Upcoming talk:
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.
Past talks:
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.
