Upcoming talk:
Speaker: Chang Liu
Time: Tues., 16:00-17:00, Mar. 25, 2025
Venue：Ningzhai 104; Tencent Meeting (VooV Meeting): 603-0692-7681
Title: Quantum eigenvalue transformation for non-unitary and non-normal matrices
Abstract: This talk reviews and explores recent advances in Quantum Eigenvalue Transformation (QET). We begin with a brief review of the Quantum Eigenvalue Transformation of Unitary matrices (QETU) proposed by Dong et al., which offers a new approach to ground-state preparation and energy estimation on early fault-tolerant quantum computers. Then, focusing on the work of Chan et al., we discuss extending it to non-unitary dynamics by using quantum signal processing and unitary block encoding. Next, we cover two recent improvements: the Laplace transform based method via linear combination of Hamiltonian simulation (Lap-LCHS) by An et al., and the Quantum Eigenvalue Processing framework introduced by Low and Su. By comparing their theory, complexity, and applications, we'll explore quantum algorithms' feasibility in near-term quantum hardware.
References:
[1] Dong, Y., Lin, L. and Tong, Y. “Ground-state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices.” PRX quantum, 2022, 3(4): 040305. https://arxiv.org/abs/2204.05955
[2] Hans Hon Sang Chan, David Muñoz Ramo, Nathan Fitzpatrick “Simulating non-unitary dynamics using quantum signal processing with unitary block encoding.” https://arxiv.org/abs/2303.06161
[3] An, D., Childs, A. M., Lin, L. and Ying, L. “Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation.” https://arxiv.org/abs/2411.04010
[4] Low, G. H. and Su, Y. “Quantum eigenvalue processing.” https://arxiv.org/abs/2401.06240
Bio: Chang Liu is a PhD student at the Institute of Applied Physics and Computational Mathematics.
Past talks:
Speaker: Hao-En Li
Time: Tues., 16:00-17:00, Mar. 18, 2025
Venue：Ningzhai 104; Tencent Meeting (VooV Meeting): 603-0692-7681
Title: Solving eigenvalue problems via quantum eigenvalue transformation of unitary matrices
Abstract: In this talk, we will introduce how to use QET-U to design early fault-tolerant quantum algorithms for solving linear eigenvalue problems, covering implementation, complexity, and applications etc. If time permits, we will also briefly review other quantum algorithms for eigenvalue problems.
Bio: 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).
Speaker: Zhaoyuan Meng
Time: Tues., 16:00-17:00, Mar. 11, 2025
Venue：Ningzhai 104; Tencent Meeting (VooV Meeting): 603-0692-7681
Title: Quantum Computing of Fluid Dynamics via Hamiltonian Simulation
Abstract: As a potentially disruptive technology, quantum computing has advanced rapidly over the past half-century, emerging as one of the most compelling research fields. Direct numerical simulation of high-Reynolds-number turbulence requires immense computational resources, exceeding the capabilities of even the most powerful supercomputers, making quantum computing highly promising for such high-demand applications. However, since turbulence is a highly nonlinear classical physics problem rather than a quantum simulation task, designing quantum algorithms specifically for fluid dynamics remains a formidable challenge. In this emerging field of quantum computing for fluid dynamics, quantum computing holds the potential to address fundamental challenges such as turbulence prediction, offering a new paradigm for fluid mechanics research.
We develop a framework of quantum computing for fluid dynamics via Hamiltonian simulation. A quantum spin representation for fluid dynamics is proposed, mapping fluid systems to a specialized quantum system, thereby providing the theoretical foundation for Hamiltonian simulation of fluid flows on quantum computers. We design a Hamiltonian simulation algorithm based on this quantum representation, enabling the simulation of both compressible and incompressible flows, with acceleration achieved via quantum Fourier transform. Furthermore, we demonstrate the first end-to-end digital simulation of unsteady fluid dynamics on a superconducting quantum computer.
Self-intro: Zhaoyuan Meng is currently a PhD candidate in fluid mechanics at Peking University, under the supervision of Prof. Yue Yang. He obtained his Bachelor of Science degree from the University of Science and Technology of China in 2020. His research interests lie in turbulence, quantum computing for fluid dynamics, and vortex dynamics.
Speaker: Muzhou (Richard) Ma
Time: Tues., 16:00-17:00, Mar. 4, 2025
Venue：Ningzhai 104; Online Zoom: 230 432 7880 Password: BIMSA
Title：Heisenberg Limited Hamiltonian Learning
Abstract：
Hamiltonian learning is a fundamental problem in quantum physics, crucial for understanding and controlling quantum systems. Accurate models of Hamiltonians are needed for tasks ranging from quantum simulation to quantum error correction, where precise knowledge of interactions allows for better optimization and control. It is also a fundamental problem in computer science, where the classically analogous task of learning undirected graphical models is central in many models of machine learning.
In this talk, I will review various methods for learning Hamiltonians under different structural assumptions and evaluate the performance of these protocols. I will then discuss approaches for learning Hamiltonians that achieve the gold-standard Heisenberg-limited scaling through quantum dynamics in two steps: learning k-body Hamiltonians and learning arbitrary Hamiltonians.
Bio: Muzhou is currently an undergrad student at the department of electronic engineering at Tsinghua. His research focuses on quantum information theory. Muzhou was an undergrad research fellow in John Preskill’s group at IQIM,Caltech, hornored to be co-mentored by John Preskill, Yu Tong, and Steven Flammia.
Speaker: Peter (Song-qing-hao) Yang
Time: Tues., 17:00-18:00, Feb. 25, 2025
Venue：Ningzhai 104; Online Zoom: 230 432 7880 Password: BIMSA
Title：A Randomized Approach to Structure-Preserving Hamiltonian Simulation
Abstract：
Accurate and efficient Hamiltonian simulation is a cornerstone application of quantum computing, yet existing digital methods often introduce errors that violate fundamental physical conservation laws. In this talk, I will present PhysDrift, a randomized Hamiltonian simulation technique that extends qDrift by incorporating physical constraints, such as particle number conservation. By leveraging structured term grouping, PhysDrift mitigates spectral errors and reduces state leakage into unphysical subspaces, improving both accuracy and feasibility for near-term quantum devices.
I will discuss the theoretical foundations of PhysDrift, its relationship to existing randomized simulation protocols, and its empirical performance on molecular systems. Additionally, I will examine how this approach interacts with noise models and error mitigation techniques, demonstrating its robustness against realistic hardware limitations. By preserving key symmetries and leveraging stochastic sampling, PhysDrift offers a promising pathway toward more reliable digital quantum simulations, bridging the gap between algorithmic efficiency and physical fidelity.
Bio:
Peter (Song-qing-hao) Yang is a first-year PhD student at the Cavendish Laboratory, Department of Physics, University of Cambridge, working under the supervision of Professor Crispin Barnes. He previously completed both his Bachelor’s and Master’s degrees at Cambridge. His research focuses on quantum information and computation, with interests spanning Hamiltonian simulation algorithms, distributed quantum architectures, quantum metrology, and quantum foundations.
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.
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.
