Goal:

Design an OCS qubit with $\frac{E_j}{E_c} \approx 20$ for fabrication through Lincoln Lab, MIT.

Constraints:

• Resonator frequency between 4 - 12 GHz (due to circulator, amplifiers and mixers)
• $\omega_{res} \approx \omega_{03}$ of qubit
• $\omega_{03} = 3 \omega_{01} - 2 * α$
• $\omega_{01}$ needs to be between 2 and 6 GHz

Notebook Files:

• ocs_transmon_qubit.ipynb to execute steps (1 - 3) from the Workflow Section
• resonator.ipynb to execute steps (4) from the Workflow Section
• full_chip.ipynb to create the final .gds for final editing in KLayout to comply with SQUILL standards

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Workflow:

1. Isolate qubit + claw design from standard candle qubit design

   a. JJ is not an element in Ansys so might need to use Lumped Element Linear Inductor with the correct $L_j$ value instead

2. Simulate (EPR) the qubit+ claw design to get $E_c , \omega_{01}, \alpha$

   a. Ensure hyperparameters meet LL SQUILL Foundry requirements

   b. Claws as port

   c. No other components on chip

   d. Be careful of mesh parameters

    - maximum meshing size should be at least half of smallest feature
    - Define mesh resolution for separate components according to the rule ^
   

   e. Calculate $E_j$

    - $\hbar \omega_{01} = \sqrt(8 E_j E_c) - E_c $
   

   f. Change simulation parameters (i.e. qubit + claw + JJ parameters) to get $E_j/E_c \approx 20$

3. Compute $\omega_{03}$

4. Simulate (S21) a claw + CPW resonator + 2-port transmission line from the standard candle qubit design

   a. Get $\omega_{res}$ - Fit with lflPython/fitTools/Resonator.py tool

   b. Change resonator length to get $\omega_{res} = \omega_{03}$

5. Choose 5 physical parameters of the qubit that have $E_j/E_c \in (10,30)$ (steps 1 and 2)

6. Get $\omega_{res}$ for these new qubits (steps 3 and 4)

7. Adjust the GDS file with the final chip design to comply with LL SQUILL Submission Requirements

   a. Get the JJ length for each qubit

    - $L_j$ from $E_j$
   
    - `L_j = junction_area * critical_current_density`
   
    - `Junction_area = JJ_length * JJ_width`
   

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Qubit Parameter Optimization Workflow:

0. Fix $L_j$ and calculate $C_j$

1. Run simulation with Standard Candle Qubit parameters and the fixed $L_j , C_j$ to get $\frac{E_j}{E_c}$

2. Numerically solve for neighborhoods of Qubit spatial parameters in stable regimes of $\frac{E_j}{E_c} \approx 20$

3. Run simulations within those neighborhoods