# Input data formats

## Single-qubit custom control

Custom control solutions defining the control Hamiltonian for single-qubit driven operations may be uploaded as a CSV file using either of the following data formats.

### Cartesian data format

To implement a custom single-qubit control Hamiltonian using cartesian controls, use the following data format:

amplitude_x amplitude_y detuning duration maximum_rabi_rate
1.00 0.00 6.16E+05 5.00E-07 1.00E+06
0.58 0.10 6.16E+05 6.00E-07 1.00E+06
0.78 0.58 6.33E+05 5.00E-07 1.00E+06
$\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$

The above data format must be followed identically, including column labels as indicated.

The column labels correspond to python objects. For example the detuning column lists all values of the physical detuning for the segments of the control solution. The numerical value in the second row (second segment) is given by detuning[2] = 6.16E+05.

The maximum Rabi rate is a global parameter of the experimental system bounding the speed of driven quantum operations. Consequently, all entries the column maximum_rabi_rate are identical. This should always be the case.

The numerical entries in each column must be uploaded with the correct units. The correct units for each column are as follows.

amplitude_x amplitude_y detuning duration maximum_rabi_rate
$(\Omega_\text{max})$ $(\Omega_\text{max})$ $(\text{rad}\cdot\text{Hz})$ $(\text{s})$ $(\text{rad}\cdot\text{Hz})$

The above data format implements the single qubit control Hamiltonian

\begin{align} H_{c}(t)& = \frac{1}{2}\left(\alpha_{x}(t)\sigma_x + \alpha_{y}(t)\sigma_y + \alpha_{z}(t)\sigma_z\right) \end{align}

where the physical (dimensionalized) parameters describing each control segments (for cartesian controls) are tabulated as

\begin{align} \left[ \begin{array}{c|ccc} - & \color{blue}\alpha_{x}(t) & \color{red}\alpha_{y}(t) & \color{OliveGreen}\alpha_{z}(t) \\ \hline \tau_{1} & \alpha_{1,x} & \alpha_{1,y} & \alpha_{1,z}\\ \tau_{2} & \alpha_{2,x} & \alpha_{2,y} &\alpha_{2,z}\\ \tau_{3} & \alpha_{3,x} & \alpha_{3,y} &\alpha_{3,z}\\ \vdots & \vdots & \vdots & \vdots\\ \end{array} \right] \end{align}.

The physical (dimensionalized) parameters are obtained by multiplying the numerical values in the CSV upload by the respective unit for that column. Thus

1. $\hspace{1.5cm}$ $\Omega_\text{max} =$ maximum_rabi_rate[i] $\text{ rad}\cdot\text{Hz}$
2. $\hspace{2cm}\alpha_{i,x} =$ amplitude_x[i]$\times\Omega_\text{max}$ $=$ amplitude_x[i]*maximum_rabi_rate[i]$\text{ rad}\cdot\text{Hz}$
3. $\hspace{2cm}\alpha_{i,y} =$ amplitude_y[i]$\times\Omega_\text{max}$ $=$ amplitude_y[i]*maximum_rabi_rate[i]$\text{ rad}\cdot\text{Hz}$
4. $\hspace{2cm}$$\alpha_{i,z} = detuning[i] \text{ rad}\cdot\text{Hz} 5. \hspace{2.5cm}$$\tau_{i} =$ duration[i] $\text{ s}$

where $\Omega_\text{max}$ is the maximum Rabi rate. That is, the maximum possible Rabi rate that the experimental device is capable of implementing.

The uploaded entries in the amplitude_x and amplitude_y columns are measured in units of $\Omega_\text{max}$. That is, these columns specify the value of the control amplitudes relative the maximum possible Rabi rate. Since $\Omega_\text{max}$ sets an upper bound on the values of these control amplitudes, these numeric entires are bounded by amplitude_x[i] $\le$ $|1|$ and amplitude_y[i] $\le$ $|1|$ for all segments.

### Cylindrical data format

To implement a custom single-qubit control Hamiltonian using cylindrical controls, use the following data format:

rabi_rate azimuthal_angle detuning duration maximum_rabi_rate
1.00 -2.01 6.16E+05 5.00E-05 1.00E+06
0.59 -1.17 6.16E+05 4.00E-05 1.00E+06
0.98 0.64 6.33E+05 9.00E-05 1.00E+06
$\vdots$ $\vdots$ $\vdots$ $\vdots$ $\vdots$

The above data format must be followed identically, including column labels as indicated.

The column labels correspond to python objects. For example the detuning column lists all values of the physical detuning for the segments of the control solution. The numerical value in the second row (second segment) is given by detuning[2] = 6.16E+05.

The maximum Rabi rate is a global parameter of the experimental system bounding the speed of driven quantum operations. Consequently, all entries the column maximum_rabi_rate are identical. This should always be the case.

The numerical entries in each column must be uploaded with the correct units. The correct units for each column are as follows.

rabi_rate azimuthal_angle detuning duration maximum_rabi_rate
$(\Omega_\text{max})$ $(\text{rad})$ $(\text{rad}\cdot\text{Hz})$ $(\text{s})$ $(\text{rad}\cdot\text{Hz})$

The above data format implements the single qubit control Hamiltonian

\begin{align} H_{c}(t)& = \frac{1}{2}\left( \Omega(t)\cos\phi(t)\sigma_x + \Omega(t)\sin\phi(t)\sigma_y + \Delta(t)\sigma_z\right) \end{align}

where the physical (dimensionalized) parameters describing each control segments (for cylindrical controls) are tabulated as

\begin{align} \left[ \begin{array}{c|ccc} - & \color{blue}\Omega(t) & \phi(t) & \Delta(t) \\ \hline \tau_{1} & \Omega_{1} & \phi_{1} & \Delta_{1}\\ \tau_{2} & \Omega_{2} & \phi_{2} &\Delta_{2}\\ \tau_{3} & \Omega_{3} & \phi_{3} &\Delta_{3}\\ \vdots & \vdots & \vdots & \vdots\\ \end{array} \right] \end{align}

The physical (dimensionalized) parameters are obtained by multiplying the numerical values in the CSV upload by the respective unit for that column. Thus

1. $\hspace{1.5cm}$ $\Omega_\text{max} =$ maximum_rabi_rate[i] $\text{ rad}\cdot\text{Hz}$
2. $\hspace{2.4cm}\Omega_{i} =$ rabi_rate[i]$\times\Omega_\text{max}$ $=$ rabi_rate[i]*maximum_rabi_rate[i]$\text{ rad}\cdot\text{Hz}$
3. $\hspace{2.5cm}\phi_{i} =$ azimuthal_angle[i]$\text{ rad}$
4. $\hspace{2.35cm}$$\Delta_{i} = detuning[i] \text{ rad}\cdot\text{Hz} 5. \hspace{2.6cm}$$\tau_{i} =$ duration[i] $\text{ s}$

where $\Omega_\text{max}$ is the maximum Rabi rate. That is, the maximum possible Rabi rate that the experimental device is capable of implementing.

The uploaded entries in the rabi_rate column is measured in units of $\Omega_\text{max}$. That is, this column specifies the value of the Rabi rate in a given segment relative the maximum possible Rabi rate. Since $\Omega_\text{max}$ sets an upper bound on the values of the Rabi rate, these numeric entires are bounded by rabi_rate[i] $\le$ $1$.

## Noise power spectral densities

Noise power spectral densities may be uploaded and will be interpreted directly in the Q-CTRL product when associated with a specific noise process. The general format is a three-column CSV where column headings are not required:

Frequency Power Spectrum Uncertainty
$\text{Hz}$ Value Value

In the event that measurement uncertainties are not available this column should contain entries of “0”, as NaNs are not permitted.

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