Upcoming talk: 

Speaker: Junkai Wang
Time: Thu., 13:30-15:00, Jan. 9, 2025
Venue：B626, Shuangqing Complex Building A
Title：An introduction to Quantum Topological Data Analysis

Abstract：
As the last talk this semester, we will delve into the topic of "Quantum Topological Data Analysis" (QTDA), a nascent quantum-accelerated algorithm designed to extract robust multi-scale information, with the potential to avoid challenges from dequantization.
The talk will begin with a friendly introduction to fundamental concepts in algebrabic topology and homology theory, followed by an explanation of classical Topological Data Analysis and Persistent Homology method. After establishing that foundational background, we'll formally present Quantum TDA proposed by Leylod et al. and its subsequent developments. Accessible examples and codes will be provided, and then the talk will conclude with some possible discussion.

Speaker: J.W. is a visiting student at YMSC, Tsinghua University

Reference: [1] Lloyd S, Garnerone S, Zanardi P. Quantum algorithms for topological and geometric analysis of data[J]. Nature communications, 2016, 7(1): 10138.

Past talks:

Speaker: Xinmiao Li

Time: Tues., 15:00-16:00, Jan. 7th, 2025
Venue：B626, Shuangqing Complex Building A
Title：Quantum Walk：Definition, Property and Application

Abstract：This talk will introduce quantum walk. We will start with a brief introduction to the background and definition of quantum walk.

Next, we will focus on the properties of continuous-time quantum walk, and use two examples, hypercube and glued tree, to show the difference between quantum and classical.

Finally, some applications of quantum walk will be introduced, particularly how to use quantum walk to perform Hamiltonian simulation.

Speaker: Xinmiao Li is an undergraduate student at Qiuzhen College, Tsinghua University, supervised by Prof. Jin-Peng Liu.

Speaker: Yuxin Zhang (AMSS)

Time: Tues., 13:30-14:30, Dec. 31, 2024

Venue：B626, Shuangqing Complex Building A

Title：Quantum Spectral Method for Gradient and Hessian Estimation

Abstract：Gradient and Hessian estimation of multivariable functions plays a vital role across a wide range of fields, including optimization problems, machine learning, and others.

In this talk, we begin by revisiting the gradient estimation algorithms proposed by Jordan in 2005 and further improved by Gilyén, Arunachalam, and Wiebe in 2019, based on the finite difference method. We will then introduce our novel quantum algorithm for gradient estimation based on the spectral method, which achieves exponential speedup over classical algorithms in terms of the dimension d. As an extension, quantum algorithms for Hessian estimation are developed using either finite difference method or spectral method. We show that our quantum spectral method for Hessian estimation is optimal in terms of dimension d by proving a nontrivial lower bound.

Furthermore, when the Hessian is sparse, we can obtain better results.

References:
[Jor05] Stephen Jordan. Fast quantum algorithm for numerical gradient estimation. PRL, 2005.
[GAW19] András Gilyén, Srinivasan Arunachalam, and Nathan Wiebe. Optimizing quantum optimization algorithms via faster quantum gradient computation. SODA, 2019.
[ZS24] Yuxin Zhang, and Changpeng Shao. Quantum spectral method for gradient and Hessian estimation. arXiv:2407.03833, 2024.

Speaker: Yuxin Zhang is a PhD student at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. Her research interests include quantum algorithms, quantum complexity theory, and other intriguing fields yet to be explored.

Speakers：Weiliang Wang
Time: Thur., 13:30-14:30, Dec. 26, 2024
Venue：B626, Shuangqing Complex Building A
Title: Accurate and efficient quantum Gibbs state preparation

Abstract: Preparing Gibbs state on quantum computer is an essential task for quantum algorithm, which is believed to be one of the natural candidates for quantum advantage. Efforts to generalize classical gibbs sampler to quantum come to a remarkable result, the first implementable quantum Gibbs sampler recently[CKBG23][CKG23]. The speaker will review these works, together with [JI24] which provides an alternative Gibbs sampler.

References:

[CKBG23] Quantum Thermal State Preparation. Chi-Fang Chen, Michael J. Kastoryano, Fernando G.S.L. Brandão, and András Gilyén.
[CKG23] An efficient and exact noncommutative quantum Gibbs sampler  Chi-Fang Chen, Michael J. Kastoryano, and András Gilyén.
[JI24] Quantum Metropolis Sampling via Weak Measurement. Jiaqing Jiang and Sandy Irani.

Speaker: Jingyao Wang is an undergraduate at Yao Class, Tsinghua University.

Speakers：Chang Liu
Time: Tues., 13:30-14:30, Dec. 24, 2024
Venue：B626, Shuangqing Complex Building A
Title：A Theory of Trotter Error
Abstract：Trotterization has been an enduring technique of Hamiltonian simulation. This talk illustrates the foundational concepts of Trotter error theories and focuses on the groundbreaking work by Childs et al., which leverages the commutativity of operator summands to derive tighter and more general error bounds. Applications span digital quantum simulation and quantum Monte Carlo methods, achieving reduced computational complexity.

References:
[1] Childs, A. M., Su, Y., Tran, M. C., Wiebe, N., and Zhu, S. “A Theory of Trotter Error.” Phys. Rev. X 11 (2021). arXiv:1912.08854.

Speaker: Chang Liu is a PhD student at the Institute of Applied Physics and Computational Mathematics.

Speakers：Jingyao Wang
Time: Thur., 13:30-14:30, Dec. 19, 2024
Venue：B626, Shuangqing Complex Building A
Title：Carleman Linearization: Theoretical Guarantees and Numerical Experiments
Abstract：Carleman linearization is a prominent tool when it comes to solving nonlinear ODEs with quantum algorithms. This talk will first address the theoretical results for Carleman method under dissipative conditions building on Jinpeng’s work.

Subsequently, the talk extends to non-resonance conditions. The speaker will also give an illustration on the results of numerical experiments, where key results will be demonstrated and analyzed.

References:
[1]J. Liu, H.Ø. Kolden, H.K. Krovi, N.F. Loureiro, K. Trivisa, A.M. Childs, Efficient quantum algorithm for dissipative nonlinear differential equations, Proc. Natl. Acad. Sci. U.S.A.
118 (35) e2026805118,
https://doi.org/10.1073/pnas.2026805118 (2021).
[2]H.Wu, J.Wang, X.LI, Quantum Algorithms for Nonlinear Dynamics: Revisiting Carleman Linearization with No Dissipative Conditions
https://doi.org/10.48550/arXiv.2405.12714

Jingyao is a senior undergraduate at Yao Class, Tsinghua University. He will be a graduate student at Department of Computer Science, Tsinghua University, supervised by Prof. Zhengfeng Ji.

Speaker：Yanqiao Wang and Yixuan Liang
Time：13:30-14:30 Dec. 17th 2024
Venue：Shuangqing B626

Title：LCHS and Schrodingerisation for non-unitary linear ODEs and PDE

Abstract：We introduce two methods for simulating general linear ODEs or PDE, called linear combination of Hamiltonian simulation(LCHS) and Schrodingerisation. Firstly, we introduce original LCHS method and its improved version in terms of theory, alogrithm and complexity. Then we illustrate Schrodingerisation method and prove the equivalence of formulas of the two methods.

报告人介绍： Yanqiao Wang and Yixuan Liang are graduate students at Qiuzhen College, Tsinghua University, supervised by Prof. Jin-Peng Liu.

Speaker：Fanzhi Lu
Time：13:30-14:30 Dec. 10th 2024
Venue：Shuangqing B626

Title：An introduction to Hamiltonian Learning: Concepts and Algorithms

Abstract：This talk mainly introduces the idea of Hamiltonian learning and 2 learning framework: learning from real-time evolution and from Gibbs state. First we will illustrate the technical details of a state-of-the-art structure learning algorithm from real-time evolution [1]. Then there is a brief introduction to learning algorithms from Gibbs states [2], highlighting some of the key techniques.

References:
[1] A.Bakshi, A. Liu, A. Moitra, E. Tang. Structure Learning of Hamiltonians from Real-time Evolution. FOCS 2024.
[2] A.Bakshi, A. Liu, A. Moitra, E. Tang. Learning Quantum Hamiltonians at Any Temperature in Polynomial Time. QIP 2024.

报告人介绍：

Fanzhi Lu is a senior undergraduate student at Zhili College, Tsinghua University, supervised by Prof. Jin-Peng Liu. Fanzhi has a broad interest in quantum algorithms and quantum learning theory, particularly in developing efficient classical and quantum algorithms for learning and predicting quantum systems.

Title: Open Quantum Systems: A Mathematical Introduction, Simulations and Algorithmic Applications

Speaker: Hao-En Li
Time: 13:30-14:30 Dec. 5th 2024
Venue: Shuangqing B626

Abstract: In this talk, we will begin with a brief mathematical introduction to quantum Markovian semigroups and the GKSL equation [BPW19]. Next, we will discuss a Hamiltonian-simulation-based quantum implementation for simulating Lindblad dynamics [DLL24]. Finally, we will present recent examples of the algorithmic application of Lindblad equations to state preparation problems in quantum physics and quantum chemistry [CKG23, DCL24, LZL24].

References:
[BPW19] D. Bahns, A. Pohl, and I. Witt. Open Quantum Systems: A Mathe-matical Perspective. Springer International Publishing, 2019.
[CKG23] Chi-Fang Chen, Michael J Kastoryano, and Andr´as Gily´en. An efficient and exact noncommutative quantum Gibbs sampler. arXiv preprint arXiv:2311.09207, 2023.
[DCL24] Zhiyan Ding, Chi-Fang Chen, and Lin Lin. Single-ancilla ground state preparation via lindbladians. Phys. Rev. Res., 6:033147, 2024.
[DLL24] Zhiyan Ding, Xiantao Li, and Lin Lin. Simulating open quantum systems using hamiltonian simulations. PRX Quantum, 5:020332, 2024.
[LZL24] Hao-En Li, Yongtao Zhan, and Lin Lin. Dissipative ground state preparation in ab initio electronic structure theory. arXiv preprint arXiv:2411.01470, 2024.

报告人介绍：

Hao-En Li is now a senior undergraduate student at Dept. of Chemistry, Tsinghua University, supervised by Prof. Han-Shi Hu and Prof. Jin-Peng Liu. His research mainly focuses on electronic structure theory; quantum many-body physics/chemistry; quantum algorithms for science; numerical analysis; etc.He receives the 2024 Tsinghua University Special Scholarship (Undergraduate). 

Title: Observable-Driven Speed-ups in Quantum Simulations 

Speaker：Wenjun Yu

Time：13:30-14:30 Dec. 3rd 2024

Venue：Shuangqing B626

Abstract: As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product formula encounters challenges due to the pessimistic gate count estimation. In this work, we elucidate how observable knowledge can accelerate quantum simulations. By focusing on specific families of observables, we reduce product-formula simulation errors and gate counts in both short-time and arbitrary-time scenarios. Our advanced error analyses, supported by numerical studies, indicate improved gate count estimation. We anticipate that the explored speed-ups can pave the way for efficiently realizing quantum simulations and demonstrating advantages on near-term quantum devices.

Bio: Wenjun Yu is now a PhD candidate in computer science at the University of Hong Kong, supervised by Prof. Qi Zhao and Prof. Giulio Chiribella. He received a Bachelor's degree in 2021 from the Institute for Interdisciplinary Information Sciences at Tsinghua University. His research interests include quantum computing, quantum algorithms, and the characterization of NISQ devices.

Title: Quantum algorithms for linear systems of equations: optimal scaling and preconditioning

Speaker：安冬（北京大学）

Time：2024年11月21日（周四）13:30-14:30

Venue：双清C626 

Abstract: Designing quantum algorithms for solving linear systems of equations has attracted great attention due to its potential exponential speedup over classical algorithms and its fundamental role in scientific and engineering computation. In this talk, we will discuss how to design a quantum linear system algorithm with asymptotically optimal complexity in both the condition number and the accuracy. The idea of the algorithm is based on adiabatic quantum computing and is a combination of an optimally tuned scheduling function and the eigenstate filtering technique. In addition, we will also discuss preconditioned quantum linear system algorithm based on fast inversion and its application to Gibbs state preparation and matrix function evaluation.  

Bio: Dong An is an Assistant Professor at Beijing International Center for Mathematical Research (BICMR), Peking University, since September 2024. He received his Ph.D. in applied mathematics from University of California, Berkeley in 2021, and his B.S. degree in computational mathematics from Peking University in 2016. He was a postdoc at the University of Maryland before joining BICMR. His research interests are quantum computing, quantum algorithms and their applications in scientific computing tasks, including solving linear systems of equations, solving differential equations, and Hamiltonian simulation problems.