dynamical decoupling

{{Short description|Control technique for improving qubit coherence in quantum computing}}

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.{{Cite journal |last1=Viola |first1=L. |author1-link=Lorenza Viola |last2=Lloyd |first2=S. |author-link2=Seth Lloyd |year=1998 |title=Dynamical suppression of decoherence in two-state quantum systems |journal=Physical Review A |volume=58 |issue=4 |pages=2733–2744 |arxiv=quant-ph/9803057 |bibcode=1998PhRvA..58.2733V |doi=10.1103/PhysRevA.58.2733 |s2cid=34939261}}{{Cite journal | last1 = Viola | first1 = L. | author1-link = Lorenza Viola | last2 = Knill | first2 = E.| last3 = Lloyd | first3 = S.| doi = 10.1103/PhysRevLett.82.2417| title = Dynamical Decoupling of Open Quantum Systems | journal = Physical Review Letters | volume = 82 | issue = 12 | pages = 2417–2421 | year = 1999| bibcode=1999PhRvL..82.2417V| arxiv = quant-ph/9809071| s2cid = 2566091 }} Different schemes exist for designing DD protocols that use realistic bounded-strength control pulses,{{Cite journal | last1 = Viola | first1 = L. | author1-link = Lorenza Viola | last2 = Knill | first2 = E. | doi = 10.1103/PhysRevLett.90.037901 | title = Robust Dynamical Decoupling of Quantum Systems with Bounded Controls | journal = Physical Review Letters | volume = 90 | issue = 3 | year = 2003 | pmid = 12570525| bibcode=2003PhRvL..90c7901V | page=037901| arxiv = quant-ph/0208056 | s2cid = 32354220 }} as well as for achieving high-order error suppression,{{Cite journal |last1=Khodjasteh |first1=K. |last2=Lidar |first2=D. |author-link2=Daniel Lidar |year=2005 |title=Fault-Tolerant Quantum Dynamical Decoupling |journal=Physical Review Letters |volume=95 |issue=18 |pages=180501 |arxiv=quant-ph/0408128 |bibcode=2005PhRvL..95r0501K |doi=10.1103/PhysRevLett.95.180501 |pmid=16383882 |s2cid=9754216}}{{Cite journal | last1 = Uhrig | first1 = G. S. | doi = 10.1103/PhysRevLett.98.100504 | title = Keeping a Quantum Bit Alive by Optimized π-Pulse Sequences | journal = Physical Review Letters | volume = 98 | issue = 10 | pages = 100504 | year = 2007 | pmid = 17358521 | bibcode=2007PhRvL..98j0504U| arxiv = quant-ph/0609203| s2cid = 14729824 }} and for making DD compatible with quantum gates.{{Cite journal | last1 = Viola | first1 = L. | author1-link = Lorenza Viola | last2 = Lloyd | first2 = S. | last3 = Knill | first3 = E. | doi = 10.1103/PhysRevLett.83.4888 | title = Universal Control of Decoupled Quantum Systems | journal = Physical Review Letters | volume = 83 | issue = 23 | pages = 4888–4891 | year = 1999 | bibcode=1999PhRvL..83.4888V| arxiv = quant-ph/9906094 | s2cid = 43014936 }}{{Cite journal | last1 = West | first1 = J. R. | last2 = Lidar | first2 = D. A. | last3 = Fong | first3 = B. H. | last4 = Gyure | first4 = M. F. | title = High Fidelity Quantum Gates via Dynamical Decoupling | doi = 10.1103/PhysRevLett.105.230503 | journal = Physical Review Letters | volume = 105 | issue = 23 | year = 2011 | pmid = 21231440| bibcode=2010PhRvL.105w0503W | page=230503| arxiv = 0911.2398 | s2cid = 18535780 }}{{Cite journal | last1 = Yang | first1 = W. | last2 = Wang | first2 = Z. Y. | last3 = Liu | first3 = R. B. | title = Preserving qubit coherence by dynamical decoupling | doi = 10.1007/s11467-010-0113-8 | journal = Frontiers of Physics | volume = 6 | pages = 2–14 | year = 2010 | issue = 1 | bibcode = 2011FrPhy...6....2Y | arxiv = 1007.0623 | s2cid = 118681892 }} In spin systems in particular, commonly used protocols for dynamical decoupling include the Carr-Purcell and the Carr-Purcell-Meiboom-Gill (CPMG) schemes.{{Cite journal|last1=Carr|first1=H. Y.|last2=Purcell|first2=E. M.|date=1954-05-01|title=Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments|journal=Physical Review|volume=94|issue=3|pages=630–638|doi=10.1103/PhysRev.94.630|bibcode=1954PhRv...94..630C}}{{Cite journal|last1=Meiboom|first1=S.|last2=Gill|first2=D.|date=1958-08-01|title=Modified Spin-Echo Method for Measuring Nuclear Relaxation Times|journal=Review of Scientific Instruments|volume=29|issue=8|pages=688–691|doi=10.1063/1.1716296|issn=0034-6748|bibcode=1958RScI...29..688M}} 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.{{Cite journal | last1 = Khodjasteh | first1 = K. | last2 = Sastrawan | first2 = J. | last3 = Hayes | first3 = D. | last4 = Green | first4 = T. J. | last5 = Biercuk | first5 = M. J. | last6 = Viola | first6 = L. | author6-link = Lorenza Viola | title = Designing a practical high-fidelity long-time quantum memory | doi = 10.1038/ncomms3045 | journal = Nature Communications | volume = 4 | year = 2013 | pmid = 23784079| page=2045| arxiv = 1206.6087 | bibcode = 2013NatCo...4.2045K | s2cid = 205317873 }}

Dynamical decoupling has also been studied in a classical context for two coupled pendulums whose oscillation frequencies are modulated in time.{{Cite journal|last1=Salerno|first1=Grazia|last2=Carusotto|first2=Iacopo|date=2014|title=Dynamical decoupling and dynamical isolation in temporally modulated coupled pendulums|url=http://stacks.iop.org/0295-5075/106/i=2/a=24002|journal=EPL|language=en|volume=106|issue=2|pages=24002|doi=10.1209/0295-5075/106/24002|issn=0295-5075|arxiv=1401.3978|bibcode=2014EL....10624002S|s2cid=119236165 }}