Limits to error correction in quantum chaos.
We study the correction of errors that have accumulated in an entangled state of spins as a result of unknown local variations in the Zeeman energy ( B) and spin-spin interaction energy ( J). A nondegenerate code with error rate kappa can recover the original state with high fidelity within a time t(R) approximately Planck's over 2pikappa(1/2)/max(B,J)-independent of the number of encoded qubits. Whether the Hamiltonian is chaotic or not does not affect this time scale, but it does affect the complexity of the error-correcting code.
Silvestrov
P G
PG
Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands and Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia.
Schomerus
H
H
Beenakker
C W
CW