No-go theorems and optimization of dynamical decoupling against noise with soft cutoff

Abstract

We study the performance of dynamical decoupling in suppressing decoherence caused by soft-cutoff Gaussian noise, using short-time expansion of the noise correlations and numerical optimization. For the noise with soft cutoff at high frequencies, there exists no dynamical decoupling scheme to eliminate the decoherence to arbitrary orders of the short time, regardless of the timing or pulse shaping of the control under the population conserving condition. We formulate the equations for optimizing pulse sequences that minimize decoherence up to the highest possible order of the short time for the noise correlations with odd power terms in the short-time expansion. In particular, we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in the short-time limit for the noise correlations with a linear order term in the time expansion.

Preserving entanglement and nonlocality in solid-state qubits by dynamical decoupling

“…Notice that we have short t ESD since the problem addressed in this paper, namely 1/f noise at pure dephasing, is the "worse scenario" for dephasing. In a single qubit, the effects of noise with a sharp uv cutoff γ M are strongly suppressed if 2n/t > γ M , with UDD yielding high fidelity at short times and CP being more efficient at longer times [28,76,77]. We find qualitatively the same behavior for entanglement, except that we consider a soft-uv cutoff obtaining only a partial noise suppression.…”

Anomalous behavior of control pulses in presence of noise with singular autocorrelation

“…They are manifest in the spectral density of cusp-like autocorrelations displaying high-frequency tails ∝ 1/ω 2 which do not converge quickly, i.e., exponentially, to zero. Similar findings have been made before in the analysis in the design of sequences of ideal pulses [14,15,17,18,61]. The sequences could not be improved beyond a certain scaling if the power spectrum of the noise displayed soft high-frequency cutoffs following power laws.…”

“…It is plausible to attribute it to the singularity in the autocorrelation. This view is supported by a similar observation made recently in the analysis of sequences of ideal pulses [14,15,17,18,61].…”

Environmental noise spectroscopy with qubits subjected to dynamical decoupling

“…When this is not the case, e.g. when the noise spectrum has a power-law tail (or when the bandwidth of quantum environment is larger than 1/T [80,81]), CP sequence leads to stronger decoherence suppression [7,9,30]. It should be clear now that an accurate measurement of W (T ) (and thus χ(T )) is a source of information on the noise spectrum, but due to the integral form of χ(T ) it is not possible, in general, to reconstruct a completely unknown S(ω) from a signal measured under a given DD sequence.…”