I am an applied mathematician and a mathematical physicist. My current research is focused on quantum computation, complexity, and information theory. I also research the generic aspects of quantum matter, which convolves random matrix theory and free probability theory with quantum many-body systems. Every once in a while I foray into classical physics, chemistry, and engineering.
I am a permanent Research Staff Member in quantum theory and algorithms group (IBMQ) based at Yorktown Heights, NY. I work at the MIT-IBM AI Research lab in Cambridge MA, USA. From 2015-2017, I was the Herman Goldstine Fellow in mathematics at IBM Yorktown Heights. In 2012-2015 I held postdoctoral positions at MIT, Northeastern University, and University of Chicago (with Leo P. Kadanoff).
I finished my Ph.D. in Mathematics at MIT in 2012 under the supervision of Peter W. Shor. At MIT I collaborated with Steven G. Johnson, Alan Edelman, Jeffrey Goldstone and Gil Strang. From 2005-2007 I was a research fellow (a “pre-doc”) at ETH-Zürich, where I worked on neuroscience and mathematical physics with Reinhard Nesper and Jürg Fröhlich respectively. I received my B.Sc. in 2004 in Applied and Engineering Physics from Cornell University, where I first started interacting with Roald Hoffmann.
Erdös Number: 3
Einstein Number: 4
I have a blog which is mostly of expository nature related to my research.
Publications:
* (with…) means I am the lead/corresponding author, or that the authors are alphabetically ordered.
39. (with Y. Kondo and R. Mori) “Fine-grained analysis and improved robustness of quantum supremacy for random circuit sampling,” arXiv:2102.01960 [quant-ph]
38. (with S. Bravyi, D. Gosset) “Classical algorithms for quantum mean values,” Nature Physics (Jan. 2021)
37. (with Y. Ouyang) “Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians”, arXiv:2012.01453 [quant-ph] (2020)
36. (with J. Schenker) “Theory of ergodic quantum processes”, arXiv: 2004.14397 (2020)
35. (with O. Shtanko) “Unitary subharmonic response and floquet Majorana modes,” Phys. Rev. Lett. 125, 086804 (2020) arXiv:1911.05795
34. (with J. Schenker) “An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states ”, arXiv: 1909.11769 (2019)
33. (with J. Gambetta, A. Mezzacapo, P.K. Temme) “Cost function deformation in quantum approximate optimization.” U.S. Patent No. 10,452,990. 22 Oct. 2019.
32. “Cayley path and quantum computational supremacy: A proof of average-case #P−hardness of Random Circuit Sampling with quantified robustness”, arXiv: 1909.06210, QIP2020 talk (2019), Featured in American Physical Society News Feb. 18., 2020 Era of quantum supremacy
31. “Efficient unitary paths and quantum computational supremacy: A proof of average-case hardness of Random Circuit Sampling”, arXiv: 1810.04681QIP2020 (2018)
30. (with O. Shtanko) “Stability of disordered Floquet topological phases”,
29. (with J. Michel, S. Reddy, R. Shah, and S. Silwal) “Directed Random Geometric Graphs”, Journal of Complex Networks, cnz006, https://doi.org/10.1093/comnet/cnz006 (08 April 2019) arXiv: 1808.02046
28. Y. Tsuji, E. Estrada, R. Movassagh, and R. Hoffmann “Quantum Interference, Graphs, Walks, and Polynomials”, Chemical Reviews Article ASAP DOI: 10.1021/acs.chemrev.7b00733 (2018), arXiv:1804.09234
27. “The gap of Fredkin quantum spin chain is polynomially small”,
Annals of Math. Sci. App., Vol. 3 No. 2, 531-562, (2018) arXiv: 1609.09160,
Annals of Math. Sci. App., Vol. 3 No. 2, 531-562, (2018) arXiv: 1609.09160,
26. “Generic local Hamiltonians are gapless,” Phys. Rev. Lett. 119, 220504 (2017) arXiv:1606.09313, QIP-18 talk
25. “Entanglement and correlation functions of the quantum Motzkin spin-chain,”
Journal of Mathematical Physics 58, 031901 (2017), arXiv: 1602.07761,
Journal of Mathematical Physics 58, 031901 (2017), arXiv: 1602.07761,
24. (with L. Levine) “The gap of the area-weighted Motzkin spin chain is exponentially small”, J. Phys. A: Math. Theor. 50 255302 (2017), arXiv: 1611.03147
23. (with G. Strang, Y. Tsuji, R. Hoffmann), “The Green’s Function for the H{\”u}ckel (Tight Binding) Model”, Journal of Mathematical Physics, 58, 033505; (2017), arXiv: 1407.4780
22. (with A. Edelman), “Eigenvalue approximation of sums of Hermitian matrices from eigenvector localization/delocalization”, arXiv:1710.09400 (2017),
21. (with L. P. Kadanoff), “Eigenpairs of Toeplitz and disordered Toeplitz matrices with a Fisher-Hartwig symbol”, Journal of Statistical Physics, 167 (3-4), pp. 959-996 (2017)
20. (with Peter W. Shor) “Supercritical entanglement in local systems: Counterexample to the area law for quantum matter”, Proceedings of the National Academy of Sciences: p. 201605716 (Nov. 7, 2016), arXiv: 1408.1657
QIP-15 talk, , Featured in MIT News Nov. 18., 2016. Entanglement bonanza
QIP-15 talk, , Featured in MIT News Nov. 18., 2016. Entanglement bonanza
19. “Eigenvalue attraction”, Journal of Statistical Physics, Feb. Volume 162, Issue 3, pp 615-643 (2016), arXiv: 1404.4113
18. (with E. Cuervo-Reyes) “Non-affine geometrization can lead to nonphysical instabilities”, J. Phys. A: Math. Theor. 48, 075101 (2015),
Featured on the Cover of issue 7, volume 48
17. Y. Tsuji, R. Movassagh , S. Datta, and R. Hoffmann “Exponential Attenuation of Through-Bond Transmission in a Polyene: Theory and Potential Realizations”,
16. (with L. Chang, M. Cheng, S. Cui, Y. Hu, W. Jin, P. Naaijkens, Z. Wang, A. Young) “On Enriching the Levin-Wen Model with Symmetry”,
J. Phys. A: Math. Theor. 48, 12, 12FT01 (2015) arXiv: 1412.6589
15. Y. Tsuji, R. Hoffmann, R. Movassagh and S. Datta “Quantum Interference in Polyenes”, The Journal of Chem. Phys. 141, 224311 (2014)
14. (with S. G. Johnson), “Optical ‘Bernoulli’ forces”, Phys. Rev. A 88, 023829 (2013) Editor’s suggestion. Featured in MIT Tech Review . arXiv: 1305.0317
13. (with M. Coudron) “Unfrustration condition and degeneracy of qudits on trees,” arXiv:1209.4395, (2013)
12. (with A. Edelman), “Condition numbers of indefinite rank-2 ghost wishart matrices,” Linear Algebra and Its Applications 483, 342–351 (2015), arXiv: 1207.3062
11. (with S. Bravyi, L. Caha, , D. Nagaj, P.W. Shor), “Criticality without frustration for quantum spin-1 chains”, Phys. Rev. Lett. 109, 207202 (2012), arXiv: 1203.5801
Featured in MIT News. Nov. 27, 2012,
10. (with J. Chen, A. Edelman, E. Hontz, J. Moix, A. Surez, M. Welborn, T. Van Voorhis) “Error analysis of free probability approximations to the density of states of disordered systems”, Phys. Rev. Lett. 109, 036403 (2012), arXiv: 1202.5839
Featured in MIT News June 22, 2012, Space Mart, Science Daily.
9. (with A. Edelman), “Density of states of quantum spin systems from isotropic entanglement”, Phys. Rev. Lett. 107, 097205 (2011) [ QIP-11 talk ]
8. “A time-asymmetric process in central force scatterings”, arXiv:1008.0875, (2010)
7. (with A. Edelman), “Isotropic entanglement”, arXiv:1012.5039 (2010)
6. (with E. Farhi, J. Goldstone, D. Nagaj, T. Osborne, P.W. Shor,) “Unfrustrated qudit chains and their ground states”, Phys. Rev. A 82, 012318 (2010), arXiv: 1001.1006
5. O.E. Rössler, D. Fröhlich, R. Movassagh and A. Moore, “Hubble-expansion in static space time”, Chaos, Solitons and Fractals 33, 770-775 (2007)
4. (with O.E. Rössler) “Bitemporal Sinai divergence: an energetic analog to Boltzmann’s entropy?” International Journal of Nonlinear Sciences and Numerical Simulation 6(4), 349-350 (2005)
3. R. C. K. Wong, L. G. Ko and R. Movassagh “A study of flow tortuosity in locked oil sand”, Canadian Journal of Petroleum and Technology Volume 43, Issue 1 (2004)
Refereed Conference Proceedings
2. C. Richmond, R. Movassagh, A. Edelman, R. Geddes, “Performance of sample covariance based capon bearing only tracker”, IEEE 45th Asilomar Conference on Signals, Systems and Computers, Nov. 7 10 (2011)
1. C. Richmond, R. Movassagh, A. Edelman, R. Geddes, “Sample covariance based estimation of capon algorithm error probabilities”, IEEE 44th Asilomar Conference on Signals, Systems and Computers, Nov. 7 10 (2010)
