# Quantum transport simulations in a programmable nanophotonic processor

## Abstract

Environmental noise and disorder play critical roles in quantum particle and wave transport in complex media, including solid-state and biological systems. While separately both effects are known to reduce transport, recent work predicts that in a limited region of parameter space, noise-induced dephasing can counteract localization effects, leading to enhanced quantum transport. Photonic integrated circuits are promising platforms for studying such effects, with a central goal of developing large systems providing low-loss, high-fidelity control over all parameters of the transport problem. Here, we fully map the role of disorder in quantum transport using a nanophotonic processor: a mesh of 88 generalized beamsplitters programmable on microsecond timescales. Over 64,400 experiments we observe distinct transport regimes, including environment-assisted quantum transport and the ‘quantum Goldilocks’ regime in statically disordered discrete-time systems. Low-loss and high-fidelity programmable transformations make this nanophotonic processor a promising platform for many-boson quantum simulation experiments.

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## References

1. 1

Schmitz, H. et al. Quantum walk of a trapped ion in phase space. Phys. Rev. Lett. 103, 090504 (2009).

2. 2

Zahringer, F. et al. Realization of a quantum walk with one and two trapped ions. Phys. Rev. Lett. 104, 100503 (2010).

3. 3

Preiss, P. M. et al. Strongly correlated quantum walks in optical lattices. Science 347, 1229–1233 (2015).

4. 4

Broome, M. A. et al. Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104, 153602 (2010).

5. 5

Svozilik, J., Leon-Montiel, R. d. J. & Torres, J. P. Implementation of a spatial two-dimensional quantum random walk with tunable decoherence. Phys. Rev. A 86, 052327 (2012).

6. 6

Kitagawa, T. et al. Observation of topologically protected bound states in photonic quantum walks. Nat. Commun. 3, 882 (2012).

7. 7

Schreiber, A. et al. Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010).

8. 8

Crespi, A. et al. Anderson localization of entangled photons in an integrated quantum walk. Nat. Photon. 7, 322–328 (2013).

9. 9

Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

10. 10

Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008).

11. 11

Schreiber, A. et al. Decoherence and disorder in quantum walks: from ballistic spread to localization. Phys. Rev. Lett. 106, 180403 (2011).

12. 12

Bromberg, Y., Lahini, Y., Morandotti, R. & Silberberg, Y. Quantum and classical correlations in waveguide lattices. Phys. Rev. Lett. 102, 253904 (2009).

13. 13

Peruzzo, A. et al. Quantum walks of correlated photons. Science 329, 1500–1503 (2010).

14. 14

Sansoni, L. et al. Two-particle bosonic–fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108, 010502 (2012).

15. 15

Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nat. Photon. 7, 473–478 (2013).

16. 16

Defienne, H., Barbieri, M., Walmsley, I. A., Smith, B. J. & Gigan, S. Two-photon quantum walk in a multimode fiber. Sci. Adv. 2, e1501054 (2016).

17. 17

Wolterink, T. A. et al. Programmable two-photon quantum interference in 103 channels in opaque scattering media. Phys. Rev. A 93, 053817 (2016).

18. 18

Harris, N. C. et al. Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems. Phys. Rev. X 4, 041047 (2014).

19. 19

Collins, M. et al. Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4, 2582 (2013).

20. 20

Silverstone, J. W. et al. On-chip quantum interference between silicon photon-pair sources. Nat. Photon. 8, 104–108 (2014).

21. 21

Najafi, F. et al. On-chip detection of non-classical light by scalable integration of single-photon detectors. Nat. Commun. 6, 5873 (2015).

22. 22

Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

23. 23

Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R. & Aspuru-Guzik, A. Boson sampling for molecular vibronic spectra. Nat. Photon. 9, 615–620 (2015).

24. 24

Levi, L., Krivolapov, Y., Fishman, S. & Segev, M. Hyper-transport of light and stochastic acceleration by evolving disorder. Nat. Phys. 8, 912–917 (2012).

25. 25

Amir, A., Lahini, Y. & Perets, H. B. Classical diffusion of a quantum particle in a noisy environment. Phys. Rev. E 79, 050105 (2009).

26. 26

Anderson, P. W. Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492–1505 (1958).

27. 27

Lahini, Y., Bromberg, Y., Christodoulides, D. N. & Silberberg, Y. Quantum correlations in two-particle Anderson localization. Phys. Rev. Lett. 105, 163905 (2010).

28. 28

Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).

29. 29

Rebentrost, P., Mohseni, M., Kassal, I., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum transport. New J. Phys. 11, 033003 (2009).

30. 30

Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-assisted quantum walks in photosynthetic energy transfer. J. Chem. Phys. 129, 174106 (2008).

31. 31

Reck, M. & Zeilinger, A. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994).

32. 32

Miller, D. A. B. Self-configuring universal linear optical component. Photon. Res. 1, 1–15 (2013).

33. 33

Mower, J., Harris, N. C., Steinbrecher, G. R., Lahini, Y. & Englund, D. High-fidelity quantum state evolution in imperfect photonic integrated circuits. Phys. Rev. A 92, 032322 (2015).

34. 34

Lloyd, S., Mohseni, M., Shabani, A. & Rabitz, H. The quantum Goldilocks effect: on the convergence of timescales in quantum transport. Preprint at http://arxiv.org/abs/1111.4982 (2011).

35. 35

Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).

36. 36

Harris, N. C. et al. Efficient, compact and low loss thermo-optic phase shifter in silicon. Opt. Express 22, 10487–10493 (2014).

37. 37

Aaronson, S. & Arkhipov, A. in Proc. 43rd Annual ACM Symposium on Theory of Computing (eds Fortnow, L. & Vadhan, S.) 333–342 (ACM, 2011).

38. 38

Spring, J. B. et al. Boson sampling on a photonic chip. Science 339, 798–801 (2012).

39. 39

Broome, M. A. et al. Photonic boson sampling in a tunable circuit. Science 339, 794–798 (2012).

40. 40

Prevedel, R. et al. High-speed linear optics quantum computing using active feed-forward. Nature 445, 65–69 (2007).

41. 41

Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

42. 42

Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135–174 (2007).

43. 43

Childs, A. M. Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009).

44. 44

Baehr-Jones, T. et al. A 25 Gb/s silicon photonics platform. Preprint at http://arxiv.org/abs/1203.0767 (2012).

45. 45

Kempe, J. Quantum random walks: an introductory overview. Contemp. Phys. 44, 307–327 (2003).

46. 46

Notaros, J. et al. in Optical Fiber Communications Conference and Exhibition (OFC), 1–3 (IEEE, 2016).

47. 47

Cardenas, J. et al. Low loss etchless silicon photonic waveguides. Opt. Express 17, 4752–4757 (2009).

48. 48

Wilkes, C. M. et al. 60 dB high-extinction auto-configured Mach–Zehnder interferometer. Opt. Lett. 41, 5318–5321 (2016).

49. 49

Yao, X.-C. et al. Observation of eight-photon entanglement. Nat. Photon. 6, 225–228 (2012).

50. 50

Silverstone, J. W. et al. Qubit entanglement between ring-resonator photon-pair sources on a silicon chip. Nat. Commun. 6, 7948 (2015).

51. 51

Gerrits, T. et al. On-chip, photon-number-resolving, telecommunication-band detectors for scalable photonic information processing. Phys. Rev. A 84, 060301 (2011).

52. 52

McCaughan, A. N. & Berggren, K. K. A superconducting-nanowire three-terminal electrothermal device. Nano Lett. 14, 5748–5753 (2014).

## Acknowledgements

N.C.H. and M.P. acknowledge support from the National Science Foundation Graduate Research Fellowship Program grants 1122374 and 1122374, respectively. G.S. acknowledges support from the Department of Defense National Science and Engineering Graduate Fellowship. Y.L. acknowledges support from the Pappalardo Fellowship in Physics. This work was supported in part by the Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (FA9550-14-1-0052) and the Air Force Research Laboratory programme (FA8750-14-2-0120). M.H. acknowledges support from the AFOSR Small Business Technology Transfer programme (FA9550-12-C-0079 and FA9550-12-C-0038) and G. Pomrenke, of AFOSR, for his support of the optoelectronic systems integration in silicon (OpSIS) effort, through a Presidential Early Career Award in Science and Engineering award (FA9550-13-1-0027) and funding for OpSIS (FA9550-10-1-0439). D.E. acknowledges support by Excitonics, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under award no. desc0001088. The authors thank C. Galland for his discussions about the result.

## Author information

Authors

### Contributions

N.C.H. designed the photonic integrated circuit and experimental set-up and performed the experiments. N.C.H. laid out the design mask, with assistance from G.S. on metal routing. N.C.H. and M.P. calibrated the system. N.C.H., Y.L., G.S., S.L. and D.E. conceived the experiment. D.B. assisted with the theory. C.C. and F.N.C.W. assisted with multiphoton experiments. T.B.-J. and M.H. fabricated the system. All authors contributed to writing the paper.

### Corresponding author

Correspondence to Nicholas C. Harris.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 3371 kb)

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Reprints and Permissions

Harris, N., Steinbrecher, G., Prabhu, M. et al. Quantum transport simulations in a programmable nanophotonic processor. Nature Photon 11, 447–452 (2017). https://doi.org/10.1038/nphoton.2017.95

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