Transmon

class boulderopal.superconducting.Transmon(dimension, frequency=None, anharmonicity=None, drive=None, name='transmon')

Class that stores all the physical system data for a transmon.

Parameters

  • dimension (int) – Number of dimensions of the Hilbert space of the transmon. Must be at least 2.
  • frequency (real or np.ndarray or RealOptimizableSignal or RealOptimizableConstant or None , optional) – The frequency of the transmon, ωt\omega_t. If not provided, it defaults to no frequency term.
  • anharmonicity (real or np.ndarray or RealOptimizableSignal or RealOptimizableConstant or None , optional) – The nonlinearity of the transmon, α\alpha. If not provided, it defaults to no anharmonicity term.
  • drive (real or complex or np.ndarray or RealOptimizableSignal or RealOptimizableConstant or ComplexOptimizableSignal or ComplexOptimizableConstant or None , optional) – The complex drive of the transmon, γt\gamma_t. If not provided, it defaults to no drive term.
  • name (str , optional) – The identifier of the transmon that is used to link interaction terms to this transmon. Defaults to “transmon”.

SEE ALSO

boulderopal.superconducting.Cavity : Class describing cavities in superconducting systems.

boulderopal.superconducting.TransmonCavityInteraction : Class describing interactions between a transmon and a cavity.

boulderopal.superconducting.TransmonTransmonInteraction : Class describing interactions between two transmons.

Notes

The Hamiltonian for the transmon is defined as

Htransmon=ωtb†b+α2(b†)2b2+12(γtb†+H.c.), H_\mathrm{transmon} = \omega_t b^\dagger b + \frac{\alpha}{2} (b^\dagger)^2 b^2 + \frac{1}{2} \left(\gamma_t b^\dagger + H.c. \right) ,

where H.c.H.c. indicates the Hermitian conjugate. All coefficients in the Hamiltonian are optional, and you should only pass those relevant to your system.

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