transmon_analytics

This code calculates the energy eigenvalues of the transmon qubit cooper pair box as a function of the offset charge and plots the corresponding results.

Key References:

• J. Koch et al. “Charge-insensitive qubit design derived from the Cooper pair box” Phys. Rev. A. 76, 042319 (2007).

Functions

kidx(m, my_ng)	This function is a placeholder which performs an additional modulo operation with an offset of ng=0.5, but is not necessary when only integer values of kidxRAW(m, my_ng) are used.
kidx_raw(m, my_ng)	This function calculates the integers which correct sort the eigenstates and eigenenergies of the solution to Mathieu's equation.
plot_eigenvalues()	This function actually creates the plot(s) of eigenvalues as a function of offset charge.
transmon_eigenvalue(m, my_ng)	This function calculate the energy eigenvalue of the transmon qubit for a given energy level (m) and offset charge (my_ng).

kidx(m, my_ng)

This function is a placeholder which performs an additional modulo operation with an offset of ng=0.5, but is not necessary when only integer values of kidxRAW(m, my_ng) are used. If non-integer values of kidxRAW are used, then the modulo operation below needs to be updated to include the offset.

Args:

m (int): The energy level of the qubit (m=0,1,2,3,etc.) ng (float): the offset charge of the Josephjunction island (in units of 2e)

Returns:

float: the calculated energy eigenvalue, after an ng=0.5 offset.

kidx_raw(m, my_ng)

This function calculates the integers which correct sort the eigenstates and eigenenergies of the solution to Mathieu’s equation.

Args:

m (int): The energy level of the qubit (m=0,1,2,3,etc.) my_ng (float): the offset charge of the Josephjunction island (in units of 2e)

Returns:

float: the calculated index

plot_eigenvalues()

This function actually creates the plot(s) of eigenvalues as a function of offset charge. No arguments need to be passed.

Returns:

A plot of the eigenvalues as a function of offset charge.

transmon_eigenvalue(m, my_ng)

This function calculate the energy eigenvalue of the transmon qubit for a given energy level (m) and offset charge (my_ng). The input values are first used to calculate the index using the function defined above, and then the calculated index is used to calculate the energy eigenvalue using Mathieu’s characteristic values.

Args:

m (int): The energy level of the qubit (m=0,1,2,3,etc.) ng (float): the offset charge of the Josephjunction island (in units of 2e)

Returns:

float: the calculated energy eigenvalue.