Shenzhen–Nagoya Workshop on Quantum Science 2023

Date and venue

5–8 Sep. 2023, Hybrid (in-person and Zoom)

509 Mathematics Bldg. Nagoya University access

The zoom link will be sent to those who register using the registration form below.

Registration

Link to Microsoft Forms

Organizing committee

• Masahito Hayashi (Chair, CUHK-SZ, IQA, and Nagoya Univ.)
• An-Si Bai (SUSTech)
• Hiroaki Kanno (Nagoya Univ.)
• Shintarou Yanagida (Nagoya Univ.)
• Ryuhei Mori (Nagoya Univ.)

ShenzhenNagoya2023@gmail.com

KouShare/YouTube live streaming

Talks will be streamed on KouShare and YouTube.

https://www.koushare.com/topicIndex/i/SNWQS

• Morning 5th https://youtube.com/live/LNfOG15Fud0?feature=share
• Afternoon 5th https://youtube.com/live/RebEfLFH69I?feature=share
• Morning 6th https://youtube.com/live/wQwsHWE0drs?feature=share
• Afternoon 6th https://youtube.com/live/yligIgxUv3I?feature=share
• Morning 7th https://youtube.com/live/zlqhPNAijxU?feature=share
• Afternoon 7th https://youtube.com/live/TboDa4SQrRE?feature=share
• Morning 8th https://youtube.com/live/cxjNe3TQRjY?feature=share
• Afternoon 8th https://youtube.com/live/cWU2ySongUE?feature=share

Program

5 Sep.

Sessoin Chair: Harumichi Nishimura (Morning)/ François Le Gall (Afternoon)

6 Sep.

Sessoin Chair: Hiroaki Kanno (Morning)/ Shintarou Yanagida (Afternoon)

7 Sep.

Sessoin Chair: Ryuhei Mori (Morning)/ Francesco Buscemi (Afternoon)

8 Sep.

Sessoin Chair: Hiroaki Kanno (Morning)/ Shintarou Yanagida (Afternoon)

Abstracts

Benyou Wang (The Chinese University of Hong Kong, Shenzhen & Shenzhen Research Institute of Big Data)

Title：What can quantum physics bring to natural language processing? slide

Abstract: Quantum physics seeks to describe the world with mathematical language. This speech will first apply the mathematical foundation to describe natural language, providing concrete physical meaning for each component in neural NLP models. Interestingly, the dynamic aspect to words (e.g. in a spatial or temporal case) will also benefit from the wave formalization which assumes that particles may change depending on their context. Wave formalization of words fundamentally explains the magic position embedding in the popular network backbone in modern natural language processing. Lastly, this speech will also preliminary explore how other tools in quantum physics (e.g., tensor networks and quantum computer) help NLP.

Ansis Rosmanis (Nagoya University)

Title: Quantum Search with Noisy Oracle

Abstract: We consider quantum search algorithms that have access to a noisy oracle that, for every oracle call, with probability \(p>0\) completely depolarizes the query registers, while otherwise working properly. Previous results had not ruled out quantum \(O(\sqrt{n})\)-query algorithms in this setting, even for constant \(p\). We show that for all \(p\) in \([1/\sqrt{n}, 1-\Omega(1)]\), the quantum noisy-query complexity of the unstructured search is \(\Omega(np)\), which is tight up to logarithmic factors. The same bound holds for the dephasing noise and even when, for every oracle call, the algorithm is provided with a flag indicating whether the noise has occurred.

François Le Gall (Nagoya University)

Title: Improved Hardness Results for the Guided Local Hamiltonian Problem slide

Abstract: Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with 6-local Hamiltonians when the guiding vector has overlap (inverse-polynomially) close to \(1/\sqrt{2}\) with a ground state. In this paper, we optimally improve both the locality and the overlap parameters: we show that this quantum advantage (BQP-completeness) persists even with 2-local Hamiltonians, and even when the guiding state has overlap (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the BQP-completeness also holds for 2-local physically motivated Hamiltonians on a 2D square lattice or a 2D triangular lattice. This makes a further step towards establishing practical quantum advantage in quantum chemistry. arXiv:2207.10250

Harumichi Nishimura (Nagoya University)

Title: More Distributed Quantum Merlin-Arthur Protocols: Improvement and Extension slide

Abstract: Quantum Merlin-Arthur (QMA) is a quantum analogue of the complexity class NP, that is, the class of Yes-No problems such that any Yes instance can be verified by a party called the verifier (or Arthur) with the help of a quantum message (a.k.a quantum witness) from a party called the prover (or Merlin). In 2021, Fraigniaud et al. introduced a distributed version of QMA protocols (dQMA protocols) where there are multiple verifiers who consists of a network. They gave an efficient dQMA protocols for the equality problem that ask whether all the input strings owned by a subset of the verifiers are the same. In this talk, I first present the formulation of dQMA protocols and revisit the protocol by Fraigniuad et al. After that, I present improvements of the protocol in several aspects, and also provide the dQMA protocols for more extended problems.

Qisheng Wang (Nagoya University)

Title: Quantum Lower Bounds by Sample-to-Query Lifting

Abstract: The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998) and the adversary method by Ambainis (STOC 2000) have been shown powerful in proving quantum query lower bounds for a wide variety of problems. In this paper, we propose an arguably new method for proving quantum query lower bounds by a quantum sample-to-query lifting theorem, which is from an information theory perspective. Using this method, we obtain the following new results:

1. A quadratic relation between quantum sample and query complexities regarding quantum property testing, which is optimal and saturated by quantum state discrimination.
2. A matching lower bound \(\widetilde{\Omega}(\beta)\) for quantum Gibbs sampling at inverse temperature \(\beta\), showing that the quantum Gibbs sampler by Gilyén, Su, Low, and Wiebe (STOC 2019) is optimal.
3. A new lower bound \(\widetilde{\Omega}(1/\sqrt{\Delta})\) for the entanglement entropy problem with gap \(\Delta\), which was recently studied by She and Yuen (ITCS 2023).

In addition, we also provide unified proofs for some known lower bounds that have been proven previously via different techniques, including those for phase/amplitude estimation and Hamiltonian simulation. arXiv:2308.01794

Geng Liu (Shenzhen International Quantum Academy)

Title: Exponential Hardness of Optimization in Variational Quantum Algorithms slide

Abstract: A leading paradigm to establish near-term quantum applications is variational quantum algorithms (VQAs). However, the trainability issue of VQAs has garnered extensive attention, spurring demand for a comprehensive analysis of VQAs in order to identify viable solutions. Here, we propose a perspective that characterizes the trainability of VQAs based on their locality. We prove that the entire variation range of the loss function via adjusting any local quantum gate vanishes exponentially in the number of qubits for a broad class of VQAs. Our findings can deepen the understanding of the role of locality in VQAs and serve as a guideline for assessing the effectiveness of diverse training strategies for VQAs.

Link to arXiv: https://arxiv.org/abs/2205.05056

Kohtaro Kato (Nagoya University)

Title: Exact and Local Compression of Quantum Bipartite States slide

Abstract: Quantum data compression is one of the most fundamental quantum information processing. We study an exact local compression of a quantum bipartite state; that is, exact and noiseless one-shot quantum data compression of general mixed state sources without side information or entanglement assistance. We provide a formula for computing the minimal achievable compression dimensions, provided as a minimization of the Schmidt rank of a particular pure state constructed from that state. We will then discuss a possible application to tensor-network states.

Liang Kong (Southern University of Science and Technology)

Title: A morphism between two QFTs

Abstract: A morphism between two mathematical objects of the same type (e.g. groups, algebras, representations, categories, etc.), which preserves the defining structures of the objects, is one of the most important notions in mathematics. However, how to define such a morphism between two QFT’s (or quantum phases) had never been considered in physics until arXiv:1502.01690. This notion is getting more and more important in the study of QFTs especially after the rise of generalized high symmetries in recent years. In this talk, I will give a review of this notion and discuss some of its applications in mathematics and physics.

Yusuke Nishinaka (Nagoya University)

Title: A review of vertex algebras and chiral algebras slide

Abstract: The notion of a vertex algebra was introduced by Borcherds in 1986, and it is known as an algebraic framework of the chiral part of two-dimensional conformal field theory. On the other hand, there is a geometric framework of chiral conformal field theory, which is called a chiral algebra. This notion was introduced by Beilinson and Drinfeld in 2004 using the theory of D-modules and that of operads.

In this talk, I will give a brief review of these topics, in particular:

1. The relationship between two (algebraic and geometric) approaches.
2. The operad of chiral algebras (chiral operad) and its algebraic counterpart.

Jiaheng Zhao (Chinese Academy of Sciences)

Title: Center functors and condensation theory

Abstract: The notion of center plays a key role in the study of topological order. In this talk I will introduce the center functor in the context of seperable \(n\)-categories. Then I will talk about some generalizations and applications in condensation theory.

Shinichiroh Matsuo (Nagoya University)

Title: Lattice gauge theory and the discretization of Dirac operators slide

Abstract: Our ultimate goal is the discretization of Seiberg-Witten theory. Considering PL = DIFF in dimension four, we would like to construct something like PL Seiberg-Witten theory. As a first step towards this goal, we try to discretize the analytic index of Dirac operators. The analytic index of Fredholm operators is, however, a truly infinite dimensional phenomenon, and that of finite dimensional self-adjoint operators is not interesting. Thus, a naive discretization of Dirac operators does not work. In this talk, I will show that the “Wilson-Dirac operator” considered in lattice gauge theory gives a correct discretization, at least from the viewpoint of the analytic index.

This talk is based on a joint work with three physicists and two mathematicians: Hidenori Fukaya, Mikio Furuta, Tetsuya Oonogi, Satoshi Yamaguchi, and Mayuko Yamashita.

Hao Xu (Georg August University of Göttingen)

Title: From group cohomology to topological quantum invariants

Abstract: Group cohomology, a powerful mathematical tool rooted in homological algebra, provides a unique perspective for studying symmetries and invariants associated with groups. By analyzing the cocycles and coboundaries that characterize group extensions, one can unveil subtle properties of symmetry which arises naturally in condensed matter physics, gauge theories and quantum informations. Topological invariants, often realized as robust quantities insensitive to continuous deformations, have recently revolutionized our understanding of topological phases of matter and quantum field theories. The talk will explore how group cohomology seamlessly generalized to the language of higher fusion categories, unveiling the elegant mathematics underlying phenomena such as fractional quantum Hall states.

Ryo Hayami (Nagoya University)

Title: dg symplectic geoemetry and (higher) Poisson vertex algebras slide

Abstract: One-to-one correspondence between Courant-Dorfman algebras and Poisson vertex algebras can be seen as an algebraic generalization of the relation between generalized tangent bundles and Alekseev-Strobl currents. In terms of dg symplectic geometry, Alekseev-Strobl currents are 1-dimensional BFV(Batalin-Fradkin-Vilkovisky) currents whose target datum are degree 2 dg symplectic manifolds(Courant algebroids). In this talk, I will introduce a higher version of the one-to-one correspondence, which is an algebraic generalization of \((n-1)\)-dimensional BFV currents whose target datum are degree \(n\) dg symplectic manifolds. Moreover, noncommutative analogue of the correspondence (dg bisymplectic geometry and (higher) double Poisson vertex algebras) will be discussed. This talk is partly based on arxiv:2302.11420.

Francesco Buscemi (Nagoya University)

Title: Measurement sharpness and incompatibility as quantum resources slide

Abstract: In this talk I will discuss two aspects of quantum measurements, namely sharpness and incompatibility, from a resource-theoretic perspective. Our construction settles a debate in the literature and fills some gaps in the mathematical and conceptual foundations of quantum theory.

References:

• F.B., E. Chitambar, W. Zhou; PRL 124, 120401 (2020)
• F.B., K. Kobayashi, S. Minagawa, A. Tosini, P. Perinotti; Quantum 7, 1035 (2023)
• F.B., K. Kobayashi, S. Minagawa; arXiv:2303.07737

Shintaro Minagawa (Nagoya University)

Title: The second law of information thermodynamics for general quantum measurement processes slide

Abstract: Information processing such as feedback control can appear to violate the second law of thermodynamics, and this problem is called Maxwell’s demon paradox. The solution of this paradox given by previous studies imposed several assumptions on the measurement process, thus giving only sufficient conditions for feedback control to be consistent with the second law. In contrast, we analyze feedback control with the most general measurement process and discuss necessary and sufficient conditions for it to satisfy the second law inequalities.

arXiv: https://arxiv.org/abs/2308.15558

Masahito Hayashi (CUHK-SZ, IQA, and Nagoya Univ.)

Title: Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming slide

Abstract: In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known how to find practical measurements with optimal precisions, even for uncorrelated measurements over probe states. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We solve this fundamental problem by introducing a framework of conic programming that unifies the theory of precision bounds for multiparameter estimates for uncorrelated and correlated measurement strategies under a common umbrella. Namely, we give precision bounds that arise from linear programs on various cones defined on a tensor product space of matrices, including a particular cone of separable matrices. Subsequently, our theory allows us to develop an efficient algorithm that calculates both upper and lower bounds for the ultimate precision bound for uncorrelated measurement strategies, where these bounds can be tight. In particular, the uncorrelated measurement strategy that arises from our theory saturates the upper bound to the ultimate precision bound. Also, we show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.

Link to arXiv paper: arXiv:2209.05218 It will appear in Quantum.

Haidong Yuan (Chinese University of Hong Kong)

Title: Precision limit of quantum metrology

Abstract: Measurement and estimation of parameters are essential for science and engineering, where the main quest is to identify the highest achievable precision with given resources and design schemes to attain it. In this talk I will present a systematic way to identify the ultimate precision limit in quantum metrology and design optimal protocols to achieve it. I will also talk about the tradeoff relation among the precision limit for the estimation of multiple parameters.

Hayato Arai (Nagoya University)

Title: Derivation of Standard Quantum Theory via State Discrimination

Abstract: It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory, which is given by the trace norm. Besides, by applying the equivalent condition, we derive standard quantum theory out of classes of general models under a condition. arXiv:2307.11271

Baichu Yu (Southern University of Science and Technology)

Title: Measurement-Device-Independent Detection of Beyond Quantum State slide

Abstract: Bell experiment is a very important type of protocol to study the theoretical and practical problems of quantum information. The device-independent property of Bell experiment makes it a convenient tool for studying theories that are more general than quantum mechanics. Recently it was pointed out that in a standard Bell experiment, we cannot distinguish non-quantum states in the set of positive over all pure tensors (POPT) states from quantum states. We found that if we use the modified measurement-device-independent Bell experiment instead of the device-independent one, namely, if we replace the classical inputs with trusted quantum states, the non-quantum POPT states can be detected effectively. We also studied the detection power of our protocol when the input sets are tomographically incomplete.

In this talk I will first introduce some notions useful for understanding this problem, and then introduce the results we have obtained.

Ryuhei Mori (Nagoya University)

Title: Lower bounds on the error probability of multiple quantum channel discrimination by the Bures angle and the trace distance slide

Abstract: Quantum channel discrimination is a fundamental problem in quantum information science. In this study, we consider general quantum channel discrimination problems, and derive the lower bounds of the error probability. Our lower bounds are based on the triangle inequalities of the Bures angle and the trace distance. As a consequence of the lower bound based on the Bures angle, we prove the optimality of Grover’s search if the number of marked elements is fixed to some integer \(\ell\). This result generalizes Zalka’s result for \(\ell=1\). We also present several numerical results in which our lower bounds based on the trace distance outperform recently obtained lower bounds. arXiv:2107.03948

Shintarou Yanagida (Nagoya University)

Title: Quick introduction to chiral quantization slide

Abstract: The notion of chiral quantization is a relatively new notion of quantization in pure mathematics, appearing in the recent development of the theory of vertex algebras, a mathematical formulation of two-dimensional chiral conformal field theory.

It involves attaching to a given Poisson manifold (the phase space of a classical mechanical system) a sheaf of vertex algebras whose 0th associated graded part recovers the original structure sheaf with Poisson structure. I will give a short introduction to this topic.

An-Si Bai (Southern University of Science and Technology)

Title: The center of a finite dimensional quantum group slide

Abstract: The center of an algebra is the subalgebra consisting of elements commuting with every element of this algebra. It has a universal property identified by Lurie (2009) which can be easily generalized to various set-ups. In this talk we announce a verification that the Drinfeld double construction of a finite dimensional Hopf algebra gives rise to the 2-categorical center of this Hopf algebra.

Shun Wakatsuki (Nagoya University)

Title: String topology from the viewpoint of algebraic topology slide

Abstract: Chas and Sullivan introduced a family of operations on the homology of the free loop space LM of a manifold \(M\), i.e., the mapping space from the circle \(S^1\) to \(M\). For example, the loop product is defined as mixture of the intersection product on \(M\) and the Pontrjagin product on the based loop space ΩM given by concatenating two loops. Moreover, it is known that these operations give rise to TQFT structure on the homology of LM. In this talk, I will explain these operations from the viewpoint of algebraic topology.

Qin Li (Southern University of Science and Technology)

Title: Quantum master equation and geometric quantization slide

Abstract: In this talk, I will describe how the method of deformation quantization can be applied in the study of Hitchin connections in geometric quantization and its relation with quantum master equation in Batalin–Vilkovisky quantization.

Masamune Hattori (Nagoya University)

Title: The algebraic structure of elliptic quantum groups slide

Abstract: Elliptic quantum groups are dynamical and elliptic analogues of quantum affine algebras, introduced by Jimbo Konno Odake and Shiraishi(1999). This algebra has a structure called a Hopf algebroid rather than a Hopf algebra. In this talk, after an overview of the definition of elliptic quantum groups, we introduces Hopf algebroid and explains that elliptic quantum groups have the structure of Hopf algebroids.

Links

• SUSTech-Nagoya 2022
• SUSTech-Nagoya 2021