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network of stochastic oscillators
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High-fidelity qubit initialization is of significance for efficient error correction in fault tolerant quantum algorithms. Combining two best worlds, speed and robustness, to achieve high-fidelity state preparation and manipulation is challenging in quantum systems, where qubits are closely spaced in frequency. Motivated by the concept of shortcut to adiabaticity, we theoretically propose the shortcut pulses via inverse engineering and further optimize the pulses with respect to systematic errors in frequency detuning and Rabi frequency. Such protocol, relevant to frequency selectivity, is applied to rare-earth ions qubit system, where the excitation of frequency-neighboring qubits should be prevented as well. Furthermore, comparison with adiabatic complex hyperbolic secant pulses shows that these dedicated initialization pulses can reduce the time that ions spend in the excited state by a factor of 6, which is important in coherence time limited systems to approach an error rate manageable by quantum error correction. The approach may also be applicable to superconducting qubits, and any other systems where qubits are addressed in frequency.
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n/a
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n/a
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injection locked oscillator
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Lock-on; streamwise oscillation; transverse oscillation; fluid forces
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classical Van der Pol oscillator.
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Modal analysis, complex modes, low frequency oscillations, participation factors, electrical power systems, electromechanical transients, small-signal stability, transient stability
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FIGURE 6. Hyalessa maculaticollis. Echemes structure. A, Power frequency spectrum represented with overlay of 52 spectra computed from echemes with high amplitude oscillations showing a dominant frequency marked by F3. B, Detailed oscillogram showing the first echeme with low amplitude oscillations and the second echeme with high amplitude oscillations. C, Power frequency spectrum represented with overlay of 71 spectra computed from echemes with low amplitude oscillations showing dominant frequencies marked by F1 and F2.
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Objective. Oscillations are an important aspect of brain activity, but they often have a low signal- to-noise ratio (SNR) due to source-to-electrode mixing with competing brain activity and noise. Filtering can improve the SNR of narrowband signals, but it introduces ringing effects that may masquerade as genuine oscillations, leading to uncertainty as to the true oscillatory nature of the phenomena. Likewise, time–frequency analysis kernels have a temporal extent that blurs the time course of narrowband activity, introducing uncertainty as to timing and causal relations between events and/or frequency bands. Approach. Here, we propose a methodology that reveals narrowband activity within multichannel data such as electroencephalography, magnetoencephalography, electrocorticography or local field potential. The method exploits the between-channel correlation structure of the data to suppress competing sources by joint diagonalization of the covariance matrices of narrowband filtered and unfiltered data. Main results. Applied to synthetic and real data, the method effectively extracts narrowband components at unfavorable SNR. Significance. Oscillatory components of brain activity, including weak sources that are hard or impossible to observe using standard methods, can be detected and their time course plotted accurately. The method avoids the temporal artifacts of standard filtering and time–frequency analysis methods with which it remains complementary.
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