Abstract

Femtosecond lasers enable three-dimensional direct writing of waveguides inside bulk transparent materials and have been applied to the fabrication of integrated photonic quantum logic gates. Up to now, the controlled-NOT (CNOT) gate, the key two-qubit quantum gate, has been realized only for polarization-encoded photonic qubits, which consists of three partially polarizing directional couplers (DCs) or two polarizing DCs. In this work, we demonstrate the femtosecond laser direct writing of a path-encoded CNOT gate formed by five DCs all with precisely controlled splitting ratios and stable symmetric phases inside glass for the first time. The quantum CNOT operation is performed using single photons with an average fidelity higher than 0.98. This provides a novel venue for the fabrication of large-scale 3D quantum computation circuits based on femtosecond laser writing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (5)

J. Zeuner, A. N. Sharma, M. Tillmann, R. Heilmann, M. Gräfe, A. Moqanaki, A. Szameit, and P. Walther, “Integrated-optics heralded controlled-NOT gate for polarization-encoded qubits,” Npj Quantum Inform. 4(1), 13 (2018).
[Crossref]

S. Atzeni, A. S. Rab, G. Corrielli, E. Polino, M. Valeri, P. Mataloni, N. Spagnolo, A. Crespi, F. Sciarrino, and R. Osellame, “Integrated sources of entangled photons at the telecom wavelength in femtosecond-laser-written circuits,” Optica 5(3), 311–314 (2018).
[Crossref]

H. Tang, X. F. Lin, Z. Feng, J. Y. Chen, J. Gao, K. Sun, C. Y. Wang, P. C. Lai, X. Y. Xu, Y. Wang, L. F. Qiao, A. L. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

J. W. Wang, S. Paesani, Y. H. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. H. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

R. Heilmann, C. Greganti, M. Grafe, S. Nolte, P. Walther, and A. Szameit, “Tapering of femtosecond laser-written waveguides,” Appl. Opt. 57(3), 377–381 (2018).
[Crossref]

2017 (1)

2016 (2)

G. N. M. Tabia, “Recursive multiport schemes for implementing quantum algorithms with photonic integrated circuits,” Phys. Rev. A 93(1), 012323 (2016).
[Crossref]

T. Meany, D. N. Biggerstaff, M. A. Broome, A. Fedrizzi, M. Delanty, M. J. Steel, A. Gilchrist, G. D. Marshall, A. G. White, and M. J. Withford, “Engineering integrated photonics for heralded quantum gates,” Sci. Rep. 6(1), 25126 (2016).
[Crossref]

2015 (5)

G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quantum Electron. 21(3), 131–137 (2015).
[Crossref]

J. Mower, N. C. Harris, G. R. Steinbrecher, Y. Lahini, and D. Englund, “High-fidelity quantum state evolution in imperfect photonic integrated circuits,” Phys. Rev. A 92(3), 032322 (2015).
[Crossref]

T. Meany, M. Grafe, R. Heilmann, A. Perez-Leija, S. Gross, M. J. Steel, M. J. Withford, and A. Szameit, “Laser written circuits for quantum photonics,” Laser Photonics Rev. 9(4), 363–384 (2015).
[Crossref]

R. Heilmann, M. Gräfe, S. Nolte, and A. Szameit, “Arbitrary photonic wave plate operations on chip: Realizing Hadamard, Pauli-X, and rotation gates for polarisation qubits,” Sci. Rep. 4(1), 4118 (2015).
[Crossref]

J. Carolan, C. Harrold, C. Sparrow, E. Martin-Lopez, 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(6249), 711–716 (2015).
[Crossref]

2013 (3)

2011 (2)

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
[Crossref]

L. A. Fernandes, J. R. Grenier, P. R. Herman, J. S. Aitchison, and P. V. S. Marques, “Femtosecond laser writing of waveguide retarders in fused silica for polarization control in optical circuits,” Opt. Express 19(19), 18294–18301 (2011).
[Crossref]

2010 (1)

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref]

2009 (3)

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
[Crossref]

G. D. Marshall, A. Politi, J. C. F. Matthews, P. Dekker, M. Ams, M. J. Withford, and J. L. O’Brien, “Laser written waveguide photonic quantum circuits,” Opt. Express 17(15), 12546–12554 (2009).
[Crossref]

A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s Quantum Factoring Algorithm on a Photonic Chip,” Science 325(5945), 1221 (2009).
[Crossref]

2008 (2)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2(4), 219–225 (2008).
[Crossref]

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref]

2007 (1)

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79(1), 135–174 (2007).
[Crossref]

2005 (1)

N. Kiesel, C. Schmid, U. Weber, R. Ursin, and H. Weinfurter, “Linear optics controlled-phase gate made Simple,” Phys. Rev. Lett. 95(21), 210505 (2005).
[Crossref]

2003 (1)

2002 (1)

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65(6), 062324 (2002).
[Crossref]

2001 (1)

E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
[Crossref]

2000 (1)

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404(6775), 247–255 (2000).
[Crossref]

1996 (1)

1995 (2)

S. Lloyd, “Almost Any Quantum Logic Gate Is Universal,” Phys. Rev. Lett. 75(2), 346–349 (1995).
[Crossref]

D. Deutsch, A. Barenco, and A. Ekert, “Universality in Quantum Computation,” Proc. R. Soc. London, Ser. A 449(1937), 669–677 (1995).
[Crossref]

1991 (1)

H. Hanafusa, M. Horiguchi, and J. Noda, “Thermally-Diffused Expanded Core Fibers for Low-Loss and Inexpensive Photonic Components,” Electron. Lett. 27(21), 1968–1969 (1991).
[Crossref]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59(18), 2044–2046 (1987).
[Crossref]

1973 (1)

A. Yariv, “Coupled-Mode Theory for Guided-Wave Optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

Acin, A.

J. W. Wang, S. Paesani, Y. H. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. H. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Aitchison, J. S.

Ams, M.

Arriola, A.

Atzeni, S.

Augusiak, R.

J. W. Wang, S. Paesani, Y. H. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. H. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Bacco, D.

J. W. Wang, S. Paesani, Y. H. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. H. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Barenco, A.

D. Deutsch, A. Barenco, and A. Ekert, “Universality in Quantum Computation,” Proc. R. Soc. London, Ser. A 449(1937), 669–677 (1995).
[Crossref]

Bell, T. B.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, “Linear optical controlled-NOT gate in the coincidence basis,” Phys. Rev. A 65(6), 062324 (2002).
[Crossref]

Bennett, C. H.

C. H. Bennett and D. P. DiVincenzo, “Quantum information and computation,” Nature 404(6775), 247–255 (2000).
[Crossref]

Biggerstaff, D. N.

T. Meany, D. N. Biggerstaff, M. A. Broome, A. Fedrizzi, M. Delanty, M. J. Steel, A. Gilchrist, G. D. Marshall, A. G. White, and M. J. Withford, “Engineering integrated photonics for heralded quantum gates,” Sci. Rep. 6(1), 25126 (2016).
[Crossref]

Bongioanni, I.

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
[Crossref]

Bonneau, D.

J. W. Wang, S. Paesani, Y. H. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. H. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360(6386), 285–291 (2018).
[Crossref]

Brod, D. J.

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7(7), 545–549 (2013).
[Crossref]

Broome, M. A.

T. Meany, D. N. Biggerstaff, M. A. Broome, A. Fedrizzi, M. Delanty, M. J. Steel, A. Gilchrist, G. D. Marshall, A. G. White, and M. J. Withford, “Engineering integrated photonics for heralded quantum gates,” Sci. Rep. 6(1), 25126 (2016).
[Crossref]

Carolan, J.

J. Carolan, C. Harrold, C. Sparrow, E. Martin-Lopez, 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(6249), 711–716 (2015).
[Crossref]

Chen, J. Y.

H. Tang, X. F. Lin, Z. Feng, J. Y. Chen, J. Gao, K. Sun, C. Y. Wang, P. C. Lai, X. Y. Xu, Y. Wang, L. F. Qiao, A. L. Yang, and X. M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4(5), eaat3174 (2018).
[Crossref]

Cheng, Y.

Corrielli, G.

S. Atzeni, A. S. Rab, G. Corrielli, E. Polino, M. Valeri, P. Mataloni, N. Spagnolo, A. Crespi, F. Sciarrino, and R. Osellame, “Integrated sources of entangled photons at the telecom wavelength in femtosecond-laser-written circuits,” Optica 5(3), 311–314 (2018).
[Crossref]

G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quantum Electron. 21(3), 131–137 (2015).
[Crossref]

Crespi, A.

S. Atzeni, A. S. Rab, G. Corrielli, E. Polino, M. Valeri, P. Mataloni, N. Spagnolo, A. Crespi, F. Sciarrino, and R. Osellame, “Integrated sources of entangled photons at the telecom wavelength in femtosecond-laser-written circuits,” Optica 5(3), 311–314 (2018).
[Crossref]

G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quantum Electron. 21(3), 131–137 (2015).
[Crossref]

A. Crespi, R. Osellame, R. Ramponi, D. J. Brod, E. F. Galvao, N. Spagnolo, C. Vitelli, E. Maiorino, P. Mataloni, and F. Sciarrino, “Integrated multimode interferometers with arbitrary designs for photonic boson sampling,” Nat. Photonics 7(7), 545–549 (2013).
[Crossref]

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2(1), 566 (2011).
[Crossref]

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization Entangled State Measurement on a Chip,” Phys. Rev. Lett. 105(20), 200503 (2010).
[Crossref]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Y. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref]

da Silva, T. F.

Davis, K. M.

Dekker, P.

Delanty, M.

T. Meany, D. N. Biggerstaff, M. A. Broome, A. Fedrizzi, M. Delanty, M. J. Steel, A. Gilchrist, G. D. Marshall, A. G. White, and M. J. Withford, “Engineering integrated photonics for heralded quantum gates,” Sci. Rep. 6(1), 25126 (2016).
[Crossref]

Deutsch, D.

D. Deutsch, A. Barenco, and A. Ekert, “Universality in Quantum Computation,” Proc. R. Soc. London, Ser. A 449(1937), 669–677 (1995).
[Crossref]

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Ding, Y. H.

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Phys. Rev. Lett. (4)

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Proc. R. Soc. London, Ser. A (1)

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Rev. Mod. Phys. (1)

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Sci. Adv. (1)

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Sci. Rep. (2)

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Science (4)

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Other (1)

Z. Y. Ou, Multi-photon Quantum Interference (Springer, 2007). Chap. 3.

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Figures (5)

Fig. 1.
Fig. 1. Schematic of a path-encoded CNOT logic gate. (a) The circuit consists of three DCs with power reflectivity R = 1/3 and two DCs with R = 1/2. The R is defined by the ratio of the output power from the through arm to the total output power of a DC where the laser is launched into either input arm. Reflection off any surface produces a π/2 phase change. The Cq (Tq) is encoded via spatial paths C0 (T0) and C1 (T1), representing logic states |0 > and |1>, respectively. The remaining two paths Ac and At represent ancillary vacuum modes. The uniform purple lines in the interaction straight regions indicate all the surfaces yielding a relative π/2 phase change upon reflection. (b) CAD layout corresponding to the actual fabricated size of the CNOT gate. The overall length is 2.5 cm. The coupling length is less than 0.4 mm.
Fig. 2.
Fig. 2. (a) Near field image of the waveguide guided mode at 808 nm for the vertical polarized light. (b) The measured coupling coefficient k as a function of the interaction distance d. (c) Microscope image of part of the coupling region at d = 8 µm of the DC.
Fig. 3.
Fig. 3. Measured reflectivity R and transmission T (a) as well as phase φ (b) of the fabricated DCs as a function of coupling length L at interaction distance d = 8 µm. The fittings for T and R indicate a trend following the square sine and square cosine curves. φ linearly varies with L. Inset: fittings for a complete period showing square of the sine and cosine laws.
Fig. 4.
Fig. 4. Experimental setup and two-photon HOMI in the central DC with R = 1/3 of the CNOT. (a) Photon pairs at 808 nm are generated through Type-I SPDC in a BBO crystal pumped by a 140-mW, 404-nm CW diode laser and are collected into SMFs. Long pass filters (LPFs) from 650 nm and interference filters (IFs) with Δλ = 3 nm are used to ensure good spectral indistinguishability. A delay line (DL) is inserted to control the temporal superposition of the photons. Half-wave plates (HWPs) and polarization controllers (PC) are used to compensate the rotation of the photon polarization in the SMFs. Single photons are launched into the waveguides inside the integrated CNOT chip and then collected at the outputs using two arrays of four SMFs. SPCMs and the connected 8-channel time to digital converter (TDC) are used to conduct two-fold coincidence detections of different output-photon combinations. (b), (c) The coincidence counts of detecting photons at $C_1^{\prime}$ and $T_1^{\prime}$ ( $T_0^{\prime}$ ) when two photons are injected into C1 and T1 (T0). The HOMI visibilities are 0.977 ± 0.007 and 0.971 ± 0.007, respectively.
Fig. 5.
Fig. 5. Experimentally constructed CNOT logical truth table. The labels on the Input and Output axes identify the state | CqTq >. Ideally, a flip of the logical state of the target qubit Tq occurs only when the control qubit Cq is in the logical state |1 > . The average fidelity is higher than 0.98.

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