Abstract

Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett. 73, 58 (1994) [CrossRef]  ]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.

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References

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2016 (3)

J. Capmany, I. Gasulla, and D. Perez, “Microwave photonics: the programmable processor,” Nat. Photonics 10, 6–8 (2016).
[Crossref]

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

2015 (4)

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

K. Tanizawa, K. Suzuki, M. Toyama, M. Ohtsuka, N. Yokoyama, K. Matsumaro, M. Seki, K. Koshino, T. Sugaya, S. Suda, G. Cong, T. Kimura, K. Ikeda, S. Namiki, and H. Kawashima, “Ultra-compact 32 × 32 strictly-non-blocking Si-wire optical switch with fan-out LGA interposer,” Opt. Express 23, 17599–17606 (2015).
[Crossref]

D. A. Miller, “Perfect optics with imperfect components,” Optica 2, 747–750 (2015).
[Crossref]

2014 (3)

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

C. Shen, Z. Zhang, and L.-M. Duan, “Scalable implementation of boson sampling with trapped ions,” Phys. Rev. Lett. 112, 050504 (2014).
[Crossref]

2013 (3)

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

D. A. Miller, “Self-aligning universal beam coupler,” Opt. Express 21, 6360–6370 (2013).
[Crossref]

D. A. Miller, “Self-configuring universal linear optical component,” Photon. Res. 1, 1–15 (2013).
[Crossref]

2012 (1)

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

2011 (3)

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

L.-N. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

1994 (1)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Alber, G.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Albores-Mejia, A.

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

Annoni, A.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

Aspuru-Guzik, A.

B. Peropadre, A. Aspuru-Guzik, and J. J. Garcia-Ripoll, “Spin models and boson sampling,” arXiv preprint arXiv:1509.02703 (2015).

B. Peropadre, G. G. Guerreschi, J. Huh, and A. Aspuru-Guzik, “Microwave boson sampling,” arXiv preprint arXiv:1510.08064 (2015).

Baehr-Jones, T.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Bosonic transport simulations in a large-scale programmable nanophotonic processor,” arXiv preprint arXiv:1507.03406 (2015).

Barbieri, M.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Bentivegna, M.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Bernstein, H. J.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Bertani, P.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

Beth, T.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Bogaerts, W.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port universal coupler,” in Group IV Photonics Conference (2016), paper PD5.

Bonneau, D.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Bowers, J.

L.-N. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Brod, D. J.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Broome, M. A.

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Capmany, J.

J. Capmany, I. Gasulla, and D. Perez, “Microwave photonics: the programmable processor,” Nat. Photonics 10, 6–8 (2016).
[Crossref]

Carminati, M.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

Carolan, J.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Chen, L.-N.

L.-N. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Ciccarella, P.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

Coldenstrodt-Ronge, H. B.

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Cong, G.

Crespi, A.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Datta, A.

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Dorenbos, S. N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Duan, L.-M.

C. Shen, Z. Zhang, and L.-M. Duan, “Scalable implementation of boson sampling with trapped ions,” Phys. Rev. Lett. 112, 050504 (2014).
[Crossref]

Engin, E.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Englund, D.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Bosonic transport simulations in a large-scale programmable nanophotonic processor,” arXiv preprint arXiv:1507.03406 (2015).

Ezaki, M.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Ferrari, G.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

Flamini, F.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Galvão, E. F.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

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F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

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B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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Kimura, T.

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B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
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N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
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J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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Matthews, J. C. F.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
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B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
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N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
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N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
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Mirsalehi, M. M.

T. K. Gaylor, E. I. Verriest, and M. M. Mirsalehi, “Integrated optical givens rotation device,” U.S. patent4950042 A (August21, 1990).

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F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

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N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Bosonic transport simulations in a large-scale programmable nanophotonic processor,” arXiv preprint arXiv:1507.03406 (2015).

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Natarajan, C. M.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
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N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
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J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
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A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
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J. Capmany, I. Gasulla, and D. Perez, “Microwave photonics: the programmable processor,” Nat. Photonics 10, 6–8 (2016).
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B. Peropadre, G. G. Guerreschi, J. Huh, and A. Aspuru-Guzik, “Microwave boson sampling,” arXiv preprint arXiv:1510.08064 (2015).

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A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
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F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

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A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
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Ribeiro, A.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port universal coupler,” in Group IV Photonics Conference (2016), paper PD5.

Rohit, A.

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

Rötteler, M.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Rudolph, T.

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[Crossref]

Ruocco, A.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port universal coupler,” in Group IV Photonics Conference (2016), paper PD5.

Russell, N. J.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Sciarrino, F.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Seki, M.

Shadbolt, P. J.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Shen, C.

C. Shen, Z. Zhang, and L.-M. Duan, “Scalable implementation of boson sampling with trapped ions,” Phys. Rev. Lett. 112, 050504 (2014).
[Crossref]

Silverstone, J. W.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Smith, B. J.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Smith, P. G. R.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

Sorel, M.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

Spagnolo, N.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Sparrow, C.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Spring, J. B.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Stabile, R.

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

Steinbrecher, G. R.

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Bosonic transport simulations in a large-scale programmable nanophotonic processor,” arXiv preprint arXiv:1507.03406 (2015).

Suda, S.

Sugaya, T.

Suzuki, K.

Suzuki, N.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Tanizawa, K.

Tanner, M. G.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Theogarajan, L.

L.-N. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Thomas-Peter, N.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

N. Thomas-Peter, “Quantum enhanced precision measurement and information processing with integrated photonics,” Ph.D. thesis (Balliol College, University of Oxford, 2012).

Thompson, M. G.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Toyama, M.

Vanacker, L.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port universal coupler,” in Group IV Photonics Conference (2016), paper PD5.

Verriest, E. I.

T. K. Gaylor, E. I. Verriest, and M. M. Mirsalehi, “Integrated optical givens rotation device,” U.S. patent4950042 A (August21, 1990).

Viggianiello, N.

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

Vitelli, C.

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

Walmsley, I. A.

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Weinfurter, H.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Werner, R.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Williams, K. A.

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

Yokoyama, N.

Yoshida, H.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

Zeilinger, A.

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

Zhang, L.

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Zhang, Z.

C. Shen, Z. Zhang, and L.-M. Duan, “Scalable implementation of boson sampling with trapped ions,” Phys. Rev. Lett. 112, 050504 (2014).
[Crossref]

Zwiller, V.

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

IEEE Photon. J. (1)

L.-N. Chen, E. Hall, L. Theogarajan, and J. Bowers, “Photonic switching for data center applications,” IEEE Photon. J. 3, 834–844 (2011).
[Crossref]

Microsyst. Nanoeng. (1)

R. Stabile, A. Albores-Mejia, A. Rohit, and K. A. Williams, “Integrated optical switch matrices for packet data networks,” Microsyst. Nanoeng. 2, 15042 (2016).
[Crossref]

Nat. Commun. (3)

A. Crespi, R. Osellame, R. Ramponi, M. Bentivegna, F. Flamini, N. Spagnolo, N. Viggianiello, L. Innocenti, P. Mataloni, and F. Sciarrino, “Suppression law of quantum states in a 3D photonic fast Fourier transform chip,” Nat. Commun. 7, 10469 (2016).
[Crossref]

B. J. Metcalf, N. Thomas-Peter, J. B. Spring, D. Kundys, M. A. Broome, P. C. Humphreys, X.-M. Jin, M. Barbieri, W. S. Kolthammer, J. C. Gates, B. J. Smith, N. K. Langford, P. G. R. Smith, and I. A. Walmsley, “Multiphoton quantum interference in a multiport integrated photonic device,” Nat. Commun. 4, 1356 (2013).
[Crossref]

A. Peruzzo, A. Laing, A. Politi, T. Rudolph, and J. L. O’Brien, “Multimode quantum interference of photons in multiport integrated devices,” Nat. Commun. 2, 224 (2011).
[Crossref]

Nat. Photonics (3)

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770–774 (2014).
[Crossref]

N. Spagnolo, C. Vitelli, M. Bentivegna, D. J. Brod, A. Crespi, F. Flamini, S. Giacomini, G. Milani, R. Ramponi, P. Mataloni, R. Osellame, E. F. Galvão, and F. Sciarrino, “Experimental validation of photonic boson sampling,” Nat. Photonics 8, 615–620 (2014).
[Crossref]

J. Capmany, I. Gasulla, and D. Perez, “Microwave photonics: the programmable processor,” Nat. Photonics 10, 6–8 (2016).
[Crossref]

New J. Phys. (2)

D. Bonneau, E. Engin, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, J. L. O’Brien, and M. G. Thompson, “Quantum interference and manipulation of entanglement in silicon wire waveguide quantum circuits,” New J. Phys. 14, 045003 (2012).
[Crossref]

N. Thomas-Peter, N. K. Langford, A. Datta, L. Zhang, B. J. Smith, J. B. Spring, B. J. Metcalf, H. B. Coldenstrodt-Ronge, M. Hu, J. Nunn, and I. A. Walmsley, “Integrated photonic sensing,” New J. Phys. 13, 055024 (2011).
[Crossref]

Opt. Express (2)

Optica (1)

Photon. Res. (1)

Phys. Rev. Lett. (2)

M. Reck, A. Zeilinger, H. J. Bernstein, and P. Bertani, “Experimental realization of any discrete unitary operator,” Phys. Rev. Lett. 73, 58–61 (1994).
[Crossref]

C. Shen, Z. Zhang, and L.-M. Duan, “Scalable implementation of boson sampling with trapped ions,” Phys. Rev. Lett. 112, 050504 (2014).
[Crossref]

Sci. Adv. (1)

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

Science (1)

J. Carolan, C. Harrold, C. Sparrow, E. Martin-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics,” Science 349, 711 (2015).
[Crossref]

Other (11)

N. C. Harris, G. R. Steinbrecher, J. Mower, Y. Lahini, M. Prabhu, T. Baehr-Jones, M. Hochberg, S. Lloyd, and D. Englund, “Bosonic transport simulations in a large-scale programmable nanophotonic processor,” arXiv preprint arXiv:1507.03406 (2015).

T. K. Gaylor, E. I. Verriest, and M. M. Mirsalehi, “Integrated optical givens rotation device,” U.S. patent4950042 A (August21, 1990).

“Birth of the programmable optical chip,” Nat. Photonics10, 1 (2016), Editorial.

F. Morichetti, A. Annoni, S. Grillanda, N. Peserico, M. Carminati, P. Ciccarella, G. Ferrari, E. Guglielmi, M. Sorel, and A. Melloni, “4-channel all-optical mimo demultiplexing on a silicon chip,” in Optical Fiber Communication Conference (2016), paper ThE3.7.

A. Ribeiro, A. Ruocco, L. Vanacker, and W. Bogaerts, “Demonstration of a 4 × 4-port universal coupler,” in Group IV Photonics Conference (2016), paper PD5.

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, 2003), Vol. 173.

B. Peropadre, A. Aspuru-Guzik, and J. J. Garcia-Ripoll, “Spin models and boson sampling,” arXiv preprint arXiv:1509.02703 (2015).

B. Peropadre, G. G. Guerreschi, J. Huh, and A. Aspuru-Guzik, “Microwave boson sampling,” arXiv preprint arXiv:1510.08064 (2015).

N. Thomas-Peter, “Quantum enhanced precision measurement and information processing with integrated photonics,” Ph.D. thesis (Balliol College, University of Oxford, 2012).

These random unitary matrices were generated using the QR decomposition of random matrices, following the code developed by Toby Cubitt, available on www.dr-qubit.org/Matlab_code.html .

http://dx.doi.org/10.5287/bodleian:6gMmJYmab .

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (601 KB)      A. Method for characterizing elements of a realistic circuit. B. General decomposition procedure.

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Figures (3)

Fig. 1.
Fig. 1. Universal N-mode multiport interferometer (shown here for N=9) can be implemented using a mesh of N(N1)/2 beam splitters such as (a) the one proposed by Reck et al. or (b) the one we demonstrate in this paper. As shown in (c), a line corresponds to an optical mode, and crossings between two modes correspond to a variable beam splitter described by a Tm,n(θ,ϕ) matrix, which can be implemented by a Mach–Zehnder interferometer consisting of two 50:50 directional couplers, preceded by a phase shift at one input port. Although the total number of beam splitters in both interferometers is identical, our scheme clearly has a much shorter optical depth and therefore suffers less propagation loss. This reduction in optical depth stems from the fact that each mode crosses its nearest neighbor at the first possible occasion in contrast to the Reck scheme, where the top modes must propagate for some distance before interacting with other modes. Furthermore, the high symmetry inherent to our design improves the loss tolerance of the interferometer, as we show in the main text.
Fig. 2.
Fig. 2. Illustration of the algorithm for programming a universal multiport interferometer for a 5×5 interferometer. The left-hand side presents our decomposition procedure, and the right-hand side shows how our decomposition corresponds to building up the corresponding interferometer. (1) We start with any random unitary matrix U, and a blank interferometer. (2) We first null the bottom-left element of U with a T1,21 matrix, which causes the first two columns of U to mix. This corresponds to adding the top-left beam splitter in the interferometer. (3) We then null the next two elements of U using a T3,4 matrix followed by a T4,5 matrix, which correspond to the two bottom-right beam splitters in the interferometer. T3,4 mixes rows 3 and 4, and T4,5 mixes rows 4 and 5. Since both the (4,1) and (5,1) elements of U had been nulled, they are not affected by T4,5. (4) and (5) At every step in the algorithm, we null a successive diagonal of the updated U matrix by alternating between Tm,n and Tm,n1 matrices, which corresponds to adding diagonal lines of beam splitters to the interferometer. Tm,n (resp. Tm,n1) matrices of a given color cause the rows (resp. columns) m and n, which are shown in the same color, to mix and null the corresponding element of that color in U. It is clear from this process that once a matrix element has been nulled, no subsequent operation can modify it. (6) After step 5, U is a lower triangular matrix, which by virtue of its unitarity must be diagonal. As explained in the main text, we can then write U in the way shown here, which by construction exactly corresponds to the desired interferometer.
Fig. 3.
Fig. 3. Left: average fidelity for an interferometer with a constant loss of 0.2 dB per beam splitter (as in the universal multiport interferometer in [6]) for interferometers built according to the Reck design (black) and our design (blue), for different interferometer sizes. Inset: close-up of the fidelity in our design. Right: fidelity as a function of loss for interferometers implementing 20×20 transformations. We see from our results that our design is much more loss-tolerant than the Reck design and maintains high fidelity with the target unitary even in the case of high loss. This is because the mismatched path lengths in the Reck design causes the loss to severely affect the resulting interference. See [24] for underlying data.

Equations (6)

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Tm,n(θ,ϕ)=[10001eiϕcosθsinθeiϕsinθcosθ10001],
U=D((m,n)STm,n),
T4,5T3,4T2,3T1,2T4,5T3,4UT1,21T3,41T2,31T1,21=D,
U=T3,41T4,51T1,21T2,31T3,41T4,51DT1,2T2,3T3,4T1,2.
U=DT3,4T4,5T1,2T2,3T3,4T4,5T1,2T2,3T3,4T1,2,
F(Uexp,U)=|tr(UUexp)Ntr(UexpUexp)|2,

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