirements of quantum algorithm execution. This framework will enable the identification of bottlenecks in quantum hardware, providing potential directions for their development. Moreover, our results will help establish a comparative framework for evaluating FTQC designs. As this benchmarking approach considers practical applications, it may assist in estimating the hardware resources needed to implement quantum algorithms and offers preliminary insights into potential timelines.

Beijing Institute of Mathematical Sciences and Applications (BIMSA)

Email: qtot@bimsa.cn