Qubit-Resonator-Interaction Calculator

Explore our Resonator-Qubit Interaction Calculator, designed to simplify quantum circuit design. Optimize resonator and qubit coupling, calculate dispersive shift, Lamb shift, Purcell decay rates and much more with precision. Whether you're working with superconducting qubits or exploring advanced quantum systems, our interactive tool provides the insights you need for efficient design and implementation.

Qubit-Cavity Coupled System Calculator

Qubit Parameters

Resonator Parameters

Coupling Parameters

Qubit Frequency Shifts

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Decay Rates

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Resonator Parameters

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Formulas Used

The following formulas define the parameters governing the qubit-resonator interaction.


Detuning (Δ) Δ = 2π⋅(fq​−fr)​​ fq = qubit frequency
fr = resonant frequency
Dispersive shiftg2/Δ g = qubit-resonator coupling strength
Lamb shift g2/Δ
AC Stark shift n.(2.g2/Δ) n = Number of photons in the cavity
Total qubit shift Lamb Shift +  AC Stark Shift
Purcell decay rate (ΓP ) ΓP ​= κ.(g/Δ​)2 κ: resonator bandwidth
Purcell decay time (TP) TP​ = 1/ΓP
Critical photon number (ncrit​) ncrit​ = Δ2​/4g2
Resonator quality factor (Q) Q=2π⋅fr/κ​​
Power Associated with Photons in the Cavity Pin​=n⋅ℏ⋅(2π⋅fr​)⋅κ

When the number of photons in the resonator exceeds the "critical photon number," the dispersive Hamiltonian approximation becomes invalid. As a result, the critical photon number defines the maximum power level of the resonator probe signal required to ensure an approximate QND (quantum non-demolition) measurement.

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