waveforms ========= .. py:module:: quantify_scheduler.waveforms .. autoapi-nested-parse:: Contains function to generate most basic waveforms. These functions are intended to be used to generate waveforms defined in the :mod:`~quantify_scheduler.operations.pulse_library`. Examples of waveforms that are too advanced are flux pulses that require knowledge of the flux sensitivity and interaction strengths and qubit frequencies. Module Contents --------------- Functions ~~~~~~~~~ .. autoapisummary:: quantify_scheduler.waveforms.square quantify_scheduler.waveforms.square_imaginary quantify_scheduler.waveforms.ramp quantify_scheduler.waveforms.staircase quantify_scheduler.waveforms.soft_square quantify_scheduler.waveforms.chirp quantify_scheduler.waveforms.drag quantify_scheduler.waveforms.sudden_net_zero quantify_scheduler.waveforms.interpolated_complex_waveform quantify_scheduler.waveforms.rotate_wave quantify_scheduler.waveforms.skewed_hermite .. py:function:: square(t: Union[numpy.ndarray, List[float]], amp: Union[float, complex]) -> numpy.ndarray Generate a square pulse. .. py:function:: square_imaginary(t: Union[numpy.ndarray, List[float]], amp: Union[float, complex]) -> numpy.ndarray Generate a square pulse with imaginary amplitude. .. py:function:: ramp(t, amp, offset=0) -> numpy.ndarray Generate a ramp pulse. .. py:function:: staircase(t: Union[numpy.ndarray, List[float]], start_amp: Union[float, complex], final_amp: Union[float, complex], num_steps: int) -> numpy.ndarray Ramps from zero to a finite value in discrete steps. :param t: Times at which to evaluate the function. :param start_amp: Starting amplitude. :param final_amp: Final amplitude to reach on the last step. :param num_steps: Number of steps to reach final value. :returns: The real valued waveform. .. py:function:: soft_square(t, amp) A softened square pulse. :param t: Times at which to evaluate the function. :param amp: Amplitude of the pulse. .. py:function:: chirp(t: numpy.ndarray, amp: float, start_freq: float, end_freq: float) -> numpy.ndarray Produces a linear chirp signal. The frequency is determined according to the relation: .. math: f(t) = ct + f_0, c = \frac{f_1 - f_0}{T} The waveform is produced simply by multiplying with a complex exponential. :param t: Times at which to evaluate the function. :param amp: Amplitude of the envelope. :param start_freq: Start frequency of the Chirp. :param end_freq: End frequency of the Chirp. :returns: The complex waveform. .. py:function:: drag(t: numpy.ndarray, G_amp: float, D_amp: float, duration: float, nr_sigma: int = 3, phase: float = 0, subtract_offset: str = 'average') -> numpy.ndarray Generates a DRAG pulse consisting of a Gaussian :math:`G` as the I- and a Derivative :math:`D` as the Q-component (:cite:t:`motzoi_simple_2009` and :cite:t:`gambetta_analytic_2011`). All inputs are in s and Hz. phases are in degree. :math:`G(t) = G_{amp} e^{-(t-\mu)^2/(2\sigma^2)}`. :math:`D(t) = -D_{amp} \frac{(t-\mu)}{\sigma} G(t)`. .. note: One would expect a factor :math:`1/\sigma^2` in the prefactor of :math:`D(t)`, we absorb this in the scaling factor :math:`D_{amp}` to ensure the derivative component is scale invariant with the duration of the pulse. :param t: Times at which to evaluate the function. :param G_amp: Amplitude of the Gaussian envelope. :param D_amp: Amplitude of the derivative component, the DRAG-pulse parameter. :param duration: Duration of the pulse in seconds. :param nr_sigma: After how many sigma the Gaussian is cut off. :param phase: Phase of the pulse in degrees. :param subtract_offset: Instruction on how to subtract the offset in order to avoid jumps in the waveform due to the cut-off. - 'average': subtract the average of the first and last point. - 'first': subtract the value of the waveform at the first sample. - 'last': subtract the value of the waveform at the last sample. - 'none', None: don't subtract any offset. :returns: complex waveform .. py:function:: sudden_net_zero(t: numpy.ndarray, amp_A: float, amp_B: float, net_zero_A_scale: float, t_pulse: float, t_phi: float, t_integral_correction: float) Generates the sudden net zero waveform from :cite:t:`negirneac_high_fidelity_2021`. The waveform consists of a square pulse with a duration of half ``t_pulse`` and an amplitude of ``amp_A``, followed by an idling period (0 V) with duration ``t_phi``, followed again by a square pulse with amplitude ``-amp_A * net_zero_A_scale`` and a duration of half ``t_pulse``, followed by a integral correction period with duration ``t_integral_correction``. The last sample of the first pulse has amplitude ``amp_A * amp_B``. The first sample of the second pulse has amplitude ``-amp_A * net_zero_A_scale * amp_B``. The amplitude of the integral correction period is such that ``sum(waveform) == 0``. If the total duration of the pulse parts is less than the duration set by the ``t`` array, the remaining samples will be set to 0 V. The various pulse part durations are rounded **down** (floor) to the sample rate of the ``t`` array. Since ``t_pulse`` is the total duration of the two square pulses, half this duration is rounded to the sample rate. For example: .. jupyter-execute:: import numpy as np from quantify_scheduler.waveforms import sudden_net_zero t = np.linspace(0, 9e-9, 10) # 1 GSa/s amp_A = 1.0 amp_B = 0.5 net_zero_A_scale = 0.8 t_pulse = 5.0e-9 # will be rounded to 2 pulses of 2 ns t_phi = 2.6e-9 # rounded to 2 ns t_integral_correction = 4.4e-9 # rounded to 4 ns sudden_net_zero( t, amp_A, amp_B, net_zero_A_scale, t_pulse, t_phi, t_integral_correction ) :param t: A uniformly sampled array of times at which to evaluate the function. :param amp_A: Amplitude of the main square pulse :param amp_B: Scaling correction for the final sample of the first square and first sample of the second square pulse. :param net_zero_A_scale: Amplitude scaling correction factor of the negative arm of the net-zero pulse. :param t_pulse: The total duration of the two half square pulses. The duration of each half is rounded to the sample rate of the ``t`` array. :param t_phi: The idling duration between the two half pulses. The duration is rounded to the sample rate of the ``t`` array. :param t_integral_correction: The duration in which any non-zero pulse amplitude needs to be corrected. The duration is rounded to the sample rate of the ``t`` array. .. py:function:: interpolated_complex_waveform(t: numpy.ndarray, samples: numpy.ndarray, t_samples: numpy.ndarray, interpolation: str = 'linear', **kwargs) -> numpy.ndarray Wrapper function around :class:`scipy.interpolate.interp1d`, which takes the array of (complex) samples, interpolates the real and imaginary parts separately and returns the interpolated values at the specified times. :param t: Times at which to evaluated the to be returned waveform. :param samples: An array of (possibly complex) values specifying the shape of the waveform. :param t_samples: An array of values specifying the corresponding times at which the ``samples`` are evaluated. :param interpolation: The interpolation method to use, by default "linear". :param kwargs: Optional keyword arguments to pass to ``scipy.interpolate.interp1d``. :returns: An array containing the interpolated values. .. py:function:: rotate_wave(wave: numpy.ndarray, phase: float) -> numpy.ndarray Rotate a wave in the complex plane. :param wave: Complex waveform, real component corresponds to I, imaginary component to Q. :param phase: Rotation angle in degrees. :returns: Rotated complex waveform. .. py:function:: skewed_hermite(t: numpy.ndarray, duration: float, amplitude: float, skewness: float, phase: float, pi2_pulse: bool = False, center: Optional[float] = None, duration_over_char_time: float = 6.0) -> numpy.ndarray Generates a skewed hermite pulse for single qubit rotations in NV centers. A Hermite pulse is a Gaussian multiplied by a second degree Hermite polynomial. See :cite:t:`Beukers_MSc_2019`, Appendix A.2. The skew parameter is a first order amplitude correction to the hermite pulse. It increases the fidelity of the performed gates. See :cite:t:`Beukers_MSc_2019`, section 4.2. To get a "standard" hermite pulse, use ``skewness=0``. The hermite factors are taken from equation 44 and 45 of :cite:t:`Warren_NMR_pulse_shapes_1984`. :param t: Times at which to evaluate the function. :param duration: Duration of the pulse in seconds. :param amplitude: Amplitude of the pulse. :param skewness: Skewness in the frequency space :param phase: Phase of the pulse in degrees. :param pi2_pulse: if True, the pulse will be pi/2 otherwise pi pulse :param center: Optional: time after which the pulse center occurs. If ``None``, it is automatically set to duration/2. :param duration_over_char_time: Ratio of the pulse duration and the characteristic time of the hermite polynomial. Increasing this number will compress the pulse. By default, 6. :returns: complex skewed waveform