🌟 Quantum many-body seminar: Summer & Fall 2024

• Topic: Open quantum systems (Summer), Sampling (Fall)
• When: 🕒 Mondays 1PM-3PM (Summer), Friday 3PM-5PM (Fall)
• Where: Evans 891
• Moderator: Zhen Huang and Raehyun Kim

Upcoming:

Quantum states (continued).

Michael Ragone, Sep 6th, 3-5 pm.

📌 Schedule (2024 Summer & Fall)

🆕✨🔨: BOOK the slot for NEW semester!, UCB calendar

#	Date	Topic	Speaker	References
1	7/29	Review of recent backgrounds and perspectives on open quantum systems.	Lin Lin
2	8/2	Review of recent projects	All
3	8/5	Quasi-free systems
4	8/19	Quantum walks	Xinzhao Wang	Paper
5	8/30	Quantum states	Michael Ragone	Notes
6	9/6	Quantum states (continued)	Michael Ragone	Notes, Ref 1, Ref 2, and Ref 3, Chap 2 & 3
7	9/13
8	9/20	Mixing time of the Swendsen-Wang algorithm	Ruizhe Zhang
9	9/27		Yulong Dong
10	10/4		Kevin Stubbs
11	11/1		Jiaqi Leng
12	11/8		Zhiyan Ding
13	11/15		Sergio Escobar
14	11/22		Jiang Hu
15	12/6		Kevin Stubbs
16	12/13		Rahul Sarkar
17	12/20

Reading materials

Open quantum systems and mixing times

1. Ilin, Y., & Arad, I. (2024). Dissipative variational quantum algorithms for Gibbs state preparation. arxiv
2. Araujo de Resende, M. F. (2020). A pedagogical overview on 2D and 3D Toric Codes and the origin of their topological orders. Reviews in Mathematical Physics, 32(02), 2030002
3. Temme, K., Pastawski, F., & Kastoryano, M. J. (2014). Hypercontractivity of quasi-free quantum semigroups. Journal of Physics A: Mathematical and Theoretical, 47(40), 1–26.
4. Funo, K., & Ishizaki, A. (2024). Dynamics of a Quantum System Interacting with White Non-Gaussian Baths: Poisson Noise Master Equation. Physical Review Letters, 132(17), 1–12.
5. Guo, H., & Jerrum, M. (2018). Random cluster dynamics for the ising model is rapidly mixing. Annals of Applied Probability, 28(2), 1292–1313.
6. Jerrum, M., & Sinclair, A. (1993). Polynomial-Time Approximation Algorithms for the Ising Model. SIAM Journal on Computing, 22(5), 1087–1116.
7. Somma, R. D., King, R., Kothari, R., O’Brien, T., & Babbush, R. (2024). Shadow Hamiltonian Simulation. arxiv

Some previous reading materials

Quantum control: He, W., Li, T., Li, X., Li, Z., Wang, C., & Wang, K. (2024). [Efficient Optimal Control of Open Quantum Systems](http://arxiv.org/abs/2405.19245).

Quantum walk Gilyén, A., Hastings, M. B., & Vazirani, U. (2021). (Sub)Exponential advantage of adiabatic Quantum computation with no sign problem.

Adiabatic algorithm Somma, R. D., Nagaj, D., & Kieferová, M. (2012). Quantum speedup by quantum annealing.

Completely bounded maps Chapter 8 of Completely bounded maps and operator algebras.

Metropolis sampling Jiang, J., & Irani, S. (2024). Quantum Metropolis Sampling via Weak Measurement.

Non-Markovian dynamics Li, X. (2021) Markovian embedding procedures for non-Markovian stochastic Schrödinger equations

📃 Previous Schedules

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Schedule (2024 Spring)

#	Date	Topic	Speaker	References
1	1/26	Lindblad equation and Davies generator	Lin Lin	Lindblad Notes
2	2/2	Quantum detailed balance and mixing	Lin Lin
3	2/9	Hybrid hierarchical equation of motion for open quantum systems	Yuanran Zhu	Hybrid HEOM Notes
4	2/16	Solving quasi-free systems	Zhen Huang	Notes
5	2/23	How to represent a quantum bath for Tensor Network simulation?	Gunhee Park	Quantum Bath for TN PPT
6	3/1	March Meeting Prep
7	3/8	open system dynamics via influence functionals	Erika Ye	Influence Functional Notes
8	3/15	Introduction to HEOM	Avijit Shee
9	3/22		No seminar
10	3/29		No seminar
11	4/5		No seminar
12	4/12	Lower bounds to the spectral gap of Davies generators	Kevin Stubbs	Spectral Gap of Davis Operator Notes
13	4/19		No seminar
14	4/26	Quantum Gibbs Samplers: the commuting case	Zhiyan Ding
15	5/3		Gil Goldshlager

Schedule (2023 Fall)

| # | Date | Topic | Speaker | References | |---|------|----------------------------------------------------------------|-------------|-----------------------------------------------------------------------------------------------------------------| | 1 | 9/1 | Quantum embedding based on coupled cluster theory | Avijit Shee | | | 2 | 9/8 | The Ferromagnetic Ground State of Spinless, Valleyless Twisted Bilayer Graphene | Kevin Stubbs | | | 3 | 9/29 (cancelled) | | | | | 4 | 10/13 (zoom) | A class of signal processing method | Zhiyan Ding | [paper1]( https://ieeexplore.ieee.org/abstract/document/9000636), [paper2](https://arxiv.org/abs/1408.1681) | | 5 | 11/3 | Hybridization expansion approach to quantum impurites in the strong-coupling regime | Zhen Huang | [paper](https://journals.aps.org/prb/pdf/10.1103/PhysRevB.82.115115) | | 6 | 11/17| Diffusion models: a concise but comprehensive introduction | Yulong Dong | [paper1](https://arxiv.org/abs/2011.13456), [paper2](https://proceedings.neurips.cc/paper/2020/hash/4c5bcfec8584af0d967f1ab10179ca4b-Abstract.html) | | 7 | 12/1 | TBD | Nilin Abrahamsen | | | 8 | 12/8 | Projected Hartree Fock | Raehyun Kim | |

Schedule (2023 Summer)

#	Date	Topic	Speaker	References
1	5/5	Green’s function methods: Theory and application to GW and GF2	Zhen Huang	paper
2	5/12	Electron-phonon interactions from first principles	Yuanran Zhu	paper
3	6/9	Quantics tensor train	Nilin Abrahamsen	paper
4	6/16
5	6/23	TBD	Avijit Shee
6	7/7	quantum sampling	Jin-Peng Liu	paper

Schedule (2023 Spring)

#	Date	Topic	Speaker	References
1	1/13	Quantum signal processing, and some structure theorems of the qudit Pauli group	Rahul Sakar (Stanford)
1'	1/17	Efficient and robust learning of fermionic reduced density matrices with classical shadows	Andrew Zhao (New Mexico)
1''	1/20	Strong correlations in quantum chemistry: numerical analysis and recent applications	Fabian Faulstich
2	1/27	Algorithms for Clifford stabilizer simulations	Sajant Anand	https://arxiv.org/abs/quant-ph/0406196
3	2/3	Algorithms for Clifford stabilizer simulations	Sajant Anand	https://arxiv.org/abs/quant-ph/0406196
4	2/24	Towards Neural Variational Monte Carlo That Scales Linearly with System Size	Nilin	http://arxiv.org/abs/2212.11296
5	3/3	Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems	Gil Goldshlager
6	3/17	Riemannian geometry approaches to quantum algorithms	Subhayan Roy Moulik
7	3/24	Learning Feynman Diagrams with Tensor Trains	Kevin Stubbs
8	4/7	Quantum simulation of partial differential equations via Schrödingerisation	Zhiyan Ding
9	4/21	Quantum Hamiltonian Descent	Jiasu Wang

Schedule (2022 Fall)

Week	Date	Topic	Speaker	References
1	09/02	Thermal state preparation: Quantum MCMC	Zhiyan Ding
2	09/09	Thermal state preparation: Linear transformation and weight modification	Zhiyan Ding
3	09/16	Analytical guarantees and limitations of QAOA's performance	Joao Basso
4	09/23	Exact parameterization of fermionic wave functions via unitary coupled cluster theory	Fabian
5	09/30	Antisymmetric neural network separation	Nilin
6	10/07	Noise-resilient algorithms with randomized compiling	Subhayan
7	10/14	Efficient Representations of Green's functions	Zhen Huang
8	10/21	Quantum Walks	Jin-Peng Liu
9	10/28	multi-particle quantum walks	Jin-Peng Liu
10	11/04	combinatorial Mori-Zwanzig theory	Yuanran Zhu
11	11/11	Decomposition augmented Lagrangian method for low-rank SDP	Jiasu Wang
12	11/18	Quantum state preparation without coherent arithmetic	Yulong Dong
13	11/25	No seminar (Thanksgiving)
14	12/02	TBD	Raehyun Kim
15	12/09	Convergence analysis of diffusion models	Gil Goldshlager
16	12/16	No seminar (Final)
17	12/23	No seminar (Winter break)
18	12/30	No seminar (Winter break)
19	01/06	No seminar (JMM)

Schedule (2022 Summer)

Week	Date	Topic	Speaker	References
1	07/29	Transformers: NLP, CV, RL, Quantum and Beyond --- part I	Jiahao Yao
2	08/05	Transformers: NLP, CV, RL, Quantum and Beyond --- part II	Jiahao Yao
3	08/12	Transformers: NLP, CV, RL, Quantum and Beyond --- part III	Jiahao Yao

Schedule (2022 Spring)

Week	Date	Topic	Speaker	References
0	02/04	Coupled-cluster theory revisited	Mihaly Csirik
1	02/11	String theory, Geometry, and Machine Learning	Challenger Mishra
2	02/18	Optimal Stochastic Trace Estimation	Kevin Stubbs
3	02/25	Twisted bilayer graphene	Raehyun Kim
4	03/04	Fermionic Neural Networks	Nilin Abrahamsen
5	03/11	(Advancing Quantum Mechanics with Mathematics and Statistics Tutorials)
6	03/18	Exact parameterization of fermionic wave functions (IPAM activities)	Fabian Faulstich
7	03/25	(Spring Recess)
8	04/01	(Workshop I: Multiscale Approaches in Quantum Mechanics)
9	04/08	lattice gauge theories	Yu Tong
10	04/15	(Workshop II: Model Reduction in Quantum Mechanics)
11	04/20	The propagation of information in power-law interacting systems (joint with applied math seminar)	Minh Tran (MIT)
12	04/29	Quantum Algorithm for computing observable of nonlinear partial differential equations	Jiasu Wang
13	05/06	(Workshop III: Large-Scale Certified Numerical Methods in Quantum Mechanics)
14	05/13	Simulating bosonic bath with error bars	Jiasu Wang
15	05/20	(miniWorkshop on Moire systems)
16	05/27	(Workshop IV: Monte Carlo and Machine Learning Approaches in Quantum Mechanics)

Schedule (2021 Fall)

Week	Date	Topic	Speaker	References
1	8/27	Quantum Subspace Diagonalization.	Ethan Epperly
2	9/3	DMET for SIAM	Raehyun Kim
3	9/10	Parallel Quantum Algorithm for Hamiltonian Simulation	Nilin Abrahamsen
4	09/17	Variational Schrieffer-Wolff Transformation	Jiahao Yao
5	09/24	Genetic column generation	Kevin Stubbs
6	10/01	Hybridized Methods for Quantum Simulation in the Interaction Picture	Di Fang
7	10/08	Fast Amplification of QMA	Subhayan Roy Moulik
8	10/15	Fast-forwarding quantum evolution	Yulong Dong
9	10/22	Quantum Algorithms to Simulate Correlated Fermions	Fabian Faulstich
10	10/29	Self-consistent second-order Green’s function perturbation theory for periodic systems	Xin Xing
11	11/05	Theory of variational quantum simulation	Ethan Epperly
12	11/11 (Special date)		Joseph Tindall (Oxford)
13	11/19	Error Bounds for Variational Quantum Time Evolution	Yu Tong
14	11/26	Thanksgiving (so no seminar)
15	12/03	Exact Factorization Embedding Theory	Zhen Huang
16	12/10	Dynamical error bounds for continuum discretisation	Jiasu Wang
17	12/16	Quantum Monte Carlo approaches for strongly correlated systems	Ankit Mahajan

Schedule (2021 Summer)

Week	Date	Topic	Speaker	References
1	5/21		Canceled due to SIAM LA
2	5/28	DRL for Quantum Phase Transition (1/2 slot) Iterative Quantum Assisted Eigensolver (1/2 slot)	Jiahao Yao Jiasu Wang
3	6/4	Quantum algorithm for simulating real time evolution of lattice Hamiltonians	Yu Tong
4	6/11	Neural tensor contractions and the expressive power of deep neural quantum states	Jeffmin Lin
5	6/18	AIM SQUARE. No seminar this week
6	6/25	Third-order algebraic diagrammatic construction theory: A Green's function approach	Xin Xing
7	7/2	Fault-Tolerant Quantum Simulations of Chemistry in First Quantization	Di Fang
8	7/9	A projector-splitting integrator for dynamical low-rank approximation	Fabian Faulstich
9	7/16	Concentration for random product formulas	Dong An
10	7/23	Neural tensor contractions and the expressive power of deep neural quantum states	Jeffmin Lin
11	7/30	Universal tripartite entanglement in one-dimensional many-body systems	Yantao Wu
12	8/6	TBD	Raehyun Kim
13	8/13	Robustness of Discretization in Digital Adiabatic Simulation	Jiasu Wang
14	8/20	Accessing scrambling using matrix product operators	Sajant Anand

Schedule (2021 Spring)

Week	Date	Topic	Speaker	References
1	1/8	Block-encoding of sparse matrices	Lin Lin
2	1/15	Projected Position Operators for Constructing Well Localized Bases	Kevin Stubbs
3	1/19	Multiconfigurational Electronic Structure Theories for Materials: Development and Applications	Hung Pham
3	1/22	Polar decomposition, Petz recovery channels and pretty good measurements	Yihui Quek (Stanford)	Special Time: 4pm-5pm
4	1/29	FBSDE based neural network algorithms for high-dimensional quasilinear parabolic PDEs	Wenzhong Zhang
4	1/29	QIP 2021 presentation	QIP 2021 presentation
5	2/5	Representing Exact Electron Densities by a Single Slater Determinant in Finite Basis Sets	Xin Xing
6	2/12	sub-exponential algorithm for 2D frustration-free spin systems with gapped subsystems	Nilin Abrahamsen (MIT)
7	2/19	Quantum algorithms for linear and nonlinear differential equations	Dong An
8	2/26	APS March Meeting 2021 Presentation
9	3/5	On Representing (Anti)Symmetric Functions	Jeffmin Lin
10	3/12	Determinantal Point Processes for Machine Learning	Jiahao Yao
11	3/19	Nearly tight Trotterization of interacting electrons	Yuan Su
12	3/26	Quantum Logspace Algorithm for Powering Matrices with Bounded Norm	Subhayan Roy Moulik
13	4/2	Quantum Hamiltonian-Based Models & the Variational Quantum Thermalizer Algorithm	Yulong Dong
14	4/9	Spectral characterization of magic angles in twisted bilayer graphene	Fabian Faulstich
15	4/16	Chiral model for twisted bilayer graphene	Maciej Zworski
16	4/23	Quantum impurity problems	Lin Lin
17	4/30	Exploiting anticommutation in Hamiltonian simulation	Qi Zhao (UMD)
18	5/7	Canceled due to final exam
19	5/14	Quantum chaos, information scrambling, and computation	Subhayan Roy Moulik

Schedule (2020 Fall)

Week	Date	Topic	Speaker	References
1	9/4	Machine Learning Exchange-Correlation Energy	Qinyi Zhu	24
		Solving Quantum Linear Algebra Problems A Proposal of Quantum LINPACK Benchmark	Yulong Dong	25
2	9/14	Computational Optimal Transport	Jeffmin Lin	27, 28
		Fast Matrix-Vector Multiplication Algorithms for Dense Kernel Matrices	Xin Xing
3	9/18	Quantum State Verification in the Linear System Problem	Yu Tong	11
		Data-Driven PDF Method for Langevin Equations with Colored Noise	Hongli Zhao
4	9/25	DMFT, DMET, and RISB: A unified perspective	Fabian Faulstish	8
5	10/2	Machine Learning for Inverse Problems in Computational Engineering	Kailai Xu
6	10/9	Finite-size Correction for Periodic MP2 and CCSD Calculations	Xin Xing	21
7	10/16	Quantum Approach to Discrete Combinatorial Optimization	Jiasu Wang	15
8	10/23	Continuous Quantum Error Correction for Time-dependent Hamiltonian	Song Zhang	26
9	10/30	Hamiltonian Simulation in the Low Energy Subspace	Yulong Dong	12
10	11/13	A straightforward introduction to continuous quantum measurement	Di Fang	2
11	11/20	Localized Edge Modes in Subwavelength Resonator Arrays	Erik Hiltunen
12	12/4	Efficient Distributed Quantum Computing	Subhayan Moulik	14
13	12/17	Variational Policy Gradient Theorem	Jiahao Yao	31
14	12/18	Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions	Fabian Faulstish	30

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Reading materials for 2023 Spring

Derivation of Lindblad dynamics and non-Markovian systems

1. Lidar, D. A. (n.d.). Lecture Notes on the Theory of Open Quantum Systems. arXiv:1902.00967 Chap VIII-X
2. De Vega, I., & Alonso, D. (2017). Dynamics of non-Markovian open quantum systems. Reviews of Modern Physics, 89(1), 1–58. https://doi.org/10.1103/RevModPhys.89.015001 Sec III-IV

Exactly solvable Linear-Quadratic open quantum systems.

1. Dzhioev, A. A., & Kosov, D. S. (2011). Super-fermion representation of quantum kinetic equations for the electron transport problem. Journal of Chemical Physics, 134(4), 1–18. https://doi.org/10.1063/1.354806
2. Barthel, T., & Zhang, Y. (2022). Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems. Journal of Statistical Mechanics: Theory and Experiment, 2022(11). https://doi.org/10.1088/1742-5468/ac8e5c
3. Cirio, M., Lambert, N., Liang, P., Kuo, P., Chen, Y., Menczel, P., Funo, K., & Nori, F. (2023). Pseudofermion method for the exact description of fermionic environments : From single-molecule electronics to the Kondo resonance. 033011, 1–16. https://doi.org/10.1103/PhysRevResearch.5.033011
4. Dorda, A., Ganahl, M., Evertz, H. G., Von Der Linden, W., & Arrigoni, E. (2015). Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model. Physical Review B - Condensed Matter and Materials Physics, 92(12), 68–70. https://doi.org/10.1103/PhysRevB.92.125145 Sec. E

Hierarchical equation of motion and influence functional approaches, Bosonic / Fermionic bath reduction

1. Fay, T. P., & Limmer, D. T. (2022). Coupled charge and energy transfer dynamics in light harvesting complexes from a hybrid hierarchical equations of motion approach. Journal of Chemical Physics, 157(17). https://doi.org/10.1063/5.0117659
2. Ye, E., & Chan, G. K. (2021). Constructing Tensor Network Influence Functionals for General Quantum Dynamics. 1–14.
3. Woods, M. P., Groux, R., Chin, A. W., Huelga, S. F., & Plenio, M. B. (2014). Mappings of open quantum systems onto chain representations and Markovian embeddings. Journal of Mathematical Physics, 55(3), 1–48. https://doi.org/10.1063/1.4866769
4. Nüßeler, A., Dhand, I., Huelga, S. F., & Plenio, M. B. (2020). Efficient simulation of open quantum systems coupled to a fermionic bath. Physical Review B, 101(15), 1–20. https://doi.org/10.1103/PhysRevB.101.155134
5. Selstø, S. (n.d.). Absorbing boundary conditions for dynamical many-body quantum systems. 1–16. https://iopscience.iop.org/article/10.1088/0953-4075/43/6/065004

Ergodicity, quantum detailed balance, mixing time.

1. Zhang, Y., & Barthel, T. (2023). Criteria for Davies Irreducibility of Markovian Quantum Dynamics. 1–20. http://arxiv.org/abs/2310.17641
2. Wocjan, P., & Temme, K. (2023). Szegedy Walk Unitaries for Quantum Maps. Communications in Mathematical Physics, 402(3), 3201–3231. https://doi.org/10.1007/s00220-023-04797-4 Sec 1-2.
3. Temme, K. (2014). Lower bounds to the spectral gap of Davies generators https://arxiv.org/abs/1305.5591
4. Spohn, H., An algebraic condition for the approach to equilibrium of an open N-level system

Previous reading materials

See here

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