Abstract

I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach–Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Neilsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000).
  2. D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
    [CrossRef]
  3. T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
    [CrossRef] [PubMed]
  4. T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
    [CrossRef]

2006 (1)

T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
[CrossRef] [PubMed]

2004 (1)

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
[CrossRef]

2002 (1)

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

Bell, T. B.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

Brun, T.

T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
[CrossRef] [PubMed]

Chuang, I. L.

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

Devetak, I.

T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
[CrossRef] [PubMed]

Hsieh, M.-H.

T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
[CrossRef] [PubMed]

Langford, N. K.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

MacKay, D. J. C.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
[CrossRef]

McFadden, P. L.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
[CrossRef]

Mitchison, G.

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
[CrossRef]

Neilsen, M. A.

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

Ralph, T. C.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

White, A. G.

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory 50, 2315 (2004).
[CrossRef]

Phys. Rev. A (1)

T. C. Ralph, N. K. Langford, T. B. Bell, and A. G. White, Phys. Rev. A 65, 062324 (2002).
[CrossRef]

Science (1)

T. Brun, I. Devetak, and M.-H. Hsieh, Science 314, 436 (2006).
[CrossRef] [PubMed]

Other (1)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

EA quantum code principle.

Fig. 2
Fig. 2

Encoding and decoding circuits for (5, 2) EA-LDPC code: (a) encoder configuration, and (b) decoder configuration. The states | δ 1 and | δ 2 are the information states.

Fig. 3
Fig. 3

Implementation of basic quantum gates needed for EA-QECC in integrated optics based on a MZI: (a) Hadamard gate, and (b) CNOT gate. PBS/C, polarization-beam splitter/combiner.

Fig. 4
Fig. 4

EA quantum LDPC codes from m-dimensional projective geometries.

Fig. 5
Fig. 5

Bit error rates (BER) versus crossover probability on a binary symmetric channel. The results are obtained assuming that the assisted entanglement state is a maximal entanglement state.

Equations (5)

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

A = ( H 0 0 H ) , H = [ 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 ] .
A = ( H 0 0 H ) , H = ( 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 | 0 1 1 ) .
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 ] .
[ ψ o , H ψ o , V ] = U [ ψ H ψ V ] , U = [ sin ( ϕ 2 ) cos ( ϕ 2 ) cos ( ϕ 2 ) sin ( ϕ 2 ) ] .
( c H , o c V , o t H , o t V , o ) = ( 1 0 0 0 0 1 0 0 0 0 sin ( ϕ 2 ) e j α cos ( ϕ 2 ) 0 0 cos ( ϕ 2 ) e j α sin ( ϕ 2 ) ) ( c H c V t H t V ) ,

Metrics