Science - USA (2021-12-03)

solvable models ( 3 , 43 ) and classical numer-
ical methods ( 35 , 36 ).
Note added in proof: During the completion
of this manuscript, we became aware of re-
lated work demonstrating the preparation of
toric code states by using quantum circuits on
a superconducting processor ( 44 ).

REFERENCES AND NOTES

1. X.-G. Wen,Rev. Mod. Phys. 89 , 041004 (2017).


2. S. Sachdev,Rep. Prog. Phys. 82 , 014001 (2019).


3. A. Kitaev,Ann. Phys. 303 ,2–30 (2003).


4. C. Nayak, S. H. Simon, A. Stern, M. Freedman, S. Das Sarma,
   Rev. Mod. Phys. 80 , 1083–1159 (2008).


5. L. Savary, L. Balents,Rep. Prog. Phys. 80 , 016502 (2017).


6. D. S. Rokhsar, S. A. Kivelson,Phys. Rev. Lett. 61 , 2376–2379 (1988).


7. N. Read, S. Sachdev,Phys. Rev. Lett. 66 , 1773–1776 (1991).


8. S. Sachdev,Phys. Rev. B Condens. Matter 45 , 12377–12396 (1992).


9. R. Moessner, S. L. Sondhi,Phys. Rev. Lett. 86 , 1881–1884 (2001).


10. G. Misguich, D. Serban, V. Pasquier,Phys. Rev. Lett. 89 ,
    137202 (2002).


11. B. I. Halperin, J. K. Jain,Fractional Quantum Hall Effects
    (World Scientific, 2020).


12. T.-H. Hanet al.,Nature 492 , 406–410 (2012).


13. M. Fu, T. Imai, T.-H. Han, Y. S. Lee,Science 350 , 655–658 (2015).


14. C. Gross, I. Bloch,Science 357 , 995–1001 (2017).


15. H. Weimer, M. Müller, I. Lesanovsky, P. Zoller, H. P. Büchler,
    Nat. Phys. 6 , 382–388 (2010).


16. M. Hermele, V. Gurarie, A. M. Rey,Phys. Rev. Lett. 103 , 135301
    (2009).


17. N. Y. Yaoet al.,Phys. Rev. Lett. 110 , 185302 (2013).


18. A. W. Glaetzleet al.,Phys. Rev. X 4 , 041037 (2014).


19. A. Celiet al.,Phys. Rev. X 10 , 021057 (2020).


20. S. de Léséleucet al.,Science 365 , 775–780 (2019).


21. T. Ozawaet al.,Rev. Mod. Phys. 91 , 015006 (2019).


22. R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, S. Sachdev,
    Proc. Natl. Acad. Sci. U.S.A. 118 , e2015785118 (2021).


23. R. Verresen, M. D. Lukin, A. Vishwanath,Phys. Rev. X 11 ,
    031005 (2021).


24. C. Songet al.,Phys. Rev. Lett. 121 , 030502 (2018).


25. C. K. Andersenet al.,Nat. Phys. 16 , 875–880 (2020).


26. S. Zhou, D. Green, E. D. Dahl, C. Chamon,Phys. Rev. B 104 ,
    L081107 (2021).


27. M. Saffman, T. G. Walker, K. Mølmer,Rev. Mod. Phys. 82 ,
    2313 – 2363 (2010).


28. P. Anderson,Mater. Res. Bull. 8 , 153–160 (1973).


29. S. Ebadiet al.,Nature 595 , 227–232 (2021).


30. P. Schollet al.,Nature 595 , 233–238 (2021).


31. Materials and methods are available as supplementary materials.


32. K. Fredenhagen, M. Marcu,Commun. Math. Phys. 92 , 81– 119
    (1983).


33. J. Bricmont, J. Frölich,Phys. Lett. B 122 , 73–77 (1983).


34. K. Gregor, D. A. Huse, R. Moessner, S. L. Sondhi,New J. Phys.
    13 , 025009 (2011).


35. S. R. White,Phys. Rev. Lett. 69 , 2863–2866 (1992).


36. J. Hauschild, F. Pollmann,SciPost Phys. Lect. Notesp. 5 (2018).


37. M. P. Zaletel, R. S. K. Mong, C. Karrasch, J. E. Moore,
    F. Pollmann,Phys. Rev. B Condens. Matter Mater. Phys. 91 ,
    165112 (2015).


38. M. B. Hastings, X.-G. Wen,Phys. Rev. B Condens. Matter Mater.
    Phys. 72 , 045141 (2005).


39. I. Cong, S. Choi, M. D. Lukin,Nat. Phys. 15 , 1273–1278 (2019).


40. E. Dennis, A. Kitaev, A. Landahl, J. Preskill,J. Math. Phys. 43 ,
    4452 – 4505 (2002).


41. M. C. Bañulset al.,Eur. Phys. J. D 74 , 165 (2020).


42. L. Tagliacozzo, A. Celi, A. Zamora, M. Lewenstein,Ann. Phys.
    330 , 160–191 (2013).


43. A. Kitaev,Ann. Phys. 321 ,2–111 (2006).


44. K. J. Satzingeret al.,Science 374 , 1237–1241 (2021).


45. G. Semeghiniet al., Probing topological spin liquids on a
    programmable quantum simulator.Harvard Dataverse(2021);
    doi:10.7910/DVN/BDCTRX.


46. R. Verresen, rubenverr/DMRG-QSL-Rydberg-experiment.
    Zenodo (2021); doi:10.5281/zenodo.5553679.

ACKNOWLEDGMENTS
We thank many members of the Harvard AMO community,
particularly E. Urbach, S. Dakoulas, and J. Doyle for their efforts
enabling operation of our laboratories during 2020-2021. We thank
S. Choi, I. Cong, E. Demler, G. Giudici, W. W. Ho, N. Maskara,
K. Najafi, N. Yao, and S. Yelin for stimulating discussions.Funding:

We acknowledge financial support from the Center for Ultracold

Atoms, the National Science Foundation, the U.S. Department

of Energy (DE-SC0021013 and LBNL QSA Center), the Army

Research Office MURI, the DARPA ONISQ program, QuEra

Computing, and Amazon Web Services. We further acknowledge

support from the Max Planck/Harvard Research Center for

Quantum Optics fellowship (to G.S.), the National Defense Science

and Engineering Graduate (NDSEG) fellowship (to H.L.), Gordon

College (to T.T.W,), the NSF Graduate Research Fellowship

Program (grant DGE1745303) and The Fannie and John Hertz

Foundation (to D.B.), the Harvard Quantum Initiative Postdoctoral

Fellowship in Science and Engineering (to R.V.), the Simons

Collaboration on Ultra-Quantum Matter (Simons Foundation grant

651440 to R.V., A.V., and S.S.). R.S. and S.S. were supported

by the U.S. Department of Energy under grant DE-SC0019030.

The DMRG simulations were performed by using the Tensor

Network Python (TeNPy) package developed by J. Hauschild and

F. Pollmann ( 36 ) and were run on the FASRC Cannon and Odyssey

clusters supported by the FAS Division of Science Research

Computing Group at Harvard University.Author contributions:

G.S., H.L., A.K., S.E., T.T.W., D.B., and A.O. contributed to building

the experimental setup, performed the measurements, and

analyzed the data. R.V., H.P., and A.V. contributed to developing

methods for detecting QSL correlations, performed numerical

simulations, and contributed to the theoretical interpretation of the

results. M.K. and R.S. contributed to the theoretical interpretation

of the results. All work was supervised by S.S., M.G., V.V., and

M.D.L. All authors discussed the results and contributed to the

manuscript.Competing interests:M.G., V.V., and M.D.L. are

cofounders and shareholders of QuEra Computing. A.K. is CEO and

shareholder of QuEra Computing. A.O. is shareholder of QuEra

Computing. Some of the techniques and methods used in this work

are included in provisional and pending patent applications filed by

Harvard University (US patent application nos. 16/630719, 63/116,321,

and 63/166,165).Data and materials availability:The data and

code are available on Harvard Dataverse ( 45 ) and Zenodo ( 46 ).

SUPPLEMENTARY MATERIALS

science.org/doi/10.1126/science.abi8794

Materials and Methods

Figs. S1 to S19

References ( 47 – 56 )

8 April 2021; accepted 28 October 2021

10.1126/science.abi8794

PLANT SCIENCE

Ground tissue circuitry regulates organ complexity in

maize andSetaria

Carlos Ortiz-Ramírez1,2, Bruno Guillotin^1 †, Xiaosa Xu^3 †, Ramin Rahni^1 †, Sanqiang Zhang^1 , Zhe Yan^4 ‡,

Poliana Coqueiro Dias Araujo^1 §, Edgar Demesa-Arevalo^3 , Laura Lee^1 , Joyce Van Eck5,6,

Thomas R. Gingeras^3 , David Jackson^3 , Kimberly L. Gallagher^4 , Kenneth D. Birnbaum^1 *

Most plant roots have multiple cortex layers that make up the bulk of the organ and play key roles

in physiology, such as flood tolerance and symbiosis. However, little is known about the formation

of cortical layers outside of the highly reduced anatomy ofArabidopsis. Here, we used single-cell

RNA sequencing to rapidly generate a cell-resolution map of the maize root, revealing an alternative

configuration of the tissue formative transcription factor SHORT-ROOT (SHR) adjacent to an

expanded cortex. We show that maize SHR protein is hypermobile, moving at least eight cell layers

into the cortex. Higher-orderSHRmutants in both maize andSetariahave reduced numbers of

cortical layers, showing that theSHRpathway controls expansion of cortical tissue to elaborate

anatomical complexity.

R

oots are radially symmetrical organs com-

posed of three fundamental tissue types:

the epidermis on the outside, the ground

tissue at the middle, and a core of vascular

elements plus pericycle that lie in a cen-

tral cylinder known as the stele ( 1 ). The ground

tissue is further divided into two different cell

types, the endodermis and cortex, which are

arranged as concentric layers around the stele.

Variations in ground tissue patterning, partic-

ularly the number of cortex cell layers, are

common across species and represent one of

the defining features giving rise to interspecies

root morphological diversity ( 1 ). This diversity

allows plants to cope with biotic and abiotic

stress and adapt to challenging environments.

For example, maize cortex plays a role in drought

and flood tolerance and hosts colonization of

beneficial mycorrhizal associations that reduce

stress and improve nutrient uptake ( 2 – 5 ). There-

fore, an ongoing question in root biology is how

tissue patterning is adjusted to produce diver-

gent root morphologies, and what alterations in

the genetic networks control developmental dif-

ferences among species.

A current limitation is that knowledge of

radial patterning mechanisms in roots comes

largely from the study ofArabidopsis, which

SCIENCEscience.org 3 DECEMBER 2021¥VOL 374 ISSUE 6572 1247

(^1) Center for Genomics and Systems Biology, Department of
Biology, New York University, New York, NY 10003, USA.
(^2) UGA Laboratorio Nacional de Genómica para la
Biodiversidad, CINVESTAV Irapuato, Guanajuato 36821,
México.^3 Cold Spring Harbor Laboratory, Cold Spring Harbor,
NY 11724, USA.^4 School of Arts and Sciences, University of
Pennsylvania, Philadelphia, PA 1904, USA.^5 Boyce Thompson
Institute, Ithaca, NY 14853, USA.^6 Plant Breeding and
Genetics Section, School of Integrative Plant Science, Cornell
University, Ithaca, NY 14853, USA.
*Corresponding author. Email: [email protected]
†These authors contributed equally to this work.
‡Present address: The National Key Facility for Crop Gene Resources
and Genetic Improvement (NFCRI)/Key Lab of Germplasm Utilization
(MOA), Institute of Crop Sciences, Chinese Academy of Agricultural
Sciences, Beijing 100081, China.
§Present address: Department of Agronomic and Forest Sciences,
Universidade Federal Rural do Semi-Árido, RN, Brazil.
RESEARCH | RESEARCH ARTICLES