ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

QUANTUM INFORMATION SCIENCE THEORY

QUANTUM ERROR CORRECTION & PURIFICATION

The ability to carry out coherent quantum operation even in the presence of inevitable noise is a key requirement for quantum information processing. Error correcting codes allow one to reduce errors by suitable encoding of logical qubits into larger systems. It has been shown that, with operations of accuracy above some threshold, the ideal quantum algorithms can be implemented. Recent ideas involving error correcting teleportation have made the threshold estimate more favorable by several orders of magnitude. This path has to be continued and adapted to realistic error models and to alternative models of quantum computation like the adiabatic model or the cluster model (see section 4.3.3).

At the same time, a fruitful connection to the theory of entanglement purification is emerging, which has been developed primarily in the context of quantum communication, and has been used in protocols such as the quantum repeater. Entanglement purification is a method to "distill" from a large ensemble of impure (low-fidelity) entangled states a smaller ensemble of pure (high-fidelity) entangled states. It seems that appropriately generalized procedures can be employed also in general quantum computation (e.g. for quantum gate purification, or for the generation of high fidelity resource states) while benefiting from the relaxed thresholds that exist for entanglement purification.

Key references

[1] A.M. Steane, General theory of quantum error correction and fault tolerance, in 'The physics of quantum information', (D. Bouwmeester, A. Ekert, A. Zeilinger, eds.), pp. 242-252, Springer, Berlin (2000).

[2] J. Preskill, Fault-tolerant quantum computation, in 'Introduction to quantum computation and information', (H.K. Lo, S. Popescu, T. Spiller, eds.) pp. 213-269, World Scientific, Singapore (1998).

[3] C.H. Bennett, D.P. [=DiVincenzo=], J. A. Smolin, and W. K. Wootters, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54, 3824 (1996).

[4] D. Deutsch, A. Ekert, R. Josza, C. Macchiavello, S. Popescu, and A. Sanpera, Quantum privacy amplification and the security of quantum cryptography over noisy channels, Phys. Rev. Lett. 77, 2818 (1996).

[5] H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81, 5932 (1998).

[6] A.M. Steane, Overhead and noise threshold of fault-tolerant quantum error correction, Phys. Rev. A 68, 042322 (2003).

[7] E. Knill, Quantum computing with very noisy devices, quant-ph/0410199, http://www.arxiv.org.