Abstract

The Bell states preparation circuit is a basic circuit required in quantum teleportation. We describe how to implement it in all-fiber technology. The basic building blocks for its implementation are directional couplers and highly nonlinear optical fiber (HNLF). Because the quantum information processing is based on delicate superposition states, it is sensitive to quantum errors. In order to enable fault-tolerant quantum computing the use of quantum error correction is unavoidable. We show how to implement in all-fiber technology encoders and decoders for sparse-graph quantum codes, and provide an illustrative example to demonstrate this implementation. We also show that arbitrary set of universal quantum gates can be implemented based on directional couplers and HNLFs.

© 2010 OSA

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References

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  1. M. A. Neilsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  2. E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
    [CrossRef] [PubMed]
  3. A. Barenco, “A universal two-bit quantum computation,” Proc. R. Soc. Lond. A 449(1937), 679–683 (1995).
    [CrossRef]
  4. D. Deutsch, “Quantum computational networks,” Proc. R. Soc. Lond. A Math. Phys. Sci. 425(1868), 73–90 (1989).
    [CrossRef]
  5. G. J. Milburn, “Quantum optical Fredking gate,” Phys. Rev. Lett. 62(18), 2124–2127 (1989).
    [CrossRef] [PubMed]
  6. E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001).
    [CrossRef] [PubMed]
  7. 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]
  8. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
    [CrossRef] [PubMed]
  9. N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
    [CrossRef]
  10. F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing (CRC Press, 2008).
  11. D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
    [CrossRef]
  12. I. Djordjevic, “Photonic quantum dual-containing LDPC encoders and decoders,” IEEE Photon. Technol. Lett. 21(13), 842–844 (2009).
    [CrossRef]
  13. T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
    [CrossRef] [PubMed]
  14. D. Gottesman, Stabilizer Codes and Quantum Error Correction. PhD Dissertation, California Institute of Technology, 1997.

2009 (2)

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

I. Djordjevic, “Photonic quantum dual-containing LDPC encoders and decoders,” IEEE Photon. Technol. Lett. 21(13), 842–844 (2009).
[CrossRef]

2008 (1)

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

2006 (1)

T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
[CrossRef] [PubMed]

2004 (1)

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
[CrossRef]

2003 (1)

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

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] [PubMed]

1995 (1)

A. Barenco, “A universal two-bit quantum computation,” Proc. R. Soc. Lond. A 449(1937), 679–683 (1995).
[CrossRef]

1989 (2)

D. Deutsch, “Quantum computational networks,” Proc. R. Soc. Lond. A Math. Phys. Sci. 425(1868), 73–90 (1989).
[CrossRef]

G. J. Milburn, “Quantum optical Fredking gate,” Phys. Rev. Lett. 62(18), 2124–2127 (1989).
[CrossRef] [PubMed]

Barenco, A.

A. Barenco, “A universal two-bit quantum computation,” Proc. R. Soc. Lond. A 449(1937), 679–683 (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]

Brainis, E.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Brun, T.

T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
[CrossRef] [PubMed]

Cerf, N. J.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Cryan, M. J.

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

Deutsch, D.

D. Deutsch, “Quantum computational networks,” Proc. R. Soc. Lond. A Math. Phys. Sci. 425(1868), 73–90 (1989).
[CrossRef]

Devetak, I.

T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
[CrossRef] [PubMed]

Djordjevic, I.

I. Djordjevic, “Photonic quantum dual-containing LDPC encoders and decoders,” IEEE Photon. Technol. Lett. 21(13), 842–844 (2009).
[CrossRef]

Edamatsu, K.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

Emplit, P.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Haelterman, M.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Hsieh, M.-H.

T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
[CrossRef] [PubMed]

Knill, E.

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

Kosaka, H.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

Laflamme, R.

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

Lamoureux, L. P.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Langford, N. K.

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]

MacKay, D. J. C.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
[CrossRef]

Massar, S.

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

Matsuda, N.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

McFadden, P. L.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
[CrossRef]

Milburn, G. J.

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

G. J. Milburn, “Quantum optical Fredking gate,” Phys. Rev. Lett. 62(18), 2124–2127 (1989).
[CrossRef] [PubMed]

Mitchison, G.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
[CrossRef]

Mitsumori, Y.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

O’Brien, J. L.

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

Politi, A.

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

Ralph, T. C.

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]

Rarity, J. G.

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

Shimizu, R.

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

White, A. G.

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]

Yu, S.

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

IEEE Photon. Technol. Lett. (1)

I. Djordjevic, “Photonic quantum dual-containing LDPC encoders and decoders,” IEEE Photon. Technol. Lett. 21(13), 842–844 (2009).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, “Sparse-graph codes for quantum error correction,” IEEE Trans. Inf. Theory 50(10), 2315–2330 (2004).
[CrossRef]

Nat. Photonics (1)

N. Matsuda, R. Shimizu, Y. Mitsumori, H. Kosaka, and K. Edamatsu, “Observation of optical-fibre Kerr nonlinearity at the single-photon level,” Nat. Photonics 3(2), 95–98 (2009).
[CrossRef]

Nature (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] [PubMed]

Phys. Rev. A (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]

Phys. Rev. Lett. (2)

E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman, and S. Massar, “Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits,” Phys. Rev. Lett. 90(15), 157902 (2003).
[CrossRef] [PubMed]

G. J. Milburn, “Quantum optical Fredking gate,” Phys. Rev. Lett. 62(18), 2124–2127 (1989).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A (1)

A. Barenco, “A universal two-bit quantum computation,” Proc. R. Soc. Lond. A 449(1937), 679–683 (1995).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

D. Deutsch, “Quantum computational networks,” Proc. R. Soc. Lond. A Math. Phys. Sci. 425(1868), 73–90 (1989).
[CrossRef]

Science (2)

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

T. Brun, I. Devetak, and M.-H. Hsieh, “Correcting quantum errors with entanglement,” Science 314(5798), 436–439 (2006).
[CrossRef] [PubMed]

Other (3)

D. Gottesman, Stabilizer Codes and Quantum Error Correction. PhD Dissertation, California Institute of Technology, 1997.

F. Gaitan, Quantum Error Correction and Fault Tolerant Quantum Computing (CRC Press, 2008).

M. A. Neilsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

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Figures (5)

Fig. 1
Fig. 1

Integrated optics implementation of arbitrary single-qubit gate based on single directional coupler: (a) Barenco-type gate, and (b) Z-Y decomposition theorem based type. PBS/C: polarization beam splitter/combiner.

Fig. 2
Fig. 2

All-fiber implementation of CNOT gate: (a) probabilistic gate proposed in [7] and (b) deterministic gate proposed here.

Fig. 3
Fig. 3

Implementation of EPR preparation circuit in integrated optics.

Fig. 4
Fig. 4

Encoding and decoding circuits for quantum (6,2) LDPC code: (a) encoder cofiguration, and (b) decoder configuration. |δ1δ2〉 represents two information qubits.

Fig. 5
Fig. 5

EA LDPC codes of large girth against dual-containing LDPC codes.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

[ ψ H , o ψ V , o ] = U B [ ψ H ψ V ] ,     U B = [ e j α cos ( θ ) j e j ( α + ϕ ) sin ( θ ) j e j ( α ϕ ) sin ( θ ) e j α cos ( θ ) ] .
[ ψ H , o ψ V , o ] = U [ ψ H ψ V ] ,     U = [ cos ( γ 2 ) e j ( α β / 2 δ / 2 ) sin ( γ 2 ) e j ( α β / 2 + δ / 2 ) sin ( γ 2 ) e j ( α + β / 2 δ / 2 ) cos ( γ 2 ) e j ( α + β / 2 + δ / 2 ) ] .
S = [ 1 0 0 j ] .
T = [ 1 0 0 e j π / 4 ] .
H = 1 2 [ 1 1 1 1 ] .
[ c H , o = ( 1 / 3 ) ( 2 v c + c H ) ,     c V , o = ( 1 / 3 ) ( c V + t H + t V ) ] T .
[ c H , o c V , o t H , o t V , o ] = 1 2 [ 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 ] I H [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] K 1 2 [ 1 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 ] I H [ c H c V t H t V ]                             = U C N O T [ c H c V t H t V ] ,       U C N O T = [ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ]
Y = [ 0 j j 0 ] .
Z = [ 1 0 0 1 ] .
X = [ 0 1 1 0 ] .
| E P R i j = 1 2 [ 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 ] [ 1 0 1 0 0 1 0 1 1 0 1 0 0 1 0 1 ] | ψ i n = 1 2 [ c H t H + c V t V c H t V + c V t V c V t H c V t V c H t H c V t H ] .
| E P R 00 = [ 1 0 0 1 ] T / 2 = ( | 00 + | 11 ) / 2 .
A = [ H 0 | 0 H ] ,
H = [ 1     0     0     1     1     1 1     1     1     0     0     1 0     1     1     1     1     0 ] .
H 1 = [ 0     0     1     0     1     0     1 1     0     0     1     1     0     0 0     1     0     1     0     0     1 1     0     0     0     0     1     1 0     0     1     1     0     1     0 1     1     1     0     0     0     0 0     1     0     0     1     1     0 ] ,
A = [ 1 0 0 1 1 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 1 1 1 ] .
g 1 = X 1 X 4 X 5 X 6                               g 2 = X 2 X 3 X 4 X 5                                     g 3 = Z 1 Z 2 Z 3 Z 6                               g 4 = Z 1 Z 4 Z 5 Z 6 ,

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