Papers and Posters

Links to recent papers are first. Links to posters are at the bottom of this page, as well as links to articles that refer to the project. 

[87]  Liyuan Chen, Roy J. Garcia, Kaifeng Bu, and Arthur Jaffe, Magic of Random Matrix Product States, arXiv:2211.10350

[86] Roy Garcia, Kaifeng Bu, and Arthur Jaffe, Resource theory of quantum scrambling, arXiv:2208.10477

[85] Lu Li, Kaifeng Bu, Dax Enshan Koh, Arthur Jaffe, and Seth Lloyd, Wasserstein Complexity of Quantum Circuits, arXiv:2208.06306

[84] Andrew Yu, Quantum Complexity of Permutations, arXiv:2207.14102

[83] Weishun Zhong, Xun Gao, Susanne F. Yelin, Khadijeh Najafi, “Many-body localized hidden Born machine,” arXiv:2207.02346.

[82] Roy J. Garcia, Chen Zhao, Kaifeng Bu, and Arthur Jaffe, Barren plateaus from learning scramblers with local cost functions, arXiv:2205.06679

[81] Kaifeng Bu, Roy J. Garcia, Arthur Jaffe, Dax Enshan Koh, and Lu Li, Complexity of Quantum Circuits via Sensitivity, Magic and Coherence, arXiv:2204.12051

[80] Zhengwei Liu, Yunxiang Ren, and Sébastien Palcoux, Triangular Prism Equations and Categorification, arXiv:2203.06522

[79] Kaifeng Bu, Dax Enshan Koh, Roy J. Garcia, and Arthur Jaffe, Classical shadows with Pauli-invariant unitary ensembles, arXiv:2202.03272

[78] Roy Garcia, Kaifeng Bu, and Arthur Jaffe, Quantifying scrambling in quantum neural networks, arXiv:2112.01440JHEP (2022) Article 27

[77] Xun Gao, Marcin Kalinowski, Chi-Ning Chou, Mikhail D. Lukin, Boaz Barak, and Soonwon Choi,  Limitations of Linear Cross-Entropy as a Measure for Quantum Advantage, arXiv:2112.01657

[76] C. Gorgulla, Süleyman Çınaroğlu, P. D. Fischer, K. Fackeldey, G. Wagner and H. Arthanari, VirtualFlow Ants—Ultra-Large Virtual Screenings with Artificial Intelligence Driven Docking Algorithm Based on Ant Colony Optimization, Int. J. Mol. Sci. 2021, 22(11), 5807;

[75] Kaifeng Bu, Dax Enshan Koh, Lu Li, Qingxian Luo, and Yaobo Zhang, “Effects of quantum resources on the statistical complexity of quantum circuits,” arXiv:2102.03282.

[74] Zhengwei Liu, Yunxiang Ren, and Sébastien Palcoux, Interpolated family of non group-like simple integral fusion rings of Lie type, arXiv:2102.01663

[73] Roy Garcia, You Zhou, and Arthur Jaffe, Quantum scrambling with classical shadows, arXiv:2012.01008, Physical Review Research, 3 (2021), 033155

[72] Kaifeng Bu, Dax Enshan KohLu Li, Qingxian Luo, and Yaobo Zhang, On the statistical conplexity of quantum circuits, arXiv:2101.06154

[71] Kaifeng Bu, Yaobo Zhang, and Qingxian Luo, Depth-Width Trade-Offs for Neural Networks via Topological Entropy, arXiv:2010.07587

[70] Christoph Gorgulla, Konstantin Fackeldey, Gerhard Wagner, Haribabu Arthanari, Accounting of Receptor Flexibility in Ultra-Large Virtual Screens with VirtualFlow Using a Grey Wolf Optimization Method. Supercomputing Frontiers and Innovations 7(3) (2020), 4–12

[69] Zhengwei Liu, Yunxiang Ren, and Sébastien Palcoux, Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six, arXiv:2010.10264

[68] Zhengwei Liu and Christopher Ryba, The Grothendieck Ring of a Family of Spherical Categories, arXiv:2007.05622 

[67] Arthur Jaffe and Boqing Xue, The Beginning and the Unfinished Story of the Millennium Prize Problems,  arXiv:2007.12473, Mathematical Culture 11:4 (2020), 65-74.

[66] Christoph Gorgulla et. al, A multi-pronged approach targeting SARS-CoV-2 proteins using ultra-large virtual screening, chemRxiv.12682316.v1, iScience 24 (2) (2021), 102021.

[65] Xiao Yuan, Jinzhao Sun, Qi Zhao, and You Zhou, Quantum simulation with hybrid tensor networks, arXiv:2007.00958

[64] Arthur Jaffe and Zhengwei Liu, A Mathematical Picture Language Project, arXiv:2006.03954, to appear in the Proceedings of the ICCM.

[63] William Norledge and Adrian Ocneanu, Hopf Monoids, Permutohedral Cones, and Generalized Retarded Functions, arXiv:1911.11736v4

[62] Boaz Barak, Chi-Ning Chou, and Xun Gao, Spoofing Linear Cross-Entropy Benchmarking in Shallow Quantum Circuits, arXiv:2005.02421

[61] Alex Wozniakowski, Jayne Thompson, Mile Gu, and Felix Binder, A New Formulation of Gradient Boosting, arXiv:2005.06194, Mach. Learn.: Sci. Technol. 2 (2021), 045022.

[60] Kibrom G. Gebremeskel and Linzhe Huang, Boundedness and Spectrum of Multiplicative Convolution Operators Induced by Arithmetic Functions, Acta Mathematica Sinica, English Series  35(8) (2019), 1300–1310.

[59] You Zhou, Pei Zeng, and Zhenhuan Liu, Single-copies estimation of entanglement negativity, arXiv:2004.11360

[58] Mark V. Lawson and Alina Vdovina, Higher dimensional generalizations of the Thompson groups, arXiv:1909.13254Advances in Mathematics, 369 (2020), 107191.

[57] Christoph Gorgulla, Andras Boeszoermenyi, Zi-Fu Wang, Patrick D. Fischer, Paul Coote, Krishna M. Padmanabha Das, Yehor S. Malets, Dmytro S. Radchenko, Yurii S. Moroz, David A. Scott, Konstantin Fackeldey, Moritz Hoffmann, Iryna Iavniuk, Gerhard Wagner, Haribabu Arthanari, An open-source drug discovery platform enables ultra-large virtual screens, Nature 580 (2020) 663–668.

[56] Arthur Jaffe, Chunlan Jiang, Zhengwei Liu, Yunxiang Ren, and Jinsong Wu, Quantum Fourier analysis, arxiv:2002.03477, PNAS 117:20 (2020), 10715-10720.

[55] Qi Zhao and You Zhou, Constructing Multipartite Bell inequalities from stabilizers, arXiv:2002.01843.

[54] Lu Li, Kaifeng Bu, and Junde Wu, Contextual robustness: An operational measure of contextuality, Phys. Rev. A 101, 012120 (2020).

[53] Pei Zeng, You Zhou, and Zhenhuan Liu, Quantum gate verification and its application in property testing, arXiv:1911.06855, Physical Review Research 2 (2020), 023306.

[52] Zhengwei Liu, Quantized Graphs and Quantum Error Correction, arXiv:1910.12065.

[51] Zhengwei Liu, Sebastien Palcaux, and Jinsong Wu, Fusion Bialgebras and Fourier Analysis, arXiv:1910.12059.

[50] Yunxiang Ren, A generating problem for subfactors, arXiv:1910.09723.

[49] Bartosz Regula, Kaifeng Bu, Ryuji Takagi, and Zi-Wen Liu, Benchmarking one-shot distillation in general resource theories, arXiv:1909.11677 Physical Review A, 101, (2020) 062315,  chosen as "Editors suggestion."

[48] Xiaoqin Gao and Zhengwei Liu, Universal Quantum Computation by a Single Photon, arXiv:1909.09535.

[47] Zhengwei Liu and Jinsong Wu, Non-Commutative Rényi entropic uncertainty principles, arXiv:1904.04292. Science China Mathematics (2020),

[46] Kaifeng Bu and Dax Koh, Efficient classical simulation of Clifford circuits with nonstabilizer input states, arXiv:1902.11257, Physical Review Letters 123 (2019), 170502.

[45] Zi-Wen LiuKaifeng Bu, Ryuji Takagi, One-shot operational quantum resource theory, arXiv:1904.05840, Physical Review Letters 123 (2019), 020401, selected as Editor’s suggestion

[44] Yunxiang Ren, Universal skein theory for group actions, arXiv:1903.02012Advances in Mathematics 356 (2019).

[43] Arthur Jaffe and Zhengwei Liu, Reflection Positivity for Levin-Wen models, arXiv:1901.10662, Expositiones Mathematicae 38 (2020), 202-216.

[42] Zhengwei Liu, William Norledge, and Adrian Ocneanu, The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations, arXiv:1901.03243.

[41] Lu Li, Kaifeng Bu and Zi-Wen Liu, Quantifying the resourse content of quantum channels: An operational approach, arXiv:1812.02572, Physical Review A 101 (2020), 022335.

[40] Kaifeng Bu and Dax Enshan Koh, Classical simulation of quantum circuits by half Gauss sums, arXiv:1812.00224.

[39] Fei Wei, Anqie entropy and arithmetic compactification of natural numbers, arXiv:1811.11000.

[38] Kaifeng BuWeichen Gu, and Arthur Jaffe, Duality of graph invariants, arXiv:1810.08633.  Science China Mathematics, 63 (2020), 1613-1626.

[37] Fei Wei, Disjointness of Möbius from asymptotically periodic functions, arXiv:1810.07360.

[36] Yunxiang RenFrom skein theory to presentations for Thompson group, of Algebra 498 (2018), 178–196.

[35] Ryuji Takagi, Bartosz RegulaKaifeng BuZi-Wen Liu, and Gerardo Adesso, Operational advantage of quantum resources in subchannel discrimination, arXiv:1809.01672Physical Review Letters 122 (2019), 140402, selected as Editor’s Suggestion.

[34] Jordan Nikkel and Yunxiang Ren, On Jones Subgroup of R. Thompson's Group T, arXiv:1710.06972, International Journal of Algebra and Computation 28 (2018), 877–903.

[33] Kaifeng BuArthur JaffeZhengwei Liu and Jinsong Wu, De Finetti Theorems for Braided Parafermions, arXiv:1805.05990Communication in Mathematical Physics 373 (2020), 435–456.

[32] Zhengwei Liu and Jinsong Wu, Antisymmetric Characters and Fourier Duality, arxiv:1805.04783.

[31]  Zhengwei Liu and Jinsong Wu, Extremal Pairs of Young’s Inequality for Kac Algebras, Pacific Journal of Mathematics 295 (2018), 103–121.

[30] Arthur Jaffe, Reflection Positivity Then and Now, arXiv:1802.07880, in "Reflection Positivity," Oberwolfach Reports, OWR 14:4 (2017), 3269-3281, European Mathematical Society Publishers, Zurich.

[29] William Norledge, Singer cyclic lattices of type M, arXiv:1711.09332.

[28] William Norledge, Quotients of buildings by groups acting freely on chambers, arXiv:1711.09330.

[27] William Norledge, Quotients of buildings as W-groupoids, arXiv:1710.06968.

[26] Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, and Yunxiang Ren, An angle between intermediate subfactors and its rigidity, arXiv:1710.00285, Transactions of the American Mathematical Society 371 (2019), 5973–5991.

[25] Zhengwei Liu, Scott Morrison, and David Penneys, Lifting shadings on symmetrically self-dual subfactor planar algebras, arXiv:1709.05023. To appear in Contemporary Mathematics.

[24] Arthur Jaffe and Zhengwei Liu, A Mathematical Picture Language Program, Proceedings of the National Academy of Sciences 115 (2018), 81–86.

[23] Zhengwei Liu, Quon Language: Surface Algebras and Fourier Duality, arXiv:1707.03995Communications in Mathematical Physics 366 (2019), 865–894.

[22] Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Block maps and Fourier analysis, arXiv:1706.03551Science China Mathematics 62 (2019), 1585–1614.

[21] Zhengwei Liu and Feng Xu, Jones-Wassermann subfactors for modular tensor categories, arXiv:1612:08573Advances in Mathematics 355 (2019), 106775

[20] Corey Jones, Zhengwei Liu, and Yunxiang Ren, Classification of Thurston-Relation Subfactor Planar Algebras, arXiv:1606.00779Quantum Topology 10 (2019). 441-480.

[19] Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Holographic Software for Quantum Networks, Science China Mathematics 61 (2018), 593–626.

[18] Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Qudit Isotopy, arXiv:1602.02671.

[17] Zhengwei Liu, Yang-Baxter Relation Planar Algebras, arXiv:1507.06030.

[16] Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Uncertainty principles for locally compact quantum groups, Journal of Functional Analysis 274 (2018), 2399-2445.

[15] Zhengwei Liu and David Penneys, The generator conjecture for 3G subfactor planar algebras, Proceedings of the 2014 Maui and 2015 Qinhuangdao Conferences in Honour of Vaughan F.R. Jones' 60th Birthday (2017), 344–366.

[14] Zhengwei Liu, Simeng Wang, and Jinsong Wu, Young’s inequality for locally compact quantum groups, Journal of Operator Theory 77 (2017), 109–131.

[13] Zhengwei Liu and Jinsong Wu, Uncertainty principle for Kac algebras, Journal of Mathematical Physics 58 (2017), 052102.

[12] Dietmar Bisch, Vaughan F. R. Jones, and Zhengwei Liu, Singly generated planar algebras of small dimension, part III, arXiv:1410.2876, Transactions of the AMS 369 (2017), 2461–2476.

[11] Zhengwei Liu and Jinsong Wu, The Noncommutative Fourier Transform: A survey, Acta Mathematica Sinica Chinese Series (In honor of the 75th birthday of Bingren Li) 60 (2017), 69–80.

[10] Zhengwei Liu, and Alex Wozniakowski, and Arthur Jaffe, Quon 3D language for quantum information, Proceedings of the National Academy of Sciences 114 (2017), 2497–2502.

[9] Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Constructive Simulation and Topological Design of Protocols, New Journal of Physics 19 (2017), 063016.

[8] Arthur Jaffe and Bas Janssens, Reflection Positive Doubles, Journal of Functional Analysis 272 (2017), 3506–3557.

[7] Arthur Jaffe and Zhengwei Liu, Planar Para Algebras, Reflection Positivity, Communications in Mathematical Physics 352 (2017), 95–133.

[6] Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Noncommutative uncertainty principles, arXiv:1408.1165Journal of Functional Analysis 270 (2016), 264–311.

[5] Arthur Jaffe and Bas Janssens, Characterization of Reflection Positivity: Majoranas and Spins, Communications in Mathematical Physics 346 (2016), 1021–1050.

[4] Arthur Jaffe and Fabio L. Pedrocchi, Reflection Positivity for Parafermions, Communications in Mathematical Physics 337 (2015), 455–472.

[3] Arthur Jaffe, Stochastic Quantization, Reflection Positivity, and Quantum Fields, Journal of Statistical Physics 161 (2015), 1–15.

[2] Arthur Jaffe, Christian Jäkel, and Roberto Martinez, Complex Classical Fields: an Example, Journal of Functional Analysis 266 (2014), 1833–1881.

[1] Arthur Jaffe and Fabio L. Pedrocchi, Topological Order and Reflection Positivity, arXiv:1310.5370EPL 105 (2014), 40002.


Links to posters by participants that are related to the project.
These may be large files, which take some time to load.

[5] 16th conference on the Theory of Quantum Computation, Communication and Cryptography, July 7, 2021 (Riga, Latvia). Poster by Roy Garcia.

[4] QIP 2019 January12, 2019 (Boulder, CO). Poster by Kaifeng Bu

[3] Harvard Physics Research Scholar Retreat September 12, 2018. Poster by Kaifeng Bu (Awarded first prize)

[2] Harvard Undergraduate Research Opportunities in Science (HUROS) November 9, 2017. Poster by Chase Bednarz

[1] Harvard Physics Research Scholar Retreat September 28, 2017. Poster by William Norledge


Links to articles that refer to the project.

[4] Perimeter Institute Interview with Zi-Wen Liu about his work with Kaifeng Bu, An All Powerful Quantum Juicer

[3] Peter Reuell, Picture Perfect Approach to Science, Harvard Gazette (January 24, 2018).  See also

[2] Daniel S. Silver, The New Language of Mathematics, American Scientist 105 (November-December 2017), 365.

[1] Peter Reuell, Making Math More Lego Like, Harvard Gazette (March 2, 2017).  See also