Markus Grassl, Thomas Beth, and Thomas Pellizzari, "Codes for the Quantum Erasure Channel", Physical Review A, vol. 56, no. 1, pp. 33--38, July 1997, see also LANL preprint quant-ph/9610042.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....appears as final goal of human made information processing [20] but it is still an open question whether quantum mechanical computation is an outstanding solution or is just a fata morgana. In this field, applications such as quantum cryptography and quantum teleportation have been demonstrated [7]. Today, these ideas today are far away from an implementation. VI. CONCLUSION AND OUTLOOK Scientists and engineers engaged in the design of nanoelectronic systems and devices have to demonstrate the capability to realize complete powerful integrated circuits including memory functions and logic ....

T. Beth, M. Grassl, and T. Pellizzari, "Codes for quantum erasure channel," Phys. Rev. A, vol. 54, no. 4, pp. 2698--2703, 1996.

....execute basic operations, such as arithmetic and Boolean operations, that are executed in single steps by conventional machines. Furthermore, these basic operations should be executable in massively parallel fashion (that is, executed on multiple inputs in parallel) Guarnieri and Bancroft [GB96] developed a DNA based addition algorithm employing successive primer extension reactions to implement the carries and the Boolean logic required in binary addition (similar methods can be used for subtraction) Guarnieri, Fliss, and Bancroft prototyped [GFB96] the first BMC addition operations ....

....A.E. Condon, M.G. Lagally, L.M. Smith, R.M. Corn, Reducing Errors in DNA Computing by Appropriate Word Design, University of Wisconsin, Department of Chemistry, October 9, 1996. GBS87] Grunbaum, S. Branko, and G.C. Shepard Tilings and Patterns, H Freeman and Company, Chapter 11, 1987) GB96] Guarnieri, F. and C. Bancroft, Use of a Horizontal Chain Reaction for DNA Based Addition, Proceedings of the 2nd Annual DIMACS Meeting on DNA Based Computers. June 10 12, 1996, American Mathematical Society, Providence, RI (in press) 1996) GFB96] Guarnieri, F. Fliss, M. and C. Bancroft, ....

Grassl, M., Beth, Th. and Pellizzari, T., Codes for the quantum erasure channel. (Online preprint quantph /9610042.), (1996).

....be reversed by a simple unitary transformation. In fact, since we know before the syndrome measurement that the damaged qubit is in a particular position within the code block, we can apply a streamlined version of error correction designed to diagnose and reverse the error at that known position (Grassl et al. 1996). 9 Dream machine Let s recall some of the important assumptions that we made in our estimate of the accuracy threshold: ffl Random errors. We have assumed that the errors have no systematic component. 12 This assumption enables us to add probabilities, rather than amplitudes, to estimate how ....

Grassl, M., Beth, Th. & Pellizzari, T. 1996 Codes for the quantum erasure channel. (Online preprint quant-ph/9610042.) Kitaev, A. Yu. 1996a Quantum error correction with imperfect gates, preprint.

....for a single qubit equation (1) reads sys sys sys sys (where , and are the Pauli matrices) For a small error probability , errors affecting a small number of qubits are more likely than errors involving a large number of qubits. A related quantum channel is the quantum erasure channel [5]. Again, the quantum state is transmitted undisturbed with probability . In case of an error, the quantum state is replaced by a quantum state that is orthogonal to all other quantum states. Equation (1) now reads sys sys Similar to classical erasures, the state indicates that an error occurred, ....

Markus Grassl, Thomas Beth, and Thomas Pellizzari, "Codes for the Quantum Erasure Channel", Physical Review A, vol. 56, no. 1, pp. 33--38, July 1997, see also LANL preprint quant-ph/9610042.

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M. Grassl, T. Beth, and T. Pellizzari, Codes for the Quantum Erasure Channel, Physical Review A, 56 (1997), pp. 33--38.

No context found.

Grassl, M., Beth, Th. and Pellizzari, T., Codes for the quantum erasure channel. (Online preprint quant-ph/9610042.), (1996).

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