Dynamical decoupling explained

Dynamical decoupling (DD) is an open-loop quantum control technique employed in quantum computing to suppress decoherence by taking advantage of rapid, time-dependent control modulation. In its simplest form, DD is implemented by periodic sequences of instantaneous control pulses, whose net effect is to approximately average the unwanted system-environment coupling to zero.[1] [2] Different schemes exist for designing DD protocols that use realistic bounded-strength control pulses,[3] as well as for achieving high-order error suppression,[4] [5] and for making DD compatible with quantum gates.[6] [7] [8] In spin systems in particular, commonly used protocols for dynamical decoupling include the Carr-Purcell and the Carr-Purcell-Meiboom-Gill schemes.[9] [10] They are based on the Hahn spin echo technique of applying periodic pulses to enable refocusing and hence extend the coherence times of qubits.

Periodic repetition of suitable high-order DD sequences may be employed to engineer a 'stroboscopic saturation' of qubit coherence, or coherence plateau, that can persist in the presence of realistic noise spectra and experimental control imperfections. This permits device-independent, high-fidelity data storage for computationally useful periods with bounded error probability.[11]

Dynamical decoupling has also been studied in a classical context for two coupled pendulums whose oscillation frequencies are modulated in time.[12]

Notes and References

  1. Viola . L. . Lorenza Viola . Lloyd . S. . Seth Lloyd . 1998 . Dynamical suppression of decoherence in two-state quantum systems . Physical Review A . 58 . 4 . 2733–2744 . quant-ph/9803057 . 1998PhRvA..58.2733V . 10.1103/PhysRevA.58.2733 . 34939261.
  2. Viola . L. . Lorenza Viola . Knill . E.. Lloyd . S.. 10.1103/PhysRevLett.82.2417. Dynamical Decoupling of Open Quantum Systems . Physical Review Letters . 82 . 12 . 2417–2421 . 1999. 1999PhRvL..82.2417V. quant-ph/9809071. 2566091 .
  3. Viola . L. . Lorenza Viola . Knill . E. . 10.1103/PhysRevLett.90.037901 . Robust Dynamical Decoupling of Quantum Systems with Bounded Controls . Physical Review Letters . 90 . 3 . 2003 . 12570525. 2003PhRvL..90c7901V . 037901. quant-ph/0208056 . 32354220 .
  4. Khodjasteh . K. . Lidar . D. . Daniel Lidar . 2005 . Fault-Tolerant Quantum Dynamical Decoupling . Physical Review Letters . 95 . 18 . 180501 . quant-ph/0408128 . 2005PhRvL..95r0501K . 10.1103/PhysRevLett.95.180501 . 16383882 . 9754216.
  5. Uhrig . G. S. . 10.1103/PhysRevLett.98.100504 . Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences . Physical Review Letters . 98 . 10 . 100504 . 2007 . 17358521 . 2007PhRvL..98j0504U. quant-ph/0609203. 14729824 .
  6. Viola . L. . Lorenza Viola . Lloyd . S. . Knill . E. . 10.1103/PhysRevLett.83.4888 . Universal Control of Decoupled Quantum Systems . Physical Review Letters . 83 . 23 . 4888–4891 . 1999 . 1999PhRvL..83.4888V. quant-ph/9906094 . 43014936 .
  7. West . J. R. . Lidar . D. A. . Fong . B. H. . Gyure . M. F. . High Fidelity Quantum Gates via Dynamical Decoupling . 10.1103/PhysRevLett.105.230503 . Physical Review Letters . 105 . 23 . 2011 . 21231440. 2010PhRvL.105w0503W . 230503. 0911.2398 . 18535780 .
  8. Yang . W. . Wang . Z. Y. . Liu . R. B. . Preserving qubit coherence by dynamical decoupling . 10.1007/s11467-010-0113-8 . Frontiers of Physics . 6 . 2–14 . 2010 . 1 . 2011FrPhy...6....2Y . 1007.0623 . 118681892 .
  9. Carr. H. Y.. Purcell. E. M.. 1954-05-01. Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments. Physical Review. 94. 3. 630–638. 10.1103/PhysRev.94.630. 1954PhRv...94..630C.
  10. Meiboom. S.. Gill. D.. 1958-08-01. Modified Spin-Echo Method for Measuring Nuclear Relaxation Times. Review of Scientific Instruments. 29. 8. 688–691. 10.1063/1.1716296. 0034-6748. 1958RScI...29..688M.
  11. Khodjasteh . K. . Sastrawan . J. . Hayes . D. . Green . T. J. . Biercuk . M. J. . Viola . L. . Lorenza Viola . Designing a practical high-fidelity long-time quantum memory . 10.1038/ncomms3045 . Nature Communications . 4 . 2013 . 23784079. 2045. 1206.6087 . 2013NatCo...4.2045K . 205317873 .
  12. Salerno. Grazia. Carusotto. Iacopo. 2014. Dynamical decoupling and dynamical isolation in temporally modulated coupled pendulums. EPL. en. 106. 2. 24002. 10.1209/0295-5075/106/24002. 0295-5075. 1401.3978. 2014EL....10624002S. 119236165 .

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