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Limits to error correction in quantum chaos.

P G Silvestrov1, H Schomerus, C W Beenakker

  • 1Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands and Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia.

Physical Review Letters
|June 1, 2001
PubMed
Summary
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This study shows that quantum error correction can efficiently fix errors in entangled spin states, even with unknown energy variations. The correction time is independent of qubit number, offering a robust method for quantum information preservation.

Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Spin Systems

Background:

  • Entangled spin states are crucial for quantum computation but susceptible to errors.
  • Unknown local variations in Zeeman (B) and spin-spin (J) energies disrupt quantum states.

Purpose of the Study:

  • To investigate quantum error correction methods for entangled spin states.
  • To analyze the impact of unknown energy variations on quantum state fidelity.
  • To determine the time scales for error recovery.

Main Methods:

  • Utilizing a non-degenerate quantum error-correcting code.
  • Analyzing error rates (kappa) and energy parameters (B, J).
  • Calculating recovery time (t(R)) based on quantum dynamics.

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Main Results:

  • High-fidelity recovery of the original entangled state is achievable.
  • Recovery time t(R) scales approximately as hbar/(2*pi*kappa^(1/2)*max(B,J)).
  • Correction time is independent of the number of encoded qubits.

Conclusions:

  • Quantum error correction is effective against unknown local energy variations in spin systems.
  • The efficiency of error correction is robust and does not scale with system size.
  • Hamiltonian chaos influences code complexity but not the fundamental recovery time scale.