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Universality proof and analysis of generalized nested Uhrig dynamical decoupling
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10.1063/1.4769382
/content/aip/journal/jmp/53/12/10.1063/1.4769382
http://aip.metastore.ingenta.com/content/aip/journal/jmp/53/12/10.1063/1.4769382

Figures

Image of FIG. 1.
FIG. 1.

A graphical way to see the normalized pulse timings and pulse intervals for the 2-layer NUDD scheme where both sequence orders are 4. The red bars indicate the pulse timings of the first UDD layer with control pulse type Ω1, and the blue bars are the pulse timings of the second UDD layer with control pulse type Ω2.

Image of FIG. 2.
FIG. 2.

Performance of NUDD as a function of the minimum pulse interval τ for the two-qubit system specified by Eqs. (88) and (89), averaged over 15 random realizations of . Error bars are included, but are very small. A four-layer construction is utilized to address all system-bath interactions, where the MOOS sets are chosen as Eq. (92) in (a) and (b), and Eq. (94) in (c) and (d). The orders of the first three layers are identical: N j = N 123, j = 1, 2, 3 and are varied as N 123 = 1, 2, …, 6. In particular, the outer layer sequence order is chosen as N 4 = 3 in (a) and (c), and N 4 = 4 in (b) and (d). Linear interpolation from log10 Jτ = −10 to approximately log10 Jτ = −2 confirms the MOOS-independent scaling , , for all simulations.

Tables

Generic image for table
Table I.

The first column classifies 2 -type errors into four groups by two values, and r , where and are defined in Eq. (49). The second column shows the function types of the Fourier expansion of the -type error modulation functions.

Generic image for table
Table II.

The second column shows the function type of the resulting integrand of after n − 1 integrations. The third column shows the maximum order up to which the function type of the resulting integrand of does not contain a constant term.

Generic image for table
Table III.

16 error types for the 4-layer NUDD scheme.

Generic image for table
Table IV.

The 16 error types for the 4-layer NUDD scheme with the MOOS {I ⊗ σ z , I ⊗ σ x , σ z  ⊗ I, σ x  ⊗ I}.

Generic image for table
Table V.

The 16 error types for the 4-layer NUDD scheme with the MOOS {σ z  ⊗ σ z , I ⊗ σ x , σ z  ⊗ I, σ x  ⊗ I}.

Generic image for table
Table VI.

For the case with N 1 = 2, N 2 = 4, N 3 = 6, N 4 = 8, analytical and numerical decoupling orders for all error types are in complete agreement. The analytical overall decoupling order also agrees with the actual overall decoupling order.

Generic image for table
Table VII.

For the case with N 1 = 2, N 2 = 4, N 3 = 6, N 4 = 3, analytical and numerical decoupling order (displayed in normal font) are in complete agreement for all error types. The analytical overall decoupling order N = min [2, 4, 6, 3] = 2 also agrees with the actual overall decoupling order. The difference between the naive (displayed in italics) and the actual decoupling orders comes from outer-odd-UDD suppression effect.

Generic image for table
Table VIII.

For the case with N 1 = 7, N 2 = 5, N 3 = 3, N 4 = 1 analytical and numerical decoupling order for all error types are in complete agreement. The analytical overall decoupling order also agrees with the actual overall decoupling order. The difference between the naive (marked in italics) and the actual decoupling orders (in normal font) comes from outer-odd-UDD suppression effect.

Generic image for table
Table IX.

For the case with N 1 = 2, N 2 = 4, N 3 = 1, N 4 = 6, the analytical overall decoupling order agrees with the actual overall decoupling order. However, the numerical decoupling order (marked in normal font) and our analytical predictions (marked in boldface) have different values for error types in the third column. Naive decoupling order is marked in italics.

Generic image for table
Table X.

For the case with N 1 = 1, N 2 = 3, N 3 = 5, N 4 = 7, the analytical overall decoupling order agrees with the actual overall decoupling order. However, for some error types, our analytical predictions (marked in boldface) only provide lower bounds for their exact decoupling orders (marked in normal font). “Naive” decoupling orders are marked in italics.

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/content/aip/journal/jmp/53/12/10.1063/1.4769382
2012-12-18
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Universality proof and analysis of generalized nested Uhrig dynamical decoupling
http://aip.metastore.ingenta.com/content/aip/journal/jmp/53/12/10.1063/1.4769382
10.1063/1.4769382
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