Shenzhen-Nagoya Workshop on Quantum Science 2024

Dates and Place

• Dates: September 19 (Thu) - 21 (Sat), 2024
• Style: Hybrid (onsite and Zoom)
• Venue: Room 509, Graduate School of Mathematics, Nagoya Univeristy (accsess)
• Organizing committee: Masahito Hayashi (Chair; CUHK-SZ, IQA, and Nagoya), Baichu Yu (SUSTech),
  Hiroaki Kanno (Nagoya), Kohtaro Kato (Nagoya), Shintarou Yanagida (Nagoya)
• Contact: shenzhennagoya2024 [at] gmail.com

Registration

For online participation, please register from Microsoft Forms.

YouTube live streaming

Talks will be streamed by YouTube.
9/19 (Thu) AM, PM; 9/20 (Fri) AM PM; 9/21 (Sat) AM, PM.

Time table

Canceled talks: F. Buscemi, H. Kanno, S. Yanagida.

Program

• 9/19 (Thu)
  • 09:30-10:10 (CST) 10:30-11:10 (JST)
    Harumichi Nishimura (Graduate School of Informatics, Nagoya University)
    Power and limitation of distributed quantum proofs slide
    Distributed quantum proofs (or dQMA: distributed quantum Merlin-Arthur proofs) were introduced by Fraigniuad, Le Gall, Nishimura, and Paz [FLNP21]. They gave efficient dQMA protocols for some problems such as the equality of the data on a network. In this talk, I report some improvements on their results and efficient dQMA protocols for other problems such as ranking verification and Hamming distance. Moreover, the first lower bound results on the proof size and communication cost are reported. The talk is based on Ref. [HKN24], a joint work with Atsuya Hasegawa and Srijita Kundu.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Yupan Liu (Graduate School of Mathematics, Nagoya University)
    Space-bounded quantum state testing and its applications slide
    We present a new complete characterization of space-bounded quantum computation, focusing on problems with one-sided error (unitary coRQL) and two-sided error (BQL) from a quantum state testing perspective. These promise problems tell whether efficiently preparable states in logarithmic qubits are far from each other concerning trace distance, quantum entropy difference, and Hilbert-Schmidt distance. Unlike the time-bounded state testing problems, we show that all space-bounded state testing problems correspond to the same class. Additionally, our algorithms on the trace distance inspire an algorithmic Holevo-Helstrom measurement, implying QSZK is in QIP(2) with a quantum linear-space honest prover. Our primary technique is a space-efficient variant of the quantum singular value transformation (QSVT), which gives a unified approach to designing space-bounded quantum algorithms. (Joint work with François Le Gall and Qisheng Wang, arXiv:2308.05079)
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Dong Yang (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Reliability Function of Classical-Quantum Channels
    We study the reliability function of general classical-quantum channels, which describes the optimal exponent of the decay of decoding error when the communication rate is below the capacity. As main result, we prove a lower bound, in terms of the quantum Renyi information in Petz's form, for the reliability function. This resolves Holevo's conjecture proposed in 2000, a long-standing open problem in quantum information theory. It turns out that the obtained lower bound matches the upper bound derived by Dalai in 2013, when the communication rate is above a critical value. Thus we have determined the reliability function in this high-rate case. Our approach relies on Renes' breakthrough made in 2022, which relates classical-quantum channel coding to that of privacy amplification, as well as our new characterization of the channel Renyi information.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Francois Le Gall (Graduate School of Mathematics, Nagoya University)
    Online Locality Meets Distributed Quantum Computing slide
    We extend the theory of locally checkable labeling problems (LCLs) from the classical LOCAL model to a number of other models that have been studied recently, including the quantum-LOCAL model, finitely-dependent processes, non-signaling model, dynamic-LOCAL model, and online-LOCAL model [e.g. STOC 2024, ICALP 2023]. First, we demonstrate the advantage that finitely-dependent processes have over the classical LOCAL model. We show that all LCL problems solvable with locality O(log n) in the LOCAL model admit a finitely-dependent distribution (with constant locality). In particular, this gives a finitely-dependent coloring for regular trees, answering an open question by Holroyd [2023]. This also introduces a new formal barrier for understanding the distributed quantum advantage: it is not possible to exclude quantum advantage for any LCL in the Θ(log n) complexity class by using non-signaling arguments. Second, we put limits on the capabilities of all of these models. To this end, we introduce a model called randomized online-LOCAL, which is strong enough to simulate e.g. SLOCAL and dynamic-LOCAL, and we show that it is also strong enough to simulate any non-signaling distribution and hence any quantum-LOCAL algorithm. We prove the following result for rooted trees: if we can solve an LCL problem with locality o(loglogn) in the randomized online-LOCAL model, we can solve it with locality O(log n) in the classical deterministic LOCAL model. Put together, these results show that in rooted trees the set of LCLs that can be solved with locality O(log n) is the same across all these models: classical deterministic and randomized LOCAL, quantum-LOCAL, non-signaling model, dynamic-LOCAL, and deterministic and randomized online-LOCAL. This talk is based on arXiv:2403.01903.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Qisheng Wang (The University of Edinburgh)
    Time-efficient quantum entropy estimator via samplizer slide
    Entropy is a measure of the randomness of a system. Estimating the entropy of a quantum state is a basic problem in quantum information. In this paper, we introduce a time-efficient quantum approach to estimating the von Neumann entropy S(ρ) and Rényi entropy S_α(ρ) of an N-dimensional quantum state ρ, given access to independent samples of ρ. Specifically, we provide the following quantum estimators. 1. A quantum estimator for S(ρ) with time complexity O~(N^2), improving the prior best time complexity O(N^6) by Acharya, Issa, Shende, and Wagner (2020) and Bavarian, Mehraba, and Wright (2016). 2. A quantum estimator for S_α(ρ) with time complexity O~(N^(4/α−2)) for 0 < α < 1 and O~(N^(4−2/α)) for α>1, improving the prior best time complexity O~(N^(6/α)) for 0 < α < 1 and O~(N^6) for α>1 by Acharya, Issa, Shende, and Wagner (2020), though at a cost of a slightly larger sample complexity. Moreover, these estimators are naturally extensible to the low-rank case. We also provide a sample lower bound Ω(max{N/ε,N^(1/α-1)/ε^(1/α)}) for estimating S_α(ρ). Technically, our method is quite different from the previous ones that are based on weak Schur sampling and Young diagrams. At the heart of our construction, is a novel tool called samplizer, which can "samplize" a quantum query algorithm to a quantum algorithm with similar behavior using only samples of quantum states; this suggests a unified framework for estimating quantum entropies. Specifically, when a quantum oracle U block-encodes a mixed quantum state ρ, any quantum query algorithm using Q queries to U can be samplized to a δ-close (in the diamond norm) quantum algorithm using Θ~(Q^2/δ) samples of ρ. Moreover, this samplization is proven to be optimal, up to a polylogarithmic factor.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Haidong Yuan (Chinese University of Hong Kong)
    Measurement incompatibility in multi-parameter quantum estimation
    The incompatibility of the optimal measurements for the estimation of different parameters constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is thus a central topic in quantum metrology. Here we generalize the measurement uncertainty relations to characterize the tradeoff relations. We demonstrate the power of the approach with a few examples.
  • 15:40-15:30 (CST) 16:40-17:30 (JST)
    Masahito Hayashi (Chinese University of Hong Kong, Shenzhen / International Quantum Academy, Shenzhen / Graduate School of Mathematics, Nagoya University)
    Asymptotic dimensional analysis on unitary representation and its application to measuring quantum relative entropy slide
    In this study, we first discuss the asymptotic analysis on the dimension of irreducible unitary representation. Using this result, we study the estimation of relative entropy $D(ρ|σ)$ when σ is known. We show that the Cramér-Rao type bound equals the relative varentropy. Our estimator attains the Cramér-Rao type bound when the dimension $d$ is fixed. It also achieves the sample complexity $O(d^2)$ when the dimension d increases. This sample complexity is optimal when σ is the completely mixed state. Also, it has time complexity $O(d^6 \polylog d)$. Our proposed estimator unifiedly works under both settings. The content is available as arXiv:2406.17299.
• 9/20 (Fri)
  • 9:30-10:10 (CST) 10:30-11:10 (JST)
    Liang Kong (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Higher Condensation Theory slide
    I will explain a unified condensation theory of topological defects of any codimensions in a topological order of any dimension based on higher categories, higher algebras and higher representations. This is a joint work with Zhi-Hao Zhang, Hao Zheng and Jia-Heng Zhao (arXiv:2403.07813)
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Kohei Yamaguchi (Graduate School of Mathematics, Nagoya University)
    Equivariant K-homology of affine Grassmannian slide
    Let $G$ be the general linear group $SL_n(C)$, and let $T$ be its maximal torus. This study focuses on the $T$-equivariant K-homology ring $K_*^T(Gr_G)$ of the affine Grassmannian $Gr_G$ of $G$. In this talk, I would like to outline two realizations of $K_*^T(Gr_G)$. One is the realization through the algebra $\hat{\Lambda}^{R(T)}_G$, which is spanned by the "double K-$k$-Schur functions" representing Schubert classes. The other is the realization through the ring of regular funations $O(Z_G)$ of the affine variety $Z_{G^\vee}$ over $T$. This talk is based on joint work with Takeshi Ikeda and Mark Shimozono.
  • 10:50-11:30 (CST) 11:50-12:30 (JST)
    Qin Li (Shenzhen Institute for Quantum Science and Engineering, SUSTech)
    Quantum Tuyman lemma in Geometric Quantization slide
    I will first recall the Tuyman lemma in geometric quantization of Kahler manifolds. Using the Fedosov quantization method on Kahler manifolds, I will explain a quantum version of Tuyman lemma, which induces a series of orthogonality relations on the Hilbert spaces. This is a joint work with Kwokwai Chan and Conan Leung.
  • 11:40-12:00 (CST) 12:40-13:00 (JST)
    Xianghang Zhang (Graduate School of Mathematics, Nagoya University)
    Twist field deformations in string field theory slide
    The background independence of string field theory states that classical solutions to string field equations of motion correspond to string backgrounds, idly spacetime with D-branes, fluxes and/or orbifolds. One example of these solutions is the exactly marginal deformations of the worldsheet CFT. We start with a marginal deformation of the twist field and solve for exact marginality perturbatively. For open strings it is a D3-D(-1) system describing a point-like Yang-Mills instanton deformed into a finite-sized one. We are also able to reproduce the ADHM constraint on the moduli. For closed strings it describes resolution of an orbifold singularity and there is no constraint on the moduli.
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Hidetoshi Awata (Graduate School of Mathematics, Nagoya University)
    Introduction to the q-deformed Virasoro algebra slide
    This is an introductory talk on the q-deformed Virasoro algebra and its representation theory. ref: arXiv:hep-th/9612233, arXiv:0910.4431, arXiv:2111.07939.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Rongge Xu (Westlake University)
    Condensable Algebras and domain walls in 2d Topological Orders slide
    We give a complete interplay between E1 condensable algebras, 2-Morita equivalent E2 condensable algebras, and lagrangian algebras in a 2d topological order. The algebraic descriptions and the domain wall descriptions can be translated back and forth. We give some physical examples including the quantum double model to illustrate these equivalences.
  • 14:50-15:30 (CST) 15:50-16:30 (JST)
    Masashi Hamanaka (Graduate School of Mathematics, Nagoya University)
    4dim WZW models and unification of integrable systems slide
    Four-dimensional Wess-Zumino-Witten (4dWZW) models are analogues of two-dimensional WZW models and describe string field theory actions of the open N=2 string theory in the four-dimensional space-time with the split signature (+,+,-,-). The equations of motion of 4d WZW models are equivalent to anti-self-dual Yang-Mills (ASDYM) equations which are, in the solit signature, reduced to various integrable equations such as KdV, Toda equations. On the other hand, 4d Chern-Simons (CS) theories give rise to various solvable models such as spin chains and principal chiral models. Furthermore, a 6dCS theory yields the 4dWZW model and 4dCS theory as a double fibration. This is considered to be a unified theory of integrable systems. In this talk we discuss the 4dWZW model and construct soliton solutions in it. We find that the multi-solitons behave as the KP-type solitons, that is, intersecting codim-one solitons (localized on three-dim hyper-planes) with phase shifts. We also propose noncommutative extension and quantization of (the unified theory of) integrable systems. This talk is based on collaboration with Shan-Chi Huang and Hiroaki Kanno (Nagoya): arXiv:2212.11800, arXiv:2408.16554
  • 15:40-16:00 (CST) 16:40-17:00 (JST)
    Zhi-Hao Zhang (BIMSA, Beijing)
    The 2-character theory of finite 2-groups slide
    The character plays an important role in the representation theory of finite groups. In this talk, I will introduce the notion of 2-character of 2-representations of a finite 2-group $\mathcal{G}$. The conjugation invariance implies that the 2-characters can be viewed as objects in the Drinfeld center $\mathfrak{Z}_1(\mathrm{Vec}_{\mathcal{G}})$. I will also introduce a topological quantum field theory (TQFT) point of view on the 2-characters and show that they are Lagrangian algebras in $\mathfrak{Z}_1(\mathrm{Vec}_{\mathcal{G}})$. If time permits, I will also discuss the orthogonality of 2-characters, which categorifies the classical orthogonality of characters. This talk is based on arXiv: 2305.18151 and 2404.01162, joint with Mo Huang and Hao Xu.
  • 16:10-16:30 (CST) 17:10-17:30 (JST)
    Hao Xu (Mathematisches Institut, Georg-August Universität Göttingen)
    Pontryagin duality for 2-groups slide
    Pontryagin duality of Abelian groups plays an important role in representation theory of groups and Fourier transforms. I would like to introduce the Pontryagin duality for symmetric 2-groups, with Mo Huang and Zhi-Hao Zhang in our recent project. We will see that very few examples of finite symmetric 2-group have Pontryagin self duality, in contrast with the fact that every finite Abelian group is Pontryagin self dual. We can also categorify the notion of Fourier transform, and use it to help us understand the general structure of representations of 2-groups.
• 9/21 (Sat)
  • 9:30-10:10 (CST) 10:30-11:10 (JST)
    Kun Fang (Chinese University of Hong Kong, Shenzhen)
    Dynamic quantum circuit compilation slide
    Quantum computing has shown tremendous promise in addressing complex computational problems, yet its practical realization is hindered by the limited availability of qubits for computation. Recent advancements in quantum hardware have introduced mid-circuit measurements and resets, enabling the reuse of measured qubits and significantly reducing the qubit requirements for executing quantum algorithms. In this work, we present a systematic study of dynamic quantum circuit compilation, a process that transforms static quantum circuits into their dynamic equivalents with a reduced qubit count through qubit-reuse. We establish the first general framework for optimizing the dynamic circuit compilation via graph manipulation. In particular, we completely characterize the optimal quantum circuit compilation using binary integer programming, provide efficient algorithms for determining whether a given quantum circuit can be reduced to a smaller circuit and present heuristic algorithms for devising dynamic compilation schemes in general. Furthermore, we conduct a thorough analysis of quantum circuits with practical relevance, offering optimal compilations for well-known quantum algorithms in quantum computation, ansatz circuits utilized in quantum machine learning, and measurement-based quantum computation crucial for quantum networking. We also perform a comparative analysis against state-of-the-art approaches, demonstrating the superior performance of our methods in both structured and random quantum circuits. Our framework lays a rigorous foundation for comprehending dynamic quantum circuit compilation via qubit-reuse, bridging the gap between theoretical quantum algorithms and their physical implementation on quantum computers with limited resources.
  • 10:20-10:40 (CST) 11:20-11:40 (JST)
    Di Yu (The University of Hong Kong)
    Symmetry-Based Quantum Circuit Mapping slide
    Quantum circuit mapping plays a vital role in the quantum circuit compilation process. It involves transforming a logical quantum circuit into a set of instructions that can be directly executed on a target quantum system. A recent advancement in this field is the introduction of a post-compilation technique called remapping. Remapping aims to adjust the initial circuit mapping to reduce errors in quantum circuits caused by system variations. In this study, we introduce a quantum circuit remapping algorithm that leverages the inherent symmetries found in quantum processors to reduce computational complexity. Our algorithm effectively identifies all topologically equivalent circuit mappings by utilizing symmetries to narrow down the search space and employing vector computation for quicker evaluation. Notably, our symmetry-based remapping algorithm exhibits a linear time complexity and is proven to be optimal. Numerical experiments were conducted to compare our approach with existing methods in the field, showcasing its superior performance on typical quantum hardware architectures.
  • 10:50-11:10 (CST) 11:50-12:10 (JST)
    Shintaro Minagawa (Graduate School of Infomatics, Nagoya University)
    Operational approaches to information and thermodynamics
    Information theory and thermodynamics are now being extended beyond classical theory into quantum theory. Along with this, the close relationship between the two has also been elucidated. The question then arises as to how far information theory and thermodynamics can be extended operationally and to what extent the close relationship between the two is universal beyond the mathematical structure of the theory. In this presentation, we would like to introduce our two approaches to these questions. In Ref. [1], we operationally extend von Neumann's thought experiment that was used to define entropy in quantum theory and discuss the conditions imposed on entropy in terms of its consistency with the second law of thermodynamics. In Ref. [2], we discuss the operational validity of the relationship between classical capacity and hypothesis testing, which Wang and Renner [Phys. Rev. Lett. 108, 200501 (2012)] provided in quantum theory.
    References
    [1] S. Minagawa, H. Arai, and F. Buscemi, Phys. Rev. Research 4, 033091, (2022).
    [2] S. Minagawa and H. Arai, Phys. Rev. A 109, 062416 (2024).
  • 11:10-11:30 (CST) 12:10-12:30 (JST)
    Duo Xu (Graduate School of Informatics, Nagoya University)
    How to Certify Deletion with Constant-Length Verification Key
    The certified deletion process involves transmitting a ciphertext and confirming its deletion via a digital certificate. In this context, the term "deletion" refers to the fact that no information-processing procedure can decipher the cyphertext if the certificate is valid. Those familiar with cryptography can recognize this type of cipher as being computationally secure before and informationally secure after deletion.
    Let $\lambda$ and $n$ be the security parameter and length of the message sent. We proposed a method for Certified Deletion that needs only $O(\lambda)$ bit of verification key, while to my knowledge, all the prior works need at least $O(\lambda n)$ bit of verification key. Imagine someone who wants to store 1GB of data on a server in a deletable manner; then the previous methods need to store 1GB of metadata, while ours do not. Our method uses PRF (short for Pseudo-random Functions) to generate certificates and its key as the verification key. Also, we conclude our result in a general form as the prior works [BK23,BKMPW23,KNY23] did. So, applying our result the same way as in the prior works gets the same applications.
    The key's length concerns storage costs and key leakage risks, and we are the first to attempt to reduce that. General ways to realize Certified Deletion are known [BK23, BKMPW23] and our result can be seen as an essential adaption to improve efficiency in practice.
    [BK23] J. Bartusek and D. Khurana, “Cryptography with certified deletion,” in Advances in Cryptography - CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023. Springer, 2023, pp. 192–
    [BKM+23] J. Bartusek, D. Khurana, G. Malavolta, A. Poremba, and M. Walter, “Weakening assumptions for publicly-verifiable deletion,” in Theory of Cryptography - 21st International Conference, TCC 2023. Springer, 2023, pp. 183-19
    [KNY23] F. Kitagawa, R. Nishimaki, and T. Yamakawa, “Publicly verifiable deletion from minimal assumptions,” in Theory of Cryptography - 21st International Conference, TCC 2023. Springer, 2023, pp. 228–245
  • 13:30-14:10 (CST) 14:30-15:10 (JST)
    Kohtaro Kato (Graduate School of Infomatics, Nagoya University)
    Exact renormalization flow for matrix product density operators slide
    Matrix Product Density Operators (MPDO) is a class of one-dimensional (1D) tensor network typically used to describe thermal states and steady states of dissipative dynamics. MPDO is a generalization of Matrix Product States (MPS), which can describe 1D pure states efficiently. MPS is known to be connected to 1D gapped ground states, and its classification is done by studying the fixed points of exact real-space renormalization flow. In this talk, we study exact renormalization flow for MPDO to characterize the descriptive capability. We find that unlike MPS, MPDO does not admit exact renormalization flows in general. We then analyze MPDO with a well-defined renormalization flow and show that these MPDO can be characterized by some kind of non-invertible symmetries.
  • 14:20-14:40 (CST) 15:20-15:40 (JST)
    Teruaki Nagasawa (Graduate School of Infomatics, Nagoya University)
    On the generic increase of observational entropy in isolated systems slide
    The concept of observational entropy, which unifies various forms of entropy, including Boltzmann's, Gibbs's, von Neumann's macroscopic entropy, and the diagonal entropy, has recently been proposed as a pivotal element in a contemporary formulation of statistical mechanics. In this study, we employ algebraic techniques derived from Petz's theory of statistical sufficiency and a Levy-type concentration bound to demonstrate rigorous theorems. These theorems illustrate how the observational entropy of a system undergoing a unitary evolution chosen at random tends to increase with overwhelming probability and to reach its maximum very quickly. We demonstrate that for any observation that is sufficiently coarse with respect to the size of the system, the random evolution renders the system's state practically indistinguishable from the uniform distribution (i.e., maximally mixed) with a probability approaching one as the system size increases. This is true regardless of the initial state of the system, whether pure or mixed. The same conclusion is applicable not only to random evolutions sampled according to the unitarily invariant Haar distribution, but also to approximate 2-designs, which are regarded as a more physically reasonable means of modelling random evolutions.
• Canceled talks
  • Francesco Buscemi (Graduate School of Infomatics, Nagoya University)
    Squashed information backflows in non-Markovian quantum stochastic processes slide
    It is well known that convex combinations of Markov processes typically result in non-Markov ones. In this talk I will review some notions of (non-)Markovianity for quantum stochastic processes focusing in particular on a recent proposal to quantify information back-flows after classical memories have been suitably squashed out. Such a "squashed" non-Markovianity, besides suggesting a notion of "genuine" or "causal" information revivals, is also able to resolve the problem of non-convexity, thus clarifying the role of non-Markovianity as a resource. The possibility of extending the same intuition to other non-convex resource theories is discussed.
  • Hioraki Kanno (Graduate School of Mathematics, Nagoya University)
    Introduction to the tetrahedron equation slide
    The Yang-Baxter equation is one of the most fundamental equations in the theory of 2D integrable lattice models. It also plays an important role in the construction of quantum invariants of knots and links. In my talk I will review the tetrahedron equation as a 3D generalization of the Yang-Baxter equation. I also explain how to obtain solutions to the tetrahedron equation from the Fock representation of the oscillator algebra. If time allows, I will mention the relation of the tetrahedron equation to our recent work on the non-stationary difference equation for the partition function of the affine Laumon space.
  • Shintarou Yanagida (Graduate School of Mathematics, Nagoya University)
    Supersymmetric vertex algebras slide
    A supersymmetic vertex algebra is an algebraic framework of two-dimensional conformal field theory equipped with supersymmetry. In this talk, I give a gentle introduction to this object, and explain some geometric aspects. First, I will give the definition, with a comparison to ordinary vertex algebras. Second, I will explain Zhu's C_2-Poisson and associative algebras of vertex algebras and the supersymmetric analogue, along with some examples. Thirdly, the chiral de Rham complex is introduced, and the relation to the factorization structure of the formal loop space is explained. Finally, I will briefly explain how to get the SUSY structure of the chiral de Rham complex from the factorization structure of the formal superloop space over a superconformal curve. This talk is partially based on a joint work with Takumi Iwane, arXiv:2409.04220.

Links

• Shenzhen–Nagoya Workshop on Quantum Science 2023
• SUSTech-Nagoya workshop on Quantum Science 2022
• SUSTech-Nagoya workshop on Quantum Science 2021

Last update: 2024/09/24