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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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frequency stability... Colpitts oscillator
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Portico Frequency of free oscillations Resonance Stiffness matrix method.
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frequency stability... CMOS, x frequency stability, delay time... ring oscillator
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Lock-on; streamwise oscillation; transverse oscillation; fluid forces
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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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FIGURE 8. Hyalessa fuscata. Echemes structure. A, Power frequency spectrum represented with overlay of 47 spectra computed from echemes with high amplitude oscillations showing dominant frequencies marked by F1, F2, F3 and F4. 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 38 spectra computed from echemes with low amplitude oscillations showing dominant frequencies marked by F1 and F2.
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oscillation phase shift
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n/a
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The intrinsic noise of the best quartz crystal resonators is significantly less than the noise observed in oscillators employing these resonators Several problem areas common to traditional designs are pointed out and a new approach is suggested for their solution. Two circuits are described which frequency lock a spectrally pure quartz crystal oscillator to an independent quartz crystal resonator. The performance of the composite system is predicted based on the measured performance of its components.
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