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:**

**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.*arXiv:1911.05795

**125**, 086804 (2020)**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,

**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,

**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

**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)

**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**

**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)