Dynamical decoupling

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]

References
  1. Viola, L.; Lloyd, S. (1998). "Dynamical suppression of decoherence in two-state quantum systems". Physical Review A. 58 (4): 2733–2744. arXiv:quant-ph/9803057. Bibcode:1998PhRvA..58.2733V. doi:10.1103/PhysRevA.58.2733.
  2. Viola, L.; Knill, E.; Lloyd, S. (1999). "Dynamical Decoupling of Open Quantum Systems". Physical Review Letters. 82 (12): 2417–2421. arXiv:quant-ph/9809071. Bibcode:1999PhRvL..82.2417V. doi:10.1103/PhysRevLett.82.2417.
  3. Viola, L.; Knill, E. (2003). "Robust Dynamical Decoupling of Quantum Systems with Bounded Controls". Physical Review Letters. 90 (3): 037901. arXiv:quant-ph/0208056. Bibcode:2003PhRvL..90c7901V. doi:10.1103/PhysRevLett.90.037901. PMID 12570525.
  4. Khodjasteh, K.; Lidar, D. (2005). "Fault-Tolerant Quantum Dynamical Decoupling". Physical Review Letters. 95 (18): 180501. arXiv:quant-ph/0408128. Bibcode:2005PhRvL..95r0501K. doi:10.1103/PhysRevLett.95.180501. PMID 16383882.
  5. Uhrig, G. S. (2007). "Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences". Physical Review Letters. 98 (10): 100504. arXiv:quant-ph/0609203. Bibcode:2007PhRvL..98j0504U. doi:10.1103/PhysRevLett.98.100504.
  6. Viola, L.; Lloyd, S.; Knill, E. (1999). "Universal Control of Decoupled Quantum Systems". Physical Review Letters. 83 (23): 4888–4891. arXiv:quant-ph/9906094. Bibcode:1999PhRvL..83.4888V. doi:10.1103/PhysRevLett.83.4888.
  7. West, J. R.; Lidar, D. A.; Fong, B. H.; Gyure, M. F. (2011). "High Fidelity Quantum Gates via Dynamical Decoupling". Physical Review Letters. 105 (23): 230503. arXiv:0911.2398. Bibcode:2010PhRvL.105w0503W. doi:10.1103/PhysRevLett.105.230503. PMID 21231440.
  8. Yang, W.; Wang, Z. Y.; Liu, R. B. (2010). "Preserving qubit coherence by dynamical decoupling". Frontiers of Physics. 6: 2–14. arXiv:1007.0623. Bibcode:2011FrPhy...6....2Y. doi:10.1007/s11467-010-0113-8.
  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. Bibcode:1954PhRv...94..630C. doi:10.1103/PhysRev.94.630.
  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. Bibcode:1958RScI...29..688M. doi:10.1063/1.1716296. ISSN 0034-6748.
  11. Khodjasteh, K.; Sastrawan, J.; Hayes, D.; Green, T. J.; Biercuk, M. J.; Viola, L. (2013). "Designing a practical high-fidelity long-time quantum memory". Nature Communications. 4: 2045. arXiv:1206.6087. Bibcode:2013NatCo...4.2045K. doi:10.1038/ncomms3045. PMID 23784079.
  12. Salerno, Grazia; Carusotto, Iacopo (2014). "Dynamical decoupling and dynamical isolation in temporally modulated coupled pendulums". EPL. 106 (2): 24002. arXiv:1401.3978. Bibcode:2014EL....10624002S. doi:10.1209/0295-5075/106/24002. ISSN 0295-5075.
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